Basic Principles and Practical Applications of Epidemiological Research (Quantitative Sciences on Biology and Medicine)

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Quantitative Sciences on Biology and Medicine - Volume 1

Basic Principles and Practical Applications in Epidemiological Research

Jung-Der

Wang

World Scientific

Basic Principles and Practical Applications m Epidemiological Research

QUANTITATIVE SCIENCES ON BIOLOGY AND MEDICINE Series Editors: Timothy T. Chen (University of Maryland, USA) Kung-Yee Liang (Johns Hopkins University, USA) & Lee-Jen Wei (Harvard School of Public Health, USA)

Vol. 1:

Basic Principles and Practical Applications in Epidemiological Research by Jung-Der Wang


Jung-Der Wang, M.D.,SC.D. Institute of Occupational Medicine and Industrial Hygiene National Taiwan University College of Public Health and Department of Internal Medicine National Taiwan University Hospital

V f e World Scientific wl

New Jersey'London • Hong Kong NewJersey London** Singapore Sine

Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

BASIC PRINCIPLES AND PRACTICAL APPLICATIONS IN EPIDEMIOLOGICAL RESEARCH Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-02-4801-6 ISBN 981-02-4925-X (pbk)

Printed in Singapore.

Preface Epidemiology has been developing rapidly over the last half a century. It has evolved to a discipline which can serve as a basic science in both public health and clinical medicine, as they all involve information collected from human observational studies. As we are entering the information age in the 21st century, all health care workers must be practically trained with the ability to judge and select valid information coming from studies of human population. The capability is particularly important as more and more health related information over flowing on the net and webpages. In this book my aim is to equip our readers with basic concepts and principles on how to conduct and critique scientific studies involving human population. Thus, the book is not only written for students majored in epidemiology as the first course and a conceptual review, but also for scholars, experts, and students who are not majored in epidemiology but need such concepts to abstract valuable information from or cooperate with others to conduct epidemiological studies. It has been my dream to uncover the principles of how scientific knowledge is produced or advanced since I was only a teenage boy in 1960's. I was first puzzled and attracted by Hume's suspicion that a hypothesis or theory coming from induction has no definite proof to be universally true. Later, I was convinced by Popper that by empirically falsifying all the hypotheses or conjectures, the only one left un-refuted is closest to the truth, and our belief of the existing physical and chemical theories has its foundation. Moreover, one must select samples from population efficiently and validly and conduct valid and sensitive measurements to empirically test these hypotheses. However, when I grew up in clinical medicine and public health, I found that health policy decision can not wait for such an un-ended quest, because we must make causal decisions to save lives and prevent morbidity. Thus, I began to accept and apply Baysian's concept of subjective probability and preference (utility) in my daily practice. The studies of

v

vi


epidemiology has given me an opportunity to summarize all these basic concepts. Hence, this book is written in such an order and hope to guide our readers step by step: from the general concept of scientific research in natural science into inference in observational studies of human population: Beginning with a classification of two types of inferences (descriptive and causal) in chapter 1, I spend chapters 2 and 3 to elucidate Popperian philosophy of science and how it can be practically applied in the search of etiologic agents. Then, I have tried to approach causal criteria and its decision from a refutationist's attitude but incorporate Baysian decision viewpoint in chapter 4. Although most epidemiology textbooks do not talk about fundamental measurement concept, I choose to tackle it from the viewpoint of "all true measurement is essentially comparative" (Helmholtz). When introducing epidemiological measurements in chapter 6, I have deliberately added some new developments in the quantification of utility of health such as quality adjusted life year (QALY). Principles of study design are presented in chapter 7, which delineates that searching for alternative explanation (or possible confounding) is the main concern for causal studies, while that of a descriptive study is how to infer from sample at hand to target population. People commonly encounter crude rates, which in fact, are sets of specific rates adjusted with sets of specific weights and should be reweighted before comparison (chapter 8). Although most epidemiologic textbook do not deal with the concept of sampling, I try to scratch it from zero to let our readers get a ball-park view in chapter 9. Causal epidemiological studies are introduced according to whether the denominator or accumulated person-time is ascertained individually for the whole population (as in cohort or follow up studies, chapter 10) or just a sample (as in case-control studies, chapter 11). Then, the principles of the whole book is summarized into a critique form of how to evaluate an epidemiological study in chapter 12. In the last chapter, I have introduced a third type of question, the decisional question, for the application of epidemiology on health policy research with a special emphasis on outcome assessment. Because my major goal is to introduce the general concept through practical examples, this book does not contain any details of data

Preface

vii

analysis. Readers who are interested in such details are encouraged to read more advanced textbook, such as "Modern Epidemiology" (edited by Rothman and Greenland, 1998) I am indebted to Professors Olli Miettinen and David Wegman for their teaching, advice and kind support during my study in Harvard University. The book was first drafted and taught in 1997 at Mahidol University School of Public Health, Bangkok, Thailand. I am greatly indebted to all the faculty members and students who attended the class and provided inputs, especially Drs. Armonrath, Charlumchai and Pathom, who read through the text and gave me many invaluable comments. Later on, the content was also taught in the epidemiology class of the National Taiwan University College of Public Health, and received more inputs, especially from Professors. Jing-Hsiang Hwang (chapter 9) and Kaiping Yao (chapter 5). Later on, it was posted on a WHO website (http://www.who.int/peh-super) for readers' comment in 1999. I am especially grateful to all of WHO officials and scholars, especially Dr. Hiko Tamashiro, for her kind, persistent encouragement and comments. Dr. Joseph Chiu, a Christian brother and a specialist in infectious diseases, kindly spent his time to read through the whole text and brought questions on parts where the text was not clear enough. His encouragement and enthusiasm actually strengthened the content of this book. To make the whole text more readable, it was very kind of Ms. Sunny Wang to carefully read and edit the whole text. I am also grateful to the National Science Council of Taiwan for funding most of the empirical research used in the book, and to Y. T. Lee's Foundation for Outstanding Scholars for their kind financial support during 1996-2000, when the whole book was drafted and under revision. I am indebted to Professor Sander Greenland's inputs before the publication. Finally, I want to thank my Lord for providing me a happy and supportive family who went through all the evenings and days with me, especially my wife, Wang-Huei who typed the first draft in Bangkok.

This page is intentionally left blank

Contents Preface

v

Chapter

1. Introduction to epidemiological research

Chapter

2. Principles of scientific research: Deductive methods and process of conjecture and refutation

1

17

Chapter

3. Scientific hypothesis and degree of corroboration

39

Chapter

4. Causal inference and decision

57

Chapter

5. Basic principles of measurement

81

Chapter

6. Basic measurements in epidemiological research

121

Chapter

7. Study design

161

Chapter

8. Adjustment and standardization of rates

197

Chapter

9. Introduction to sampling method and practical applications

211

Chapter 10. Follow-up study

233

Chapter 11. Case-control study

259

Chapter 12. How to critically review an empirical study

291

Chapter 13. Application of epidemiological methods in health service research and policy

307

References

341

Index

363 ix


Chapter 1 Introduction to Epidemiological Research 1.1 1.2 1.3 1.4 1.5

Definition of epidemiology Evolving trends of epidemiological research Types of inferences in epidemiological research Outline of the basic principles of epidemiological research Summary

Introduction In the last several decades, epidemiology has evolved from the simple observation of mortality and/or morbidity figures to a scientific discipline with versatile applications. With this expansion, we have witnessed a constant influx of innovative concepts and statistical tools of such magnitude that may confuse a beginner in the field. Consequently, the aim of this textbook is to use examples from actual research to provide the reader with a clear and simple concept on how to conduct epidemiological research. Since epidemiological research is based on the basic principles of scientific research, readers from any field can benefit from this fundamental understanding. Essentially, the principles of epidemiological research will be introduced as a liberal art (Fraser, 1987). In this chapter, we shall start with the definition of epidemiology. Then, we will discuss how its scope of study has expanded and summarize its different studies into two types of questions or inferences. Finally, I shall give an outline of what we will learn in this book. 1.1

Definition of epidemiology

The word epidemiology comes from the late Latin or Greek epidemia Epi indicates on or among, while demos means people, and logos or logy denotes science or theory. Thus, the word conveys the idea that

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2


epidemiology is the study of some event or characteristics occurring or prevalent among people. Since the 19th century, epidemiology has been commonly used to study people's illnesses, and as a result, it has become customary that the main subject matter of epidemiology involves disease or health-related events or states. MacMahon and Pugh (1970) defined it as the study of the distribution and determinants of disease frequency in man. Later, Miettinen (1985a) defined it as the principles of studying the occurrence of illness and related states and events, including those of health care. However, these two definitions only emphasize the study of illness and health-related issues. Since the scope of epidemiological study has expanded to cover health care and policy, I will tentatively define epidemiology as the study of the occurrence of health-related events, states and policy in a human population. Referring back to its broader Greek definition, I believe that the methodology of epidemiological research is useful in any discipline involved in the study of a human population, such as sociology and psychology. Thus, the clarification of the basic principles of epidemiological research will help facilitate their broader applications. 1.2

Evolving trends of epidemiological research

During the past half-century, there have been three developing trends in epidemiological research: from acute to chronic diseases, from disease-oriented to determinant-oriented approaches, and from health-related events to health policy research and decision. From acute to chronic diseases In the late 19th and early 20th centuries, the subject matter of epidemiology focused mainly on fatal acute or infectious diseases (Snow, 1936; Durkheim, 1951). After World Wars I and II, the rapid development of microbiology and antibiotics quickly conquered most infectious diseases caused by bacteria. Today, except for AIDS (acquired immune deficiency syndrome), the mortality rates of most infectious diseases have progressively dropped and are no longer one of the top 10 leading causes of death in most

Chapter 1 Introduction

3

developed countries, such as the United States (Table 1.1). Table 1.1

Rani:

Comparison of ten leading causes of death between 1940 and 1995 in the United States (U.S. Department of Commerce, 1945; Rosenberg HM et al, 1996). 1940

1. Heart diseases 2. Malignant neoplasm 3. Cerebrovascular diseases 4. Nephritis

1995 Crude mortality rate(x 10"5;) 292.5 Heart diseases 121.3 Malignant neoplasm Cerebrovascular diseases 90.9 81.5

5. Pneumonia

70.3

6. Accidents (excluding motor vehicle) 7. Tuberculosis 8. Diabetes mellitus

47.4

9. Motor vehicle accidents 10. Premature birth

45.9 26.6 26.2 24.6

Chronic obstructive pulmonary diseases Accidents and adverse effects (including motor vehicle) Pneumonia and influenza Diabetes mellitus Human immunodeficiency virus infection Suicide Chronic liver disease

Crude mortality rate(x 10"5) 281.2 204.7 60.2 39.9 34.1 31.8 22.5 16.2 11.8 9.5

This shift of leading causes of death from infectious to non-infectious or chronic diseases, such as cancer and cardiovascular diseases, is even more obvious in some recently industrialized countries, such as Taiwan (Table 1.2).

4


Table 1.2

Comparison often leading causes of death between 1952 and 1997 in Taiwan.

1. 2. 3. 4. 5. 6.

Gastroenteritis Pneumonia Tuberculosis Cardiovascular diseases Cerebrovascular diseases Perinatal mortality

Crude mortality rate (x 10"5) 135.0 131.5 91.6 49.0 48.8 44.1

7. 8. 9. 10.

Nephritis and nephropathy Malignant neoplasm Bronchitis Malaria

36.3 30.7 28.1 27.5

Rank

1952

1997

Malignant neoplasm Cerebrovascular diseases Accidents and injuries Cardiovascular diseases Diabetes mellitus Chronic hepatitis and cirrhosis Pneumonia Nephritis and nephropathy Hypertension Suicide

Crude mortality rate (x 10" 134.10 59.56 52.22 49.71 34.67 22.03 16.73 16.20 12.07 10.04

Since epidemiologists are primarily interested in studying how to prevent morbidity and mortality from all kinds of diseases, epidemiological research now also covers chronic and/or non-infectious diseases. Faced with this new challenge, epidemiologists quickly sensed the importance of the concept of time in chronic health problems. Thus, total person time at-risk has been developed to replace number of person(s) or population at risk for the denominator of incidence rate. Although, in general, responsible agents for acute infectious diseases can be clearly identified because of their acute onset and simple causal relationship(s), determining the etiology of chronic diseases seems to be more difficult. Chronic diseases pose a more complex problem because of their longer induction time and more complicated pathophysiology. As a result, there is a greater opportunity for other (extraneous) agents or determinants to affect the outcome under study, as well. In this book, the existence of such extraneous determinants, which may partially or totally explain the causal effect, will be regarded as confounding.


5

For example, when cigarette smoking was first proposed to cause lung cancer by Hill (1953), many eminent scholars continued to dispute these findings (Stolley, 1991). Therefore, the concepts of cause (Hill, 1965; Rothman, 1976, 1981, 1986, 1988; Susser, 1977, 1986, 1991) and confounding (Miettinen, 1974b; Miettinen and Cook, 1981; Greenland and Robins, 1986; Greenland and Rothman, 1998) have gone through a long period of development to accommodate the growing coverage of chronic diseases. Prolonged observation time has also facilitated the development of a more efficient sampling and observation method for studying health-related events using a case-control study design (Cornfield, 1951; Miettinen, 1976; Breslow, 1980). A case-control study is one type of epidemiological study, which will be discussed later in Chapter 11. From disease-oriented to determinant-oriented approaches By understanding the agent(s) or determinant(s) of a disease, one can take appropriate and specific protective measures against the disease. For example, the drive to understand microbiological agents led to the development of vaccinations and the field of microbiology. In similar fashion, today's epidemiologists are examining determinants of chronic diseases for possible methods of treatment and prevention. Yet, the more complex interaction of chronic disease agents and factors of daily life, such as life-style, diet, occupation, living environment, etc., further heighten the demand for a more detailed understanding. This need for a more refined conceptualization and measurement of each individual determinant has extended traditional disease-oriented epidemiology to determinant-oriented epidemiology. Since such an approach frequently involves other scientific disciplines, such as occupational health and nutritional science, new methods of interdisciplinary approach and subdomains of epidemiology have been developed. For example, the incorporation of knowledge from occupational health into epidemiology has led to the formation of occupational epidemiology. Likewise, the use of nutritional science and sociology has resulted in the development of nutritional epidemiology and

6


social epidemiology, respectively. In these new subdomains, one can now utilize specific measurement methods from other disciplines and attempt to examine the effect of multiple determinants on the pathophysiology in question. Thus, epidemiology has also extended from a disease or illness-centered approach, e.g., breast cancer epidemiology, stroke epidemiology, tuberculosis epidemiology, etc., to include the aforementioned determinant-oriented subdomains, such as occupational epidemiology, nutritional epidemiology, etc. Of course, such an extension does not necessarily mean that a disease-oriented approach will be abolished or lose its importance. Rather, the latter approach will continue to thrive, while the former will add to the understanding of the pathophysiology and natural history of a specific disease. Due to the above two approaches, epidemiology has gradually become the basic science of public health (Morris, 1975) and even of clinical medicine (Feinstein, 1983, 1985). From health-related events to health policy research and decisions While, initially, epidemiologists may have mainly focused on fatality due to disease, i.e., mortality, they have gradually extended their work to morbidity and even quality of life (QOL) because of today's general longer life expectancy. Given the limited resources of health services, there is a growing demand for people to make choices among different preventive, diagnostic, therapeutic and rehabilitative measures that affect survival and QOL. For example, a 63-year-old patient must choose whether or not to be operated on if she suffers from an aggravating hip joint pain and a 10-year history of stable angina pectoris (Sackett et al, 1991). Because the operation may result in long-term disability or even mortality, she may be worse off than in her current health state. The decision is not obvious and is very difficult to make. Take an example of public health decision-making: Should we spend more resources on the prevention of AIDS (acquired immune deficiency syndrome), cancer or stroke? Since all three diseases may result in mortality or chronic poor quality of life, we cannot rely on only mortality rate to decide policy. As a result, epidemiologists (or biostasticians) have now sought to quantify both survival


7

and QOL or even the total utility of health gained from the reduction of an exposure because no other discipline has shown genuine interest in nor is trained to carry out such a task. Therefore, epidemiological research now also attempts to assess the effectiveness of health service or policy (Tsauo et ah, 1999). Or, at least epidemiologists should learn how to cooperate with people in other disciplines, such as biostasticians, economists, oncologists, on tackling the health policy issues. 1.3 Types of inferences in epidemiological research The development of new concepts and methods in the broadening field of epidemiology often creates confusion among aspiring young epidemiologists and health professionals who have not majored in epidemiology. For example, case-control study design, which has potential applications in disciplines like sociology, already has many different names: retrospective study, case-referent study, case-base study, case-cohort study, case control study nested in a cohort, control initiated case control study multiple control series, multiple case series, etc. Similarly, people often worry about sampling procedures and response rates. One of the most common questions is: "Suppose that I have a 40% (or, X%) response rate, is the sample representative enough?" I believe that such questions are commonly raised from the lack of a systematic understanding of the basic principles of epidemiological research, although there are many standard textbooks of epidemiology on the market. Consequently, I take this opportunity to provide readers with the most intuitive approach: Begin by asking the research question in either a causal or descriptive form, conduct the study in a scientific manner, and then draw inferences from either causal or descriptive viewpoints, as summarized in Figure 1.1. By "scientific manner," I mean drawing representative samples for descriptive studies, and proposing all possible hypotheses and falsifying them one by one for causal studies. We shall discuss the detailed process of scientific research in the next two chapters and in Chapter 7. For now, let us first examine some real examples of descriptive and causal research for

8


illustration: Descriptive: 1. What are the disease pattern and demand for the emergency medical system in Taipei (Chiang et al., 1986)? In other words, how many visits for each different disease are there in one year? What is the proportion, i.e., prevalence rate of alcoholism among Taiwan aborigines (Hwue/a/., 1990)? Causal: 1. What are the different causal agents for outbreaks of different diseases inside printing factories, such as polyneuropathy, respiratory paralysis or hepatitis (Wang et al, 1986; Tsai et al, 1990; Deng et al, 1987)? 2. Does wearing a helmet protect motorcycle riders from head injuries (Tsai etal, 1995)? In descriptive studies, one generally desires to find facts pertaining to an entire population; while in causal studies, one's questions focus on causal agents that produce the outcome of interest. The key question of the former is: How do we perform representative sampling? Or, how do we draw appropriate inferences for a particular population group from our collected sample? The most important question of the latter is: Is there any alternative determinant, which can explain the causal relationship of interest, indicating a mixed effect (i.e., confounding) in causality? Although the two studies ask two very different types of questions, one must always recruit subjects and perform measurement(s) for both. From asking the right question to understanding the basic principles, one should be able to design a valid study and appropriately interpret the results. Therefore, the objective of this book is to equip our readers with such ability. How can we achieve such a goal? What are the basic principles of epidemiological research?


Raise a question to be answered. It Causal?

Descriptive?

* Propose all possible hypotheses:

Define what and whom to measure.

Deduce facts to be found from each

Perform representative sampling

hypothesis.

and measurements.

H| ->F,,F 1 2 ... F,, H, -> F,, F„ ... F,

H„ Perform measurements to observe what has

Examine your sampling data of

actually happened and begin to falsify the

respondents, and draw inferences for

hypotheses.

the appropriate population group.

Apply statistical tools to summarize the data and control confounding. (Perform more falsification.)

Rule out all alternative hypotheses. Regard as valid the only hypothesis left unrefuted.

Figure 1.1

How to approach a problem.

9

10 Basic Principles and Practical Applications in Epidemiological Research

1.4

Outline of the basic principles of epidemiological research

In the last half-century, different applications of epidemiological research have grown and expanded to cover a wide range of fields. It has evolved into both a liberal art and basic science of both clinical medicine and public health. Throughout its progress, different authors have tried to summarize the common principles of these studies (MacMahon and Pugh, 1970; Kupper era/., 1982; Miettinen, 1985a; Rothman, 1986; Rothman and Greenland, 1998; Kelsey et ai, 1996). This book has the same objective. Its main themes are abstracted as follows: 1. To understand how scientific research is performed. In fact, according to Sir Karl Popper, a philosopher of science, objective knowledge is obtained through the repeated cycle of proposing hypotheses and falsifying them one by one. He labeled this concept "conjectures and refutations" (Popper, 1965). This concept serves as major part of the foundation of this book and will be delineated in Chapter 2. 2. To learn how to propose hypotheses that are scientific, falsifiable or testable. Empirical tests can only be performed on hypotheses that are falsifiable. Without such tests, we are unable to differentiate which hypothesis is closest to the truth. Thus, one must know how to propose a falsifiable and relevant hypothesis. This will be discussed in Chapter 3. 3. To make causal decisions from a refutationist's point of view. While the scientific quest for natural laws or causal hypotheses may never end, public health and medicine often demand us to make causal decisions under different scenarios and degrees of uncertainties. Thus, an epidemiologist needs to learn about the causal criteria for decision-making. Still, it is better to look at these criteria from a refutationist's viewpoint, in order to avoid causing any harm during the intervention process. This will

Chapter I

Introduction

11

be discussed in Chapter 4. 4. To accurately conceptualize and measure the objects under study. To perform an empirical test, one must be able to conceptualize and measure the subject matter of interest. As a result, one first needs to grasp the fundamental principles of measurement and be able to apply them in empirical studies. This topic will be presented in Chapter 5. 5. To carry out valid and precise epidemiological measurements. Epidemiologists have tried to discern health events from health states and develop specific indicators to measure them, such as incidence rate, prevalence rate and quality-adjusted life-year, as well as indicators for effect such as rate ratio, rate difference and odds ratio. These indicators will be discussed in Chapter 6. 6. To design causal and descriptive studies and draw appropriate inferences. Concepts of confounding and response rate will be discussed in Chapter 7 as the basis for proper study design and inferences. One should approach confounding by looking for any alternative hypotheses that have not yet been falsified; while with low response rate, one should consider if there is a large difference between respondents and non-respondents. Chapter 7 will delineate the basic concepts of a valid and efficient study design and proper inference of results. 7. To apply adjustment of rates as a means of controlling confounding, and to look at crude rate as a summation of weighted specific rates. These topics will be covered in Chapter 8.


8. To select the most efficient sampling procedures and to know how to properly generalize the study result obtained from a sample to the population. These topics are covered in Chapter 9. 9. To conduct follow-up or cohort studies in a manner such that no extraneous factor can also explain the effect under study. Chapter 10 discusses all related topics of follow-up studies, including clinical trials. 10. To understand why case-control study design is a general solution when no denominator or person year data are available, and to conduct proper sampling on such a design. Chapter 11 will cover the concept and development of case-control study, including density sampling, mortality odds ratio and other related topics. 11. To critically evaluate research based on the above conceptual development. All principles covered in previous chapters are summarized into two practical formats, i.e.,descriptive and causal, in order to assess the scientific merit of a study. Moreover, guidelines on how to approach a problem and how to write a scientific paper will also be provided in Chapter 12. 12. To apply the concept and measurements of utility of health in health policy research. To carry out such a task, one needs to understand the concept of decision analysis and estimate the utility of health by combining survival with the quality of life function into a common unit, e.g., quality-adjusted life-year (QALY). Effectiveness of health services can thus be evaluated, in addition to the risk of a specific condition. Chapter 13 will introduce the


13

usual format of decisional questions and measurement method of utility of health, making the quantification of health policy research more feasible. 1.5

Summary

The principles of studying the occurrence of health events, states and related issues among a population have developed into a scientific discipline called epidemiology. During the last half-century, it has expanded rapidly to cover new areas: from acute or infectious diseases to chronic diseases, from disease-oriented to determinant-oriented, and from health-related events to health policy research. To complement this growth, new concepts and measurements, as well as powerful statistical tools have been developed to tackle the different questions. Yet. this rapid development and varied approaches may often confuse beginners and/or investigators coming from other scientific disciplines. The goal of this book is to summarize these new developments into basic principles consistent with the scientific inquiry of proposing hypotheses and falsifying them one by one, i.e., conjectures and refutations. This task may be accomplished by classifying all epidemiological research questions into two types: descriptive or causal, although the involvement of health policy research may involve a decisional type of question.


Quiz of Chapter 1

Please write down the probability (%) that the assertion is true. You will be scored according to the credibility of your subjective judgment. Score

% 1. The primary concern of study in epidemiology is human population, which is also the main subject field of social sciences. 2. In the 21 century, infectious diseases epidemiology will become less important as almost all such diseases will be under control. 3. Since the study of etiological agent will provide scientific basis for proactive prevention of diseases, epidemiology will become more and more important in 21 century. 4. One must understand the detailed mechanism of an etiologic agent and its pathophysiology in order to implement effective prevention. Thus, it is very natural that epidemiological study will also focus on details of different major determinants for the disease. 5. If a disease takes a longer period of time for the development of symptom, there will be more other determinants to confound the causal effect. 6. The ultimate goal of epidemiological study usually includes some implication for making preventive health policy. 7. If the response rate of a population sample is below 50%, then one cannot draw any conclusion or inference at the end. 8. Most epidemiological research can be classified into 2 different types of inference: causal and descriptive.

Chapter I

Introduction

15

9. Basic concepts and principles of epidemiological research are quite different from those of other natural sciences. 10. Concepts and principles learn from epidemiology cannot be applied to clinical science, because the former primarily deals with population while the latter studies an individual. Answer: (1) T (2) F (3) T (4) T (5) T (6) T (7) F (8) T (9) F (10) F


Chapter 2

2.1 2.2 2.3 2.4 2.5 2.6

Principles of Scientific Research: Deductive Methods and Process of Conjecture and Refutation

The process of scientific research Deductive methods Conjectures and refutations Why take a refutational attitude? The limitations of conjectures and refutations Summary

Introduction Epidemiological research, with its specific focus on the health of a human population, is still a discipline based on the general principles of scientific research in searching for objective knowledge. Consequently, we shall start by understanding these principles, a repetitive process of proposing and disproving (falsifying) hypotheses one by one, or in Popper's terms, conjectures and refutations (Popper 1965, 1968). Because our hypothesis may not be directly tested or falsifiable empirically, we need to deduce statements from it, which then may be more testable or falsifiable. Thus, hypothesis formation, deduction and empirical tests form the basis of scientific research. In contrast to a verificationist's view, however, I take a refutationist's stand because empirical tests can only disprove hypotheses and can never prove any one to be true. Since human populations can only be observed or at most randomized with informed consent, taking a falsificationist's attitude in such studies may help one to avoid and detect erroneous conclusions. Let us first examine some examples of scientific research in this chapter, and clarify its basic principles and limitations.

17


2.1 The process of scientific research The example of nosocomial infection is a good illustration of the process of scientific research. Although Himpel (1966) used this research to advocate his verificationist's viewpoint, I, on the other hand, will discuss this example from the point of view of a refutationist. Example: Etiologic agent of puerperal fever During 1844-8, a Hungarian doctor, Semmelweis, served as an obstetrician in the Vienna General Hospital. He found that the mortality rate due to puerperal fever in obstetric ward I was higher than that of ward II, as listed on Table 2.1. At the time, microbiology was still a developing science and knowledge of infectious diseases was very limited. I will attempt to show how one uses empirical tests to refute rather than verify the proposed hypotheses, by specifically looking at the difference of mortality rates between the two obstetric wards of the same hospital.

Table 2.1

Mortality rates of puerperal fever in the obstetric wards of Vienna General Hospital, during 1844-6.

Calendar year

1844

1845

1846

Ward I

8.2 %

6.8%

11.4%

Ward

2.3%

2.0%

2.7%

II

Hypothesis 1: The agent of puerperal fever was infectious via atmospheric-cosmic-telluric change. Refutation: If hypothesis 1 were true, then the agent would easily spread to other areas, such as obstetric ward II or other nearby obstetric clinics in Vienna. However, the fact that ward II and nearby clinics were relatively spared from the disease contradicts this hypothesis.

Chapter 2

Hypothesis 2: Refutation:

Hypothesis 3:

Refutation:

Hypothesis 4:

Refutation: Hypothesis 5:

Refutation:

Conjectures and refutations

19

Crowding in obstetric ward I produced a higher mortality in ward I. Initially, ward I was more crowded. However, because many women moved to ward II for fear of high mortality in ward I, the two wards were almost similarly crowded later. Yet, the difference in mortality rate persisted. Hypothesis 2 was thus refuted. Patients in obstetric ward I were examined by medical students whose poor examination skills resulted in high mortality. Injuries resulting from the delivery of baby are in general much greater traumas than rough examinations. Midwives who received their training in ward II might examine the patient in a similar manner but did not show the same ill effect. Moreover, the mortality rate of puerperal fever persisted after examinations performed by medical students were minimized or even terminated temporarily. The psychological stress of death produced high mortality. During this time, a dying person was usually given an anointing ceremony for consecration, in which a minor priest would ring a bell, while walking in front of the senior pastor. The huge psychological stress, created by the ringing noise of the "dying" bell, facilitated the deaths of the women in ward I. Dr. Semmelweis asked the minor priest not to ring the bell, but high mortality rate persisted. The posture of delivery caused the difference in mortality rate. Women in ward I usually delivered their babies in supine position, while women in ward II delivered in lateral position. Dr. Semmelweis ordered all women in ward I to deliver their babies in lateral position, but mortality rate remained high.


Hypothesis 6:

Failed Refutation:

Puerperal fever was transmitted through substances originating from a dead body. Dr. Kolletschka, a colleague of Dr. Semmelweis, developed symptoms similar to puerperal fever after he was cut by a student's autopsy knife, which had touched a patient who had died of puerperal fever. Dr. Kolleschka later died. If doctors or medical students examined patients in ward I after they finished an autopsy, such actions may have spread the puerperal fever agent from the dead to the living. Since knowledge of infectious agents was limited at this time, it was not possible to directly test the primary hypothesis, i.e., observe and measure what substances came from the dead bodies. Thus, in order to test this hypothesis, Semmelweis invoked an auxiliary hypothesis, which he could then test. He conjectured that water containing calcium chlorite destroys the agent, i.e., it sterilizes the doctors' hands. Semmelweis required every doctor and student to wash their hands after autopsy. As a result, the mortality rate in ward I dropped down to 1.27% in 1848, while that of ward II showed a 1.33% rate. Moreover, women who delivered their babies during transport also had a lower mortality rate because they were not examined, and thus, were not transmitted any contaminating agent before delivery. If a mother suffered from puerperal fever, her newborn baby was also more likely to die of a similar fever because the agent might be transmitted to the baby during delivery. These facts seemed to support the hypothesis that the agent came from a dead body.

Popper (1965) called the above process of scientific research "conjectures and refutations." It is a repetitive cycle of proposing hypotheses (or, conjectures) and attempting to test each one, instead of

Chapter 2


21

confirming them. As with the example of puerperal fever, one cannot ever prove a hypothesis, but can fail to refute it. One is, thus, left with the more valid conclusion by deductively eliminating all other possible causes. Figure 2.1 summarizes the principles of scientific research. In human observational studies, one often makes the mistake of only looking for confirmatory facts, and consequently, one may more easily become self-deluded. By taking a refutational attitude, one can better avoid this fallacy. For example, if Dr. Semmelweis had stopped his refutation effort, he would have failed to consider the possibility of transmission of an agent from living bodies. Later, he noticed that in one instance, he had not washed his hands after examining a patient with cervical cancer and proceeded to examine another 12 women awaiting delivery. Later, 11 of them died of puerperal fever. Consequently, he immediately modified his hypothesis and proposed that the agent could also be transmitted through a living body. In fact, even if the refutation of hypothesis 6 were successful, it does not necessarily follow that the primary hypothesis was refuted because an auxiliary hypothesis was invoked, i.e., that the disinfection of hands with calcium chlorite was effective in killing the agent. Thus, if one has refuted a hypothesis indirectly, one should consider whether or not one has only falsified the auxiliary hypothesis and not the primary hypothesis. To do so, one must examine all auxiliary hypotheses made during the empirical tests and measurements. This process can be expressed in more abstract terms: Let H denote the primary hypothesis; A,, A2, , An denote the auxiliary hypotheses invoked; and B denote the predicted outcome or effect. Then, if H, A b A2, , An are all true, then B is true. If we have found B to be false, then at least one of H, A,, A2, , An should be false, but not necessarily A or every An. In all empirical scientific studies, one always assumes or invokes the auxiliary hypothesis that measurements made are accurate enough to detect


the effect predicted by the hypothesis. For epidemiological studies, which are empirical observations on human population, one usually invokes additional auxiliary hypotheses. Thus, one should be careful to avoid possible confounding or mixing of effects by any extraneous factors, such as auxiliary hypotheses.

Conjectures Propose all possible explanations or hypotheses: Hi, H,,

Repeat the cycle to explore the details of the mechanism.

,H„

Deductions

Refutations

Assume that each hypothesis

Falsify and rule out each

is true, then predict what

hypothesis by examining the

should or should not happen.

observed and predicted facts.

H, 'Fu> Fi2 H, >F 2 ,,F 2;

The more valid hypothesis .Fa

will remain unrefuted.

Hn => F n ,, Fn2, ... , Fn,

Observations and measurements Design a study and observe the target facts predicted by the hypotheses. Because of ethical concerns against experimentation, one can only conduct observational studies on human beings.

Figure 2.1

Data analysis Use statistics as a summary tool and control confounding so that the causal relationship is clear.

Conjectures and refutations are the basis for causal epidemiological research. This figure also shows the proper places for observations and measurements, as well as statistical analysis (Wang, 1991).

Chapter 2

2.2


23

Deductive methods: Common logical reasoning

The example of the preceding section reminds us that we often use deductive logic to provide more specific statements derived from the hypothesis, which can then be tested empirically. Such statements are very useful because according to deductive logic, these statements are guaranteed to be true if the premise is true. Therefore, we should use these deductive rules in our everyday research. In this book, I only list the most common ones, as on Table 2.2. Further details may be found in standard textbooks of logic, like those written by Tarski (1957) or Copi (1972).

Table 2.2

Most frequent forms of logical reasonings.

" n"— implies " v"~- or

" = " — is equivalent to " ~ " — not

" • " — and

(1) Modus Ponens piDq

_B

e.g., If p, "Smokers are more likely to develop lung cancer," is true, then q, "Chinese women who smoke are more likely to develop lung cancer," is also true because Chinese women smokers are implied in all smokers.

(2) Modus Tollens P -D 1 -^-9 ' *~P

e.g., If "Smokers are more likely to develop lung cancer" is true, then "Chinese women who smoke are more likely to develop lung cancer" is also true. If we have evidence to demonstrate that Chinese women smokers are not more likely to develop lung cancer than nonsmokers, then we can conclude that the premise is not true either.


(3) Hypothetical Syllogism qp r

e.g., If "Smokers are more likely to develop lung cancer" is true, then "Women who smoke are more likely to develop lung cancer" is true. If "Women smokers are more likely to develop lung cancer" is true, then "Chinese women smokers are more likely to develop lung cancer" is also true. If the first premise is true, then "Chinese women smokers are more likely to develop lung cancer" should be true.

(4) Disjunctive Syllogism pvq ~P

.. q

e.g., Assume that "Today Mr. John Doe is either attending school or going home," is true. If we know that Mr. Doe is not attending school now, then he must be going home.

(5) Constructive Dilemma (p -D q) • (r => s) p vr qvs

e.g., "If you want to write a good thesis, then you should first carry out a good study." And "If you want to be a good epidemiologist, then you should first study epidemiological methods." Since you want to either write a good thesis or be a good epidemiologist, you ought to carry out a good study or you should study epidemiological methods.

Chapter 2 Conjectures and refutations

(6) Absorption p=>q p 3 ( p • q) (8) Conjugation P q ••• p • q

2.3

25

(7) Simplification p- q

(9) Addition P q •pvq

Conjectures and Refutations

Traditionally, one applies the induction method to propose a more general hypothesis after observing several incidences. For example, after observing 100 black ravens, one may propose a hypothesis stating that all ravens are black. Then, the hypothesis or "theory" as some may contend, implies that the 101th raven or even the unborn ravens in the future are also black. This hypothesis is only a guess or conjecture. One can never prove that it is true even after observing thousands or more black ravens because one has no logical basis on which to guarantee that the next one will be black. Just as Hume claimed in the 18th century: "We are never able in a single instance, to discover any power or necessary connection, any quality which binds the effect to the cause, and renders the one an infallible consequence of the other. We only find that one does actually, in fact, follow the other. Hume argued that one can never prove a causality such as A causes B. Instead, one can only say that whenever A occurs, B is frequently observed. The doubt that Hume gave remained unanswered, until in the late 1930's Popper (1965,1972) proposed an alternative viewpoint to tackle the issue.

26


Popper considered that although one cannot prove that a hypothesis is always true, one can still refute or prove a hypothesis to be false. The one that remains unrefuted is more likely to be true in comparison with those already falsified. Since the search for truth and causal mechanisms never ends, the process of conjecture and refutation should continue indefinitely. Epidemiological research is one of the many types of scientific research, focusing on the human population. Due to ethical concerns, scientists are forbidden to perform experiments on human beings, and can only conduct randomized clinical trials once obtaining the patients' informed consent. Thus, research conducted among a human population must rely mostly on observations of the population under study. Yet, scientists must be very careful in how they obtain such observations. Since a large multitude of events happen each day, it is very natural for one to simply pick what one wants to observe, i.e., confirmatory facts, and ignore evidence that may contradict the proposed hypothesis. The Popperian approach, as shown in Figure 2.1, can help one to avoid such a fallacy and seems to fit quite well in etiologic research. The following is a typical process of an etiologic diagnosis by an occupational physician (Wang, 1991). Astute occupational physicians or health professionals usually start to suspect an occurrence of occupational disease whenever there is a clustering of cases during a certain time period and within a specific workplace. They then propose all possible etiologies or causes according to present-day medical knowledge and toxicological databases. For each individual hypothesis, they deduce several consequences or try to predict what could and/or should happen. Then, they design a study and go to the field to obtain {i.e., observe and measure) target facts predicted by each hypothesis. After collecting such information, they summarize their findings and try to control for any confounding by statistical tools. Also, they attempt to challenge each hypothesis by examining the observed and predicted facts. After ruling out all false hypotheses by deduction, they may only have one hypothesis left unrefuted. Consequently, they may consider this hypothesis to be the most valid. By repeating this cycle, they can further explore the mechanism in finer detail.

Chapter 2


27

It is very natural that one usually looks for facts confirming one's own intuitive conjecture or hypothesis and, consequently, be misled in that direction. However, a skeptical refutational attitude can help one to always looks for alternative hypotheses and facts contrary to the proposed hypothesis. From my experience, such an attitude helps one to avoid misdiagnoses and guides one to the most valid etiology. 2.4

Why take a refutational attitude?

People familiar with the induction method may argue that inductivists also resort to empirical tests to decide which hypothesis is true and deserves to be called a theory. Then, why should one take the side of the Popperian philosophy of science? From my personal experience, a verificational or confirmatory approach usually leads to a very complacent attitude, preventing one from searching for alternative explanations or hypotheses. Thus, one is more likely to ignore evidence that are contradictory to the favorite hypothesis, while a refutational attitude encourages one to look for contradictions and alternatives. Take the example of the documentation of an outbreak of botulism, which was initially thought to be the result of occupational hazard. Example 2.1 Outbreak of acute bilateral weakness of extremities and respiratory paralysis in a color printing factory (Wang and Chang, 1987;Tsaiefa/., 1990) In September 1986, an apprentice in a color printing factory in Chang-Hwa suddenly developed acute bilateral weakness and respiratory paralysis. The victim's father alleged via phone that there were several other workers with similar symptoms. Since occupational diseases resulting from organic solvent exposures, i.e., n-hexane induced polyneuropathy and carbon-tetrachloride induced hepatitis, were once documented in color printing shops (Wang et al, 1986; Deng et al, 1987; Huang et al, 1987, respectively), investigators went to the work site, proposing the hypothesis of possible solvent intoxication (Figure 2.2).

28


In practice, however, the investigators also considered all alternative conjectures, including other medical problems due to the impaired function of upper motor neurons, lower motor neurons, as well as of the neuromuscular junction. They then deduced outcome statements from the different hypotheses: If solvent poisoning were the cause (H,), it would impair consciousness at a certain point in the clinical course. If any solvent reported to produce polyneuropathy, e.g., n-hexane, acrylamide, methylbutyl ketone, etc., were the cause (H2, H3), it would also impair the nerve conduction velocity (NCV). If the cause were other medical problems involving upper motor neurons (Hn.2), there would be signs of impaired consciousness and/or involuntary movement. Moreover, if it were a case of Guillain-Barre syndrome, a specific lower motor neuron disease (Hn_,), it would usually not show case clustering in space and time, and would lead to a demyelination effect, e.g., impaired NCVs. If it were a case of myasthenia gravis or syndrome, a disease of the neuromuscular junction Hn(1), the neostigmine test would be positive. If it were a neuromuscular blockade caused by drugs, pesticides (such as organophosphrites), spider bites, or snake bites H„(2), there would be a history of medication or bite before the onset of symptoms. If it were botulism, another neuromuscular junction disease Hn(3), we would be able to culture the clostridium and find botulinum toxin in the food they consumed. Field observations disclosed that all affected workers had a clear consciousness throughout the clinical course. An NCV study of three affected workers showed intact lower motor neurons. There was no involuntary movement, no history of medication or bites prior to the appearance of symptoms, and the neostigmine test was found to be negative. A significant association between illness and eating breakfast in the factory cafeteria on September 26 or 27 was found; seven of seven affected workers vs. seven of 32 unaffected workers ate breakfast in the factory on these two days (p = 0.0002 by Fisher's exact test) (Chou et al, 1988). Further testing effort showed that type A botulinum toxin was detected in canned peanuts manufactured by an unlicensed company, and its specimen also showed a

Chapter 2


29

Clustering of cases with sudden onset of bilateral weakness of extremities with respiratory paralysis in a printing shop

Conjectures H,: Acute solvent poisoning H2: n-hexane induced Polyneuropathy H3: Acrylamide or methyl butylketone induced polyneuropathy

Deductions H[—'Consciousness disturbance tt-r* Impaired NCVs H3-»Impaired NCVs H^-^-Consciousness disturbance and/or involuntary movement Hn.!—"-Impaired NCVs Guillain-Barre Syndrome H„(i)^Myasthenia gravis or syndrome Hn(2)-»Dnig or toxin induced Hn(3) ^Botulism

H„.2:Other upper motor neuron disease H„.|:Other lower motor neuron diseases: Guillain-Barre Syndrome H„: Neuromuscular junction disease l)Myasthenia gravis 2)Drug or toxin induced 3)Botulism

Rare clustering in space & time. Rare clustering in space & time and neostimine test(+) History of medication, or spider or snake bites Clostridium botulinum(+) and toxin (+)

Future refutation attempts Eliminated the canned peanuts, and no more new cases occurred.

Refutations Hi, H2,...Hn(i)iHn(2) were all excluded as the diagnosis.

Data analysis Eating breakfast on Sept. 25-26 was shown to be associated with the appearance of symptoms.

Observations and measurements All affected workers had clear consciousness throughout. NCV was intact. No involuntary movement. Neostigmine test (-). No history of specific drug usage or animal bites. Culture showed Clostridium botulinum and toxin in Canned peanuts.

Figure 2.2

Outbreak of botulism in a printing factory: An example of taking a refutational attitude (Wang, 1991).

30


full growth of Clostridium botulinum. A final refutation trial involved the removal of such products from the commercial market, resulting in no more new cases. This investigation documented the first cases of botulism due to a commercial food product in Taiwan. Confounding or mixing of effect in the search for causal agents Let us examine some more examples: During the study of "association between the air concentration of S0 2 and occurrence of asthma," investigators found that the prevalence rate of asthma was higher among communities with higher ambient S0 2 concentrations (Lin et al, 1981). There was an almost linear association between the two. Can one then conclude that the high prevalence of asthma was caused by high S0 2 concentration in air? If one takes a refutational attitude, one must also consider other determinants of asthma, such as occupational exposure for these asthma patients, house dusts, familial tendency, etc. Moreover, one must distinguish between asthma cases developed after moving in from those cases developing asthma before moving into the community. In other words, one should always consider and rule out alternative explanations or hypotheses before reaching any conclusion. In the search for the etiological agent of polyneuropathy among press-proofing workers (Wang et al, 1986), if investigators had simply confirmed that a pigment of printing paste contained lead and concluded that workers' polyneuropathy resulted from this lead exposure, we should have missed the true cause - n-hexane. Fortunately, we considered other alternative hypotheses, including lead, carbon disulfide, methylbutyl ketone, acrylamide, etc., and successfully ruled out each one to demonstrate that n-hexane was the responsible agent. Finally, when all such factories removed n-hexane, no new cases occurred, corroborating our hypothesis. Consider another study, in which researchers sought to find the etiologic agent for an outbreak of hepatitis among printing workers (Deng et al, 1987). The employer and most employees originally blamed viral

Chapter 2


31

hepatitis B because the hepatitis B surface antigen carrier rate was approximately 15-20 % in Taiwan (Chen and Sung, 1978). If we had not considered alternative hypotheses, investigators would have missed that the cleaning agent, carbon tetrachloride, produced the outbreak. Similarly, researchers have demonstrated that an outbreak of hepatitis among synthetic leather workers was caused by dimethyl formamide, a chemical used in the manufacturing process (Wang etal., 1991). Consider this hypothetical study attempting to determine whether there is an association between noise and hypertension. If one finds that there is a high prevalence rate of elevated blood pressure among people living in a noisy region and conclude that such evidence supports the association, one may reach an erroneous conclusion. The people in these noisy communities may also be on a high salt diet, they might have higher body mass indices (BMI) or their job stresses may be higher, etc. Before all these alternative explanations are addressed, one should not jump to any early conclusions. In fact, mixing of the effect by alternative hypotheses or explanations is known as confounding (Miettinen, 1974b, Miettinen and Cook, 1981). The basic principle for determining the existence of confounding involves first finding any unrefuted alternative explanations, which are major determinants of the outcome under study and associated with the exposure of interest. We shall return with a more detailed discussion on confounding in Chapters 4 and 7. All the above examples have indicated that one should take a refutational attitude in scientific research to avoid the pitfall of jumping to false conclusions. Dr. John C Eccles, a Nobel laureate, once wrote an essay entitled "In praise of falsification," (1981) attributing his success in neurobiology to the falsificationist attitude of constantly testing and renewing his original hypothesis. Table 2.3 displays a summary of the comparison between verificational and falsificational attitudes in scientific research.


Table 2.3

Comparison of the verificationist and falsificationist's views in science (modified from Maclure, 1985). Verificationist

Falsificationist

Fundamental view Origins of hypotheses

Science is based on verifying hypotheses. Observation comes first, and reveals a hypothesis.

Theory

A good theory is the one that has been verified multiple times.

Axiom

Induction is logical.

Science is based on disproving or falsifying hypotheses Explanation comes during observation. The observer thinks of a hypothesis first, and then imposes it on what he observes or expects to observe. A good theory is a hypothesis that stands firm after many critical attempts of falsification. Thus, one can only regard a theory to be more corroborated than other alternative hypotheses. Only deduction is logical. A hypothesis found by the induction method is still a guess or conjecture. We can never prove that a hypothesis is always true, but we can disprove or falsify hypotheses.

2.5

The limitations of conjectures and refutations

A scientific theory, regardless of the number of failed attempts at critical refutation, can only be regarded as more corroborated than other alternative hypotheses or theories, and is not guaranteed to remain unrefuted in the future. For example, scientists upheld Newton's law of motion for more than two centuries and once regarded it as universally true. However, in the early 20th century, Einstein's theory of relativity replaced Newton's laws of physics. Similarly, we cannot say that the theory of relativity will remain unchallenged, either. Instead, we have faith to accept it as more corroborated than all other falsified theories attempting to explain our

Chapter 2 Conjectures and refutations

33

physical world. Thus, our faith is not blind because the theory of relativity is the only one not yet disproven. In order to empirically test a hypothesis, we must propose hypotheses that can be falsified. Otherwise, we may be left with many unrefuted hypotheses that cannot be tested. We will examine this issue in Chapter 3. Another possible limitation of this approach is that one can only consider alternative explanations or hypotheses that one can imagine. If the real etiologic agent is not included in one's list of hypotheses because of one's limited knowledge, one may be left with no answer after all proposed hypotheses have been falsified. Therefore, inviting an expert in the field and looking into a comprehensive database of published literature that covers the subject area is crucial to the success of this strategy. For example, the OSH-ROM database (Silver Platter, 1998), which contains about 200,000 abstracts, may be one of the most comprehensive for making an etiologic diagnosis of occupational and/or environmental diseases. Furthermore, if one is confronted with a new disease, one may search such a database and rule out all known etiologic agents. In such a condition, one may try to identify or define the new agent as specifically as possible. Otherwise, one must use a surrogate variable (Wang and Miettinen, 1982), which is amenable to change, so that the problem can first be mitigated, while the causal mechanism is relegated to later study. The case of pre-malignant skin lesions among paraquat manufacturers (Wang et al, 1987) is a good example of this kind: In June 1983, two workers from a paraquat manufacturing factory visited a dermatology clinic complaining of numerous bilateral hyperpigmented macules with hyperkeratotic changes on parts of their hands, neck, and face exposed to the sun. Specimens showed increased melanin in the basal layer, hyperkeratosis, epidermal hyperplasia, and dysplasia. Some specimens also showed Bowenoid changes. Since malignant and premalignant skin lesions were reported among bipyridyl manufacturing workers (Bowra et al, 1982), investigators strongly suspected an


occupational cause. However, they also considered other alternative causes (hypotheses) of skin cancer, such as exposure to ionizing radiation, coal tar, soot, pitch or any other polyaromatic hydrocarbons (PAH), efc.(Scotto and Fraumeni, 1982), as shown in Figure 2.3. If ionizing radiation had been the cause, all affected workers should have had a positive exposure history through occupational or medical origin. Similarly, if PAH or tars had been the cause, all affected workers should have been exposed to them. To falsify all of these conjectures and deductive statements, the investigators conducted a study in 1985 and visited all 28 factories engaged in paraquat manufacturing and packaging, and examined the manufacturing processes as well as workers. They examined 228 workers and none of them had ever been exposed to the aforementioned skin carcinogens except sunlight and 4, 4,-bipyridine and its isomers. In an attempt to falsify paraquat itself as an alternative, the researchers stratified workers according to their work assignments: administrative jobs, paraquat packaging, bipyridine crystallization and centrifugation, and multiple job assignments. After excluding workers with multiple exposure, they found that 1 out of 7 administrators and 2 out of 82 paraquat packaging workers developed hyperpigmented skin lesions, as compared with 3 out of 3 workers involved in only bipyridine crystallization and centrifugation. Moreover, all 17 workers with hyperkeratotic or Bowen's lesions had a history of direct exposure to bipyridyl and its isomers. The longer the exposure to bipyridyls, the more likely the development of skin lesions. This trend could not be explained by sunlight or age as demonstrated by stratification and logistic regression analysis (Table 7.10). The skin lesion was tentatively attributed to a combination of bipyridyl exposures and sunlight. In the follow-up study, the investigators made additional attempts to refute their hypothesis by enclosing all processes involving bipyridyl exposure. Since no more new cases occurred at the enclosed factory, their conclusion presently remains valid.

Chapter 2


35

Example 2.2 Outbreak of premalignant and malignant skin lesions among paraquat manufacturers (Wang et al, 1987)

Cases of Bowen's disease and hyperkeratosis in a paraquat manufacturing factory Conjectures H,: Ionizing radiation H2: Tars, soots, pitch, etc. Hn.,:Paraquat Hn: Bipyridyl and/or its isomers Deductions H,: Affected workers should have a history of exposure to ionizing radiation, e.g., X-ray, etc. H2:Affected workers should have a history of contact with tars, soots, pitch, etc. H,,.,: Affected workers were exposed to paraquat. H„: Affected workers were Observations and Measurements exposed to bipyridyls. All workers were exposed neither to ionizing radiation, nor to tars, soots, pitch, etc.2 out of 82 workers, exposed only to paraquat, developed skin lesions, while all 17 workers with hyperkeratotic skin lesions had a direct exposure to bipyridines.

Figure 2.3

Future refutation attempts Enclosure of all of processes involving bipyridine resulted in no more new cases.

* Refutations H b H2, ... ,H„.| were all refuted. Only Hn remain unrefuted, and sunlight was found to be a co-factor.

* Data analysis Stratified analysis showed that the longer workers were involved in bipyridine crystallization and centrifugation the more likely they were to develop skin lesions. This association cannot be explained by age and the amount of sunlight exposure.

Premalignant and malignant skin lesions caused by bipyridyls as an example of conjectures and refutations.


2.6 Summary Epidemiological research is based on the basic principles of scientific research, and thus the deductive methods involved in conjectures and refutations. Since deductive methods are defined by common logical reasoning, one can be sure that if the premise is true, then the end statement is true. The method of conjecture and refutation is a process of proposing hypotheses and trying to falsify each one of them. Although one can never be sure that a conjecture is true, one can tentatively conclude that a hypothesis which stands firm after many empirical tests is nearest to the truth compared with those refuted. A refutational attitude causes one to always consider alternative hypotheses and look for evidence contradictory to the hypothesis. Thus, it can help one to avoid the pitfalls of complacency and self-delusion. However, this strategy is still limited to those hypotheses one can imagine. As a result, one may falsify all proposed hypotheses or be left with too many unrefuted ones. For the former, one needs to first mitigate the damage and expand one's hypotheses. For the latter, one should propose hypotheses which can be empirically tested.

Chapter 2


37

Quiz of Chapter 2 Please write down the credibility of each assertion in terms of percentage (%). Your score will be calculated according to the percentage of credibility that you actually obtain after comparison with the instructor's "gold standard". Score

% 1. The scientific knowledge on human population is progressed through repeated falsifying hypotheses instead of confirming hypotheses. 2. A limitation of conjecture and refutation is that one can only consider hypotheses that one can imagine. If the true etiological agent is not included in one's list of hypotheses, then one may end up with no answer after refuting all proposed hypotheses. 3. One can never be sure that a theory will be forever true even after one thousand times of refutation tests. 4. One can be sure that the un-refuted hypothesis is closer to the truth than those already refuted ones. 5. A refutational attitude tends to guide the investigator to avoid self-delusion or accepting a hypothesis which is contradictory to the facts. 6. Inductive reasoning guarantees that if the premise is true, then the statement that follows should be also true. 7. A scientist should try to verify his/her hypothesis and disprove other people's hypotheses. 8. The observation itself will automatically show one the hypothesis or even theories. 9. A good scientist should try to falsify his/her favorite hypothesis, because it may be easily overlooked without

38


scrutiny. 10. In an observation of human population, one easily invokes some auxiliary hypothesis, which may not be highly corroborated, because one can not conduct strict experimentation on human. Answer: (1) T (2) T (3) T (4) T (5) T (6) F (7) F (8) F (9) T (10) T

Chapter 3 Scientific Hypothesis and Degree of Corroboration 3.1 3.2 3.3 3.4 3.5 3.6

Hypothesis formation What makes a hypothesis scientific? Successful refutation and auxiliary hypotheses Failure to falsify and degree of corroboration Credibility of a hypothesis and decision-making Summary

Introduction In applying the principles of conjecture and refutation, one attempts to propose the most comprehensive list of hypotheses in order to find the most valid etiologic agent. Yet, how does one propose a scientific hypothesis? What characteristics should a hypothesis possess in order to be called "scientific"? How many of these repetitive cycles of conjecture and refutation need one undergo before an unrefuted hypothesis deserves to be called a theory? In other words, how can we evaluate the credibility of a hypothesis after many empirical tests? These are the issues to be discussed in this chapter. 3.1

Hypothesis Formation

—

How to form a conjecture?

Conjectures usually precede observations Traditional inductivists argue that hypothesis is generally formed after one's observation of facts or phenomena. However, most hypotheses are not formed in this manner because natural phenomena do not directly spell out the laws of nature. For example, everyone observes sunset and sunrise, yet it was Copernicus who proposed that the earth revolves around the sun rather than the sun revolving around the earth. Similarly, everyone observes that apples fall to the ground but only Newton proposed the theory

39

40


of gravitation. Only those who dare to propose alternative hypotheses or explanations of nature are more likely to provide a hypothesis or theory closest to the true law. In fact, purposeful observations always involve explanations or interpretations already formed in the observer's mind. The observer then tries to select and fit the observed phenomena to his/her different explanations or hypotheses. As Popper (1965) pointed out, man typically first conjectures and then observes his expectation, namely, his conjecture precedes his observations. For example, Popper once asked his students to observe the blackboard. After half an hour, his students inquired, "What aspect or characteristics of the board did you want us to observe?" Thus, our conjecture is often based on our personally biased view — a view heavily influenced by our past experiences. A person with a verificationist's attitude tends to see only those facts which he/she expects, while remaining blind to any fact contradictory to the favored hypothesis. Therefore, a verificationist is more likely to believe a hypothesis which, in fact, may already be refuted. In other words, since hypothesis usually comes to mind before purposeful observation, taking a refutational attitude to propose all kinds of alternative hypotheses, will help one to avoid false conclusions. How to propose a hypothesis How, then, does one form a hypothesis and propose alternative or new hypotheses? This question falls in the larger domain of psychology (Tweney et ai, 1981). Here I shall share some of my own personal views. In general, the ability to propose various hypotheses depends on one's previous experiences and educational background. The better able one is to approach an issue from different angles, the more hypotheses one can propose to explain the phenomena. Although many hypotheses may be quickly falsified even before one can write them down, the habit of thinking of all possible alternative explanations will increase the likelihood that one will include the true etiologic agent. Mill's five methods of induction can certainly help in this process (Please see next paragraph). Consultation of any database, review article, literature, or expert specialized in the field can

Chapter 3 Scientific hypothesis

41

also provide one with more alternative hypotheses. In fact, one of Popper's students, Feyerabend (1975), even proposes that any method will do; no formative method is needed. For example, if one wants to consider the possible etiologic factors of suicide among Taiwanese aborigines, one may look at the problem from a sociological viewpoint, which may provide one with possibilities, such as culture shock, economic pressure, disintegration of their social system, etc. One may also consider it from a clinical psychiatric viewpoint and propose alcoholism, affective disorder, etc. Or, one may think of family problems such as marital instability, divorce, or destruction of the traditional family system, etc. With a pluralistic approach, one will less likely neglect any important etiologic factor. Moreover, occasionally, a consultation of a specialist in the field can shed light on a discovery. The structure of the DNA double helix proposed by Crick and Watson (1968) was developed from consulting with Pauling on the concept of hydrogen bonding. Pauling used this same idea to construct the alpha—helix structure of proteins. Traditionally, inductivists believe that certain rules must be followed to form a hypothesis; this is generally summarized as Mill's five rules of induction (Copi, 1972). To broaden our approach to the proposal of hypotheses, I have also included these rules for the readers' reference, as described on the following page and in Table 3.1. In summary, Mill's methods of induction are only rules for proposing a hypothesis or explanation. They are simply based on the principle of consistency (See chapter 4). And all the proposed hypotheses are only explanatory conjectures. They are not universal truths and may not even be the true etiologic agent. Therefore, one must empirically test or falsify each one of them. Mill's five methods of induction (1) Method of agreement: If the same disease (health effect) always appears following a specific common agent under various environmental or occupational settings, then the common agent may be the cause of the

42


disease. For example, if workers exposed to asbestos fibers under various manufacturing processes, like asbestos textile, brake lining, asbestos cementing, etc., have an increased occurrence of mesothelioma, one can propose asbestos as a cause of mesothelioma. Similarly, since the occurrence of lung cancer frequently increases among smokers, whatever their gender, ethnicity, place of living, etc., one may propose the hypothesis that smoking causes lung cancer. (2) Method of difference: If two or more populations have different frequencies of a specific disease, yet they share similar distributions of all determinants except the exposure of interest, then that exposure may be considered a cause of the disease. For example, different frequencies of polyneuropathy were observed at different press-proofing factories. Among the 15 factories we observed, only workers in the three factories using n-hexane as the cleaning solvent developed polyneuropathy, while those at the 12 factories using toluene did not. Since all workers shared the same demographic characteristics except the cleaning agent, we proposed n-hexane as the causal agent. (Wang, et al, 1986) (3) Joint method of agreement and difference: This rule is a combination of (1) and (2). If more than two populations are observed and a specific disease always has an increased frequency only if a particular agent exists, one may suggest that this agent is a cause of the disease. For example, if after observing increased occurrences of mesothelioma among asbestos textile and brake lining workers, but not among cotton and wool workers, then one could propose that asbestos is a causal agent for mesothelioma. (4) Method of residue: According to this rule, after observing increased frequencies of several diseases following several possible agents, one can rule out those diseases already linked to particular agents, and can conclude that the remaining disease is caused by the residual agent. For example, suppose one finds increased frequencies of hearing impairment, lung cancer, and low back pain among asbestos textile workers who have worked for more than 10 years. Since one knows that hearing impairment is caused by noise and back pain is caused by lifting heavy objects, one may propose that asbestos fibers, the only obvious agent remaining, causes lung cancer.


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(5) Method of concomitant variation: This rule refers to a condition similar to a linear dose-response relationship. In other words, if the variation of specific disease frequencies in different populations changes relative to different distributions of a particular agent, then the agent may be the cause of the disease. For example, if the occurrence of lung cancer in different population groups increases with the increased amount of smoking, one may propose that smoking causes lung cancer.

Table 3.1 Mill's rules of induction — How to observe relevant facts and propose hypotheses. Please refer to the text for a more detailed explanation. (1) Method of agreement ABCD — abed AEFG — aefg

A, B, C, D, E, F, G = events/agents observed a, b, c, d, e, f, g = outcomes/effects observed

Propose the hypothesis: A is the cause of a.

(2) Method of difference AB—ab B—b Propose the hypothesis: A is the cause of a.

(4) Method of residue ABC - abc B is a known cause of b. C is a known cause of c. Propose the hypothesis: A is the cause of a.

(3) Joint AB AC B

method of agreement and difference: — ab — ac — b

Propose the hypothesis: A is the cause of a.

(5) Method of concomitant variation ABC — abc A*BC — a+bc A-BC — a"bc Propose the hypothesis: A is the cause of a.

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3.2


What makes a hypothesis scientific?

To propose hypotheses that can be tested or falsified, one must consider what characteristics a scientific hypothesis should possess. Is there any principle one can use to differentiate a scientific hypothesis from pseudo-scientific ones? The answer to the above question is quite straightforward when one considers that scientific knowledge only advances through the process of conjecture and refutation. Specifically, only hypotheses that can be empirically tested or refuted belong to the "scientific" category, although one can propose many explanations or hypotheses for a phenomenon. Conducting empirical tests allows one to distinguish between the many different hypotheses to find the one that best explains the phenomena. The advancement of scientific knowledge is based on this search for the irrefutable hypothesis. No matter how broad its explanatory power, any hypothesis cannot be called scientific if it cannot be tested or falsified. Popper first proposed this rule in the 1930s, demarcating scientific from pseudo-scientific hypotheses or theories (1965). At the time, he found that the theories proposed by Freud, Adler, Marx and Einstein all possessed very broad explanatory powers, i.e., these hypotheses could explain practically everything happening within their own fields. However, only Einstein's relativity theory clearly predicted the phenomenon of red shift when light passes through a gravitational force. Since one can deduce statements from the theory of relativity, which forbid or predict events, one can empirically test it. The Freudian and Adlerian hypotheses, however, cannot be contradicted empirically. Popper gave two contrasting examples: A man pushed a child into the water with the intention to drown it, and another man sacrificed his life in an attempt to save it. Both of these cases can be equally explained in Freudian and Adlerian terms. According to Freud, the first man suffered from repression, while the second man achieved sublimation. According to Adler, the first man suffered so greatly from a feeling of inferiority that he dared to commit a crime to prove himself, as did the second man, who tried to prove himself by daring to rescue the


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child. In fact, one can look at all kinds of human behavior and find "confirmation" of these hypotheses. However, has one really confirmed anything? No, since these hypotheses cannot predict any future behavior, one cannot empirically verify anything at all and cannot distinguish which one is the more corroborated hypothesis. The conditions for Marx's hypothesis are different. Popper (1966) provided a great deal of argument in his book entitled, "The open society and its enemies", and claimed that Marx's hypothesis was already refuted by empirical evidence from capitalist societies or nations. However, Marx's followers tried to save his theory by creating an "ad hoc hypothesis," making it immune to falsification and thus, pseudo-scientific. Einstein's relativity theory has stood firm against many refutational attempts. Besides correctly predicting the red shift phenomenon, Einstein's theory also proposes that the speed of light is absolute and that the velocity of any particle will not exceed the speed of light. In reality, the largest speed ever achieved by an elementary particle produced by an accelerator was 99.999999985% that of the light speed. Moreover, the relativity theory predicts that the life of a moving body achieving almost light speed will be prolonged. Experimental physicists have already found that, if moving at 99.5% the speed of light, a particle's life span is prolonged ten times that of an inert particle. Since all critical falsification attempts have failed, Einstein's theory of relativity is the only theory of motion that remains unfalsified. Popper claimed that it is precisely this falsifiabilty which distinguishes scientific from pseudo-scientific hypotheses. Although one may consider Popper's view to be too narrow and only applicable to the natural sciences, it still provides one with a conceptual understanding on how to propose a scientific hypothesis. I have found Popper's concept quite useful in my daily practice of causal epidemiological research. In addition, I believe that in other less developed health-related disciplines, such as traditional medicine or folk therapy, one must also try to propose hypotheses that can be tested. Even though Chinese herbal medicine has lasted for more than 3000 years, the advancement of this discipline has been relatively limited. This lack of progress may be a result

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of Chinese herbal doctors' reliance on a traditional system of Yin-Yang-Wu-Xing hypothesis, which similar to Freudian or Adlerian theory, is immune to refutation. This lack of falsifiability has restrained the progress of Chinese herbal medicine for the last hundreds of years. Only in the past few decades have people tried to propose falsifiable hypotheses for acupuncture and have enhanced the objective knowledge on this aspect of Chinese medicine. In one example of folk medicine, many Southeast Asian migrant workers believe that SUDS (Sudden Unexpected Death Syndrome) is caused by a widow ghost who sucks away a young male's soul. As there is no method to measure this widow ghost, one has no practical way to test the validity of this hypothesis and distinguish it among the different proposed hypotheses. Pseudo-scientific hypotheses simply cannot be tested through the process of conjectures and refutations. However, this irrefutability is not related to the usefulness of a theory. For example, ethical theories cannot be disproven or proven through conjectures and refutations, but they are highly useful and influential to our everyday life because they provide the guidelines for one's behavioral conduct. While science is useful in developing and demonstrating how an animal can be cloned, one must consider the moral values needed to set the appropriate range of applications for the new technology. Although principles of scientific research are advocated in this book in the search for natural laws, one should also understand their limitations so that these principles do not become a juggernaut. 3.3

Successful refutation and auxiliary hypotheses — disproved the primary hypothesis?

Has one

In the process of conjectures and refutations, one may observe facts contradictory to the deductions made from the primary hypothesis, leading one to conclude that the primary hypothesis is false. However, one should not jump to such an early conclusion in any human observational study, including that of epidemiology. Owing to the reliance on observation


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rather than experimentation, one cannot control all determinants of a particular outcome and must then invoke auxiliary hypotheses. For example, one must always make the assumption that one's measurements are accurate and sensitive enough to detect the effect predicted by the primary hypothesis. If the instrument for red shift measurement is inadequately sensitive, it may mislead one into believing that one's refutational attempt is successful. However, the contradictory data obtained only falsifies the auxiliary hypothesis rather than the theory of relativity. Similarly, if Dr. Semmelweis' attempts to decrease the mortality rate of puerperal fever by washing every examining doctors' or students' hands were unsuccessful, he may have thought he refuted the conjecture. Yet, the empirical data may have refuted the auxiliary hypothesis of the effectiveness of calcium chlorite disinfection, rather than the primary hypothesis. Take another example: If one wants to test the hypothesis that asbestos causes lung cancer, one may collect information on asbestos textile workers and analyze the data to determine whether exposed workers have a higher morbidity or mortality rate of lung cancer. During the research process, one must invoke at least following two auxiliary hypotheses: first, assume the adequate induction time for lung cancer; and second, assume that the diagnosis of lung cancer in our study is sufficiently accurate and sensitive. If one has not found an increased occurrence of lung cancer among exposed workers, one must first check the validity of the above two auxiliary hypotheses before concluding that our primary hypothesis is refuted. About 5-6 years after the core meltdown of the Three Mile Island nuclear power plant in 1979, there was a study showing negative radiation effect on nearby residents (Hatch et al., 1990), which in fact invoked similar auxiliary hypotheses of adequate induction time and accurate and sensitive measurements. It was not until 7 years later that Wing et al (1997) found increased incidences in several types of cancer (including lung cancer and leukemia) and falsified the early conclusion. In this case as well, one must avoid premature conclusions regarding the health effect of such an event, by first attempting to falsify all auxiliary hypotheses. To express this argument in more logical terms, let us denote H as the

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primary hypothesis and A,,A2, A 3 ,...A n as the auxiliary hypotheses invoked during our refutation attempt, while F is the fact observed or effect. A refutation attempt is shown below: If H, Al5 A2,...An are true, then F is true. Suppose we have found F to be false, then at least one statement of H, A,,A 2 ,...A n is false. However, if we know that A,, A2,A3,...Anare all true, then H is false. Critical refutation requires one to invoke only highly corroborated hypotheses, so that one is not confused as to whether the auxiliary or primary hypothesis is refuted. Since in all studies, one invokes the auxiliary hypothesis that measurement errors are smaller than the real difference, one should attempt to improve the accuracy of measurement in all studies, which will be discussed in Chapter 5. 3.4 Failure to falsify and degree of corroboration — Do the results of the study corroborate the primary hypothesis? During one's refutation attempt, one may fail to falsify the hypothesis. In this situation, the primary hypothesis seems to be corroborated and corresponds well with the facts. However, one must still examine the relevancy of our refutation attempt and analyze whether the range of consistency of our hypothesis can be expanded in time and place. Scientists believe a priori that natural laws exist and are universally true. Consequently, in scientific research, our refutation attempt should also adhere to these beliefs in determining degree of corroboration. Examine the following refutation attempt of the hypothesis that all ravens are black. Refutation 1: By deductive reasoning, i.e., modus tollens (p =D q; ~ q; .'. ~ p), an equivalent statement of this hypothesis is: Anything (including birds) that is not black is not a raven. Therefore, after observing a red vase, one has corroborated the hypothesis. Similarly, observation of a white man, a green tree, yellow clothes, etc. all seem to corroborate or fail to refute the hypothesis. But in fact, many such observations seem to have little relevance to the color of a raven. Refutation 2: One conducts a replicative study by expanding the


49

number of ravens observed from 10 to 100. If one's sample of ravens is randomly drawn and all of them are shown to be black, then one fails to falsify the hypothesis. This refutation attempt apparently has direct relevance to the hypothesis but only shows that the hypothesis is corroborated for local ravens. Refutation 3: One observes whether ravens in other continents (e.g., Australia, Africa, and Asia, etc.) and at different times (e.g., historical records of bird museums in 1796, 1896, 1946, etc.) are all black. If the hypothesis resists refutation under different time and spatial orientations, then the range of consistency of one's hypothesis is expanded to an even larger time and spatial dimension. Refutation 4: One invites a critic of the hypothesis to perform observations under the alternative hypothesis that some ravens are yellow or any other color. If he fails to find a raven with a different color, then this failure to falsify the primary hypothesis certainly corroborates the primary hypothesis. The above four types of refutation attempts increase in degree of corroboration of the hypothesis. The first attempt has no direct relevance to the hypothesis, and thus, the hypothesis remains uncorroborated. The second attempt, a merely replication study, has relevance but seems to challenge the hypothesis in only the local area. The third attempt challenges the consistency of the hypothesis in various times and places, and the failure to refute corroborates the hypothesis to a high degree. The fourth attempt, based on refuting challenging alternative hypotheses, strongly corroborates the primary hypothesis since the refutation of such alternatives eliminates the existence of competing hypotheses. Therefore, in attempting to refute a hypothesis, one should aim for direct relevance, expand the range of consistency at different times and places, and attempt to refute challenging alternative hypotheses. A failed refutation attempt, based on these criteria, more strongly corroborates the primary hypothesis and can help save resources as well. The above discussion leads to a broader view of applying subjective Bayesian analysis (Greenland, 1998b) in evaluating hypothesis after many refutation attempts.

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3.5


Credibility of a hypothesis and decision-making

Public health involves decision-making Even if a hypothesis has stood firm after many critical refutation attempts, can it be regarded as truth? Let us first define a true statement as a statement that corresponds to the fact (Tarski 1969; Popper, 1965). Then, most cause-effect relationships in our common daily life, such as who turns on the light in the office or what causes an outbreak of food poisoning, can be clarified through the process of conjecture and refutation as discussed in Chapter 2. Whereas in scientific research, the pursuit of truth (or law of nature) is an unending quest, and all un-refuted hypotheses are still considered conjectures subject to future challenge. When all competing alternative hypotheses are refuted, one may claim that the only hypothesis that remains corresponds more to the fact than all the other hypotheses. Such a highly corroborated hypothesis is one's closest approximation to the true natural law but may still be replaced in the future if falsified. In the public health field, however, one must take action at certain time in order to prevent morbidity and mortality. For example, the hypothesis that smoking causes lung cancer was proposed by Doll and Hill in the 1950s after their epidemiological studies, and since then, many have attempted to critically refute it in various times and spatial orientations without any success (U.S. Department of Health, Education, and Welfare, 1964, 1979). Moreover, presently there exists no alternative hypothesis that can explain the high proportion of lung cancer patients who are smokers. Although further refutation attempts may be still in need, public health authorities must take action now to prevent the increasing numbers of people possibly developing and dying of lung cancer. Thus, one is dealing with a different issue from that in the research of pure natural science. Instead of only searching for more definite answers, one must make decisions under some uncertainty, which is called decision-making (Bell, et al, 1988; Raiffa, 1976). In general, one needs to weigh the cost and benefits or cost and effectiveness, as well as medical ethics, for making such policy decisions in public health. This will be discussed in more depth in Chapters 4 and 13.


51

Credibility change for a hypothesis To help measure one's degree of belief for a hypothesis to facilitate rational action, I recommend Bayesian's approach of quantifying subjective probability (Savage, 1972; Howson and Urbach, 1993; Greenland, 1998a). In practice, one may be neutral to a hypothesis in the beginning, i.e., credibility of 50%. After he examines the results of all refutation attempts, in terms of relevance, consistency, different times and places, and challenging hypotheses, etc., he may start to move incrementally toward either one of two sides •credibility of 0% or 100%. If deciding whether a hypothesis is true further involves one's subjective preference, i.e., expected utility, then this should also be taken into consideration. If one assumes that as a scientist, one has no subjective preference for any specific hypothesis, then one simply draws his/her subjective opinion on credibility from posterior credibility, which is obtained by combining prior subjective probability of the hypothesis (assuming 0.5 if one is neutral) with the merit of the study after review. However, since public health decision-making frequently calls for the opinions or perceptions of a group of scientists, and since such decisions frequently affect people's autonomy (e.g., the choice to smoke or chew betel nuts), in general, I would recommend an expert to take a relatively conservative position on assessing the credibility of a hypothesis. Furthermore, due to the medical ethic of non-maleficence, to not inflict any harm or evil on others, (Beauchamp and Childress, 1994), one should not place too much credibility on a hypothesis by just looking at a particular study's statistical significance, e.g., p-value < 0.05 (or even p-value < 0.01). In fact, this is just a summary statistic calculated based on the assumption that the null hypothesis is true. Neither should one completely abandon a new hypothesis with a p-value exceeding 0.05. Instead, one should examine the study from every aspect, looking for any conflict with alternative explanations or auxiliary hypotheses, which one invokes in the refutation attempt. For example, before 1950, one might put a credibility of 0.5 on the hypothesis that smoking causes lung cancer. After reading many studies and Hill's discussion of probable causation (Hill, 1965), one's credibility

52


may increase to 70%. If the hypothesis is wrong, one may still have a credibility of 30%. Furthermore, after reading the Surgeon General's report (U.S. Department of Health, Education and Welfare, 1979), one's credibility might increase to 85% and up. However, if one immediately takes a relatively extreme position, at about 95%, then one will have only a subjective credibility of 5% if the hypothesis is found to be false. Thus, it is advisable to start with a relatively conservative position, rather than begin with an extreme level of credibility, especially when the utility or harm of taking an extreme position is high. 3.6

Summary

Scientists usually first form hypotheses and then impose them on their observations of nature. As a result, they should take a critical or refutational attitude toward the proposed hypothesis. Mill's five rules of induction are an excellent way to propose hypotheses. However, since they are all based on the principles of consistency, one should not limit hypothesis formation only from these rules. In order to understand the laws of nature, one relies mainly on the process of conjectures and refutations. Thus, any hypothesis that cannot be empirically falsified or tested escapes from refutation and is unscientific. If one's refutation attempt is successful, one should examine the primary and auxiliary hypotheses and determine which hypothesis is actually refuted. In designing a study, one should avoid invoking any unfounded auxiliary hypotheses. Moreover, one should ensure the validity of the auxiliary hypothesis that measurements made are accurate and sensitive enough to detect the predicted effect, as this assumption is invoked in every empirical study. If one fails to falsify the hypothesis of interest, then one determines a hypothesis's degree of corroboration by examining its relevancy and consistency in different time and spatial settings, as well as considering the possibility of any other unrefuted alternative hypotheses. Although in scientific research one may continue the search for natural laws even after many failed refutation attempts, in public health one often must make decisions under some


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uncertainty in the effort to decrease morbidity and mortality. I recommend Bayesian's approach to assess one's subjective credibility for a hypothesis: Start from a neutral stance, and then incrementally increase credibility after careful evaluation of all studies that can corroborate one's hypothesis. Based on the medical ethic not to inflict unnecessary harm on others, I also recommend taking a more conservative attitude towards one's subjective credibility of a hypothesis.


Quiz of Chapter 3 Please write down the credibility of each assertion in terms of percentage (%). Your score will be calculated according to the percentage of credibility that you actually obtain after comparison with the instructor's "gold standard". Score

% 1. With a verificationist's attitude, one tends to only see facts which one expects and often ignores any fact contradictory to the favorite hypothesis. As a result, one is more liable to believe a hypothesis that may in fact be false. 2. Mill's rules of induction can be summarized as been based on a rule of consistency. 3. Methods of induction are rules for proposing hypotheses or explanations. only, there is no guarantee that the hypothesis it true. 4. Popper proposed that the falsifiability of a hypothesis is the demarcation between scientific and pseudo-scientific hypotheses. Therefore, anything unscientific is of no use. 5. If A, A2, ..., A n are true, thenB is true. Suppose we have found B to be false, then all the statements A,_ A2, , An are false, as well. 6. One's attempts to refute a hypothesis should aim to obtain more direct relevance to the hypothesis, expand the hypothesis' range of consistency in time and space, and equally challenge alternative hypotheses. Then, a failure to refute will more likely corroborate the primary hypothesis.


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7. In public health, the pursuit of truth is an unending quest, and all unrefuted hypotheses are still considered conjectures subject to challenge in the future. Thus, Popper's principles can be applied in all circumstances. 8. In medical ethics, one should first consider the principle of doing no harm before recommending any preventive measure. 9. In public health, decision-making frequently involves subjective judgments. 10. The assumption that measurements made are accurate and sensitive enough to detect the effect under study is always an auxiliary hypothesis invoked during one's empirical refutation attempt.

Answer: (1) T (2) T (3) T (4) F (5) F (6) T (7) F (8) T (9) T (10) T


Chapter 4 4.1 4.2

4.3 4.4

Causal Inference and Decision

Causal concepts in medicine and public health Proposed criteria for causal decisions 4.2.1 Necessary criteria 4.2.2 Quasi-necessary criteria 4.2.2.1 Consistency 4.2.2.2 Chance is not a causal factor 4.2.2.3 No alternative explanation 4.2.2.4 Coherence 4.2.3 Other supportive criteria 4.2.3.1 Strength of association 4.2.3.2 Specificity of association 4.2.3.3 Biological gradient or dose-response relationship 4.2.3.4 Biological plausibility Objective knowledge and consensus method Summary

Introduction The process of conjectures and refutations lies at the heart of science. Scientists propose conjectures and perform refutations in their search for the laws of nature. Scientific "theories" are the hypotheses, which have resisted all kinds of refutation attempts. Yet, from a Popperian scientist's point of view, such theories remain conjectures. Although scientists can usually wait for more critical tests of causality, public health investigators may need to take more immediate actions to prevent morbidity or mortality, as predicted by the hypothesis. Public health policy-making is not too different from daily life decision-making, where one makes decisions under some extent of uncertainty. For example, will it rain today? Should one carry an umbrella? Should one drive a more direct path to the office and face a potential traffic jam or take an

57

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alternative highway? In public health and medicine, one often asks questions, such as: should one add beta-blockers to a patient with hypertension, in addition to the angiotensin-converting enzyme inhibitor? Should one propose to a breast cancer patient, with no palpable local lymph node, a modified radical mastectomy or just a simple mastectomy? Based on the available evidence for potentially detrimental health effects of secondary or environmental tobacco smoke, should one adopt a regulation prohibiting smoking in all public places and offices? Should one still advocate a mandatory BCG vaccination for every newborn in Taiwan? In such circumstances, one must consider the utility or harm produced by the event, in addition to the subjective risk. Before further discussion of the utility that may be involved, I recommend that one carefully consider the criteria of causal decisions proposed by Hill (1965) and Susser (1986) from a refutational point of view. As pointed out in Chapter 3, public health decisions can conflict with a person's autonomy. For example, the US Surgeon General's warning on a cigarette pack may influence a smoker's decision by inducing some psychological stress. As a result, it is important to take a refutational attitude when reviewing causal criteria, in order to avoid wrong decisions or at least minimize any adverse effects. This notion to avoid inflicting harm on others is a major ethical priority among medical professionals, known as non-maleficence (Beauchamp and Childress, 1994). It is also more in accord with the precautionary principle of today's scientific and public community (Appell 2001; The European Commission 2000). This chapter will first examine some characteristics of causal concepts in medicine and public health, followed by a review of causal criteria, and comments on how to minimize erroneous conclusions made in public health work.

Chapter 4

4.1

Causal inference and decision

59

Causal concepts in medicine and public health

Defining a cause amenable to modification A cause is an event, state or agent of nature, which initiates, alone or in conjunction with other causes, a sequence of events resulting in an effect. In medicine and public health, a cause is defined and measured relative to an alternative condition. For example, "smoking" is defined in contrast to "nonsmoking." In order to make more accurate and quantitative measurements, one may further classify smoking into "smoking more than 1.5 packs/day," "smoking 0.5-1.5 packs/day," "smoking less than 0.5 packs/day," "never smoking," and "ex-smoker" for comparison. As recommended by MacMahon and Pugh (1967), a cause must be amenable to manipulation or modification. The definition of cause must be as specific as possible, in order to effectively avoid adverse effects on the human population. Moreover, this definition will most likely gain acceptance by other scientists and the public. For example, most people accept the polio vaccine since it is directed against a specific infectious agent. In the prevention of skin cancer among paraquat manufacturers, if one defines the cause as the entire manufacturing process, then one cannot take any preventive action, other than wiping out the whole process. However, since our study pointed out that skin cancer was closely related to only the crystallization and centrifugation processes, (Wang et al., 1987), the industry found it acceptable to simply enclose these two processes. Still, it would have been even more helpful to pinpoint the main responsible agent and elucidate the pathophysiology, e.g., link the exposure of bipyridyl or its isomers to skin cancer (Wang et al., 1987; Jee et al., 1995). Then, we could have implemented preventive actions against exposure to bipyridyl or its isomers in other non-paraquat manufacturing processes. In the nineteenth century, doctors noticed that a considerable number of chimney sweepers developed scrotal cancer. What form of prevention could be implemented? Completely outlawing chimney sweeping was certainly not feasible. However, if one could demonstrate that a specific


agent inside the chimney produced scrotal cancer, then one could prevent scrotal cancer by removing the carcinogen while still preserving the job. Furthermore, this knowledge could then be applied elsewhere. Take another example: If smoking-related cancer is caused by the specific content of tar inside the smoke of a burning cigarette, then the tobacco industry may more easily preserve their market, by simply selling cigarettes with a lower content of such carcinogens. Sufficient vs. necessary cause Causal concepts can be further examined in two ways: sufficient cause and necessary cause. 1. Sufficient cause In medicine or public health, several factors or component causes generally act together to produce an effect. In only a few cases, is there only one component cause, such as death by beheading. The minimum combination of different component causes, which act together or in sequence, to produce the effect, is called a sufficient cause. For example, a sufficient cause for contracting AIDS (acquired immune deficiency syndrome) involves an infection by HIV (human immunodeficiency virus), lack of immunity to the HIV virus, adequate induction time, and many other genetic and pathologic factors. Moreover, different combinations of component causes may produce the same effect. Rothman (1976) proposed a model of component causes to express that an effect can be produced by different mechanisms, as shown in Figure 4.1. 2. Necessary cause A necessary cause is a component cause or agent, which is always required to produce the effect. For example, mycobacterium tuberculosis is a necessary cause in producing pulmonary tuberculosis. Exposure to lead source(s) is a necessary cause for lead poisoning, etc.

Chapter 4

Sufficient cause I

Figure 4.1

Sufficient cause II

Causal inference and decision 61

Sufficient cause III

There are three different sufficient causes that can produce the effect (hypothetical disease). Factor A may be a necessary cause for the effect (modified from Rothman, 1976).

However, a necessary cause itself may not be sufficient to produce the effect. For example, exposure to HIV virus is a necessary cause to induce AIDS. Yet, only exposure to HIV will not be sufficient to produce AIDS. Other component causes are required, such as the lack of immunity to the HIV virus, a wound at the exposed site, etc. For sufficient causes, which component cause or factor is the most important for our concerns of treatment and prevention? If the necessary component is difficult to remove, then the answer usually depends on which component cause is more feasibly removed or replaced. In fact, the least frequently present component cause or factor may be more easily removed. For example, to prevent asbestos-related mesothelioma and lung cancer among community residents, Chang et al. (1999) conducted an environmental survey of 41 asbestos factories throughout Taiwan. They found that five factories were responsible for three-fourths of the projected cases of lung cancer and mesothelioma. Thus, the EPA (Environmental Protection Agency) of Taiwan tried to first relocate and improve control in these five factories. Similarly, for the prevention of AIDS, HIV-infected case identification and counseling guidance are generally more feasible in a community like Taiwan, where the HIV incidence rate is still low. However, once the incidence rate grews higher, such as that of Thailand or

62


Uganda in early 1990's, a general promotion of the use of condoms may be more feasible and effective. 4.2

Proposed criteria for causal decisions

One also needs to examine some proposed rules for the consideration of causal criteria (Yerushalmy and Palmer, 1959; Hill 1953, 1965; Susser 1977, 1986; Evans 1978). Although agreeing on a few common principles, such as consistency and correct temporality, different authors have proposed and emphasized different criteria. From a refutational point of view, proposing necessary criteria can reduce the difficulty of determining causality, as such criteria will allow one to rule out other possible causal relationships. Thus, I have tried to classify causal criteria into categories of necessity: necessary, quasi-necessary and other. 4.2.1 Necessary criteria In theory, there are two necessary criteria for causality: temporality and consistency. By definition, a cause should always precede its effect, and a universal law of nature should remain valid in any place, time, condition or setting. However, in any refutation attempt, one always invokes auxiliary hypotheses that may not always be correct, such as measurement accuracy and sensitivity. In epidemiological research, in which one can only observe a human population, one invokes an even greater number of auxiliary hypotheses. With so many additional assumptions involved, obtaining consistency is often difficult. As a result, the criterion of consistency is only a quasi-necessary one. The characteristics of a quasi-necessary criteria will be discussed in the next section, 4.2.2. Temporality is a necessary criterion for determining causal relationships. If one demonstrates that the effect precedes the cause, then the latter can at most be considered an aggravating factor rather than the main cause. To apply this criterion in practice, one must also know the minimal induction time and maximal latency period for the cause to produce

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the effect. For example, in cases of HIV infection, Person B could not have transmitted the HIV virus to Person A, if A and B's first sexual exposure was just one day prior to A's HIV blood test. The assumed induction time for HIV infection is simply too short. Similarly, one would not attribute Person A's recent sero-conversion of HIV to an exposure occurring 5 years earlier because this length of time exceeds the maximum latency period. Temporality is also a key factor in the diagnosis of occupational diseases. The European Commission (1994) has published an information guideline that clearly specifies the minimal induction time and maximal latency period for almost every occupational disease on the list, in order to avoid confusion and to decrease legal disputes. In fact, in my own work, I often use temporality as a necessary criterion and, subsequently, rule out about half of the cases who come to seek a diagnosis for occupational or environmental disease. The following examples illustrate this point. Case 1. Mediastinal tumor of an engineer in a nuclear power plant A 36 year-old male patient, an engineer in a nuclear power plant, was found to have a tumor mass located in the upper right mediastinum. Surgical removal of the tumor was performed immediately, and the histological pathology showed a granuloma. Since he had been working in an environment, which involved occasional exposure to ionizing radiation and beryllium dusts during the 6 years prior to admission, he demanded a determination of the work-relatedness of his illness. A retrospective review of all the serial chest X-ray films from the Veterans General Hospital (VGH), where the annual physical examinations were performed, revealed that the tumor mass was recognizable (about 0.3 cm) in the first film, which was taken during the pre-employment physical. Therefore, the claim of work-relatedness was denied because the lesion had existed well prior to any exposure. Furthermore, any aggravation of mediastinal granuloma by either ionizing radiation or beryllium has not been documented in previous research.


Case 2. Asthma and facial palsy among residents living near a petrochemical refinery Two patients with bronchial asthma and two patients with facial palsy were found in a community near a petrochemical refinery of Southern Taiwan. People were concerned that such illnesses might be related to air pollutants evaporating from VOCs (volatile organic compounds), contained in the wastewater discharge of the petrochemical plant. The company's plan to expand and build a fifth oil cracking plant further complicated the issue. Were these illnesses environmentally related? A detailed history taking revealed that the first patient developed asthma about 12 years earlier, but moved into the community only about 10 years ago. Similarly, the second patient began suffering from asthmatic attack approximately 8 years ago and had been regularly taking bronchodilators before moving into the community about 5 years earlier. According to the criterion of temporality, the VOCs contained in the wastewater of the plant could not have caused their asthma. Moreover, one needs more evidence to document whether the frequency and severity of asthmatic attack was aggravated by the VOCs evaporating from the wastewater. Both patients with facial palsy were in their mid-40s and suffered from the disease only on one side of their faces. A detailed search of the NIOSHTIC (National Institute of Occupation Safety and Health) database showed no previous report of any association between VOCs and facial palsy. The unilateral lesion also suggested a local etiology. Thus, an environmental association could not be established. Case 3. Brain tumor of a worker in a nuclear power plant A 47 year-old man came to my occupational clinic and asked if I could certify that exposure to ionizing radiation from working in a nuclear power plant had caused his recently diagnosed brain tumor. The patient had worked at the power plant for only 18 months. Doctors diagnosed his tumor as an astrocytoma and estimated it to be 1 kg at the time of

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craniotomy. In order to produce a tumor of 1 kg size, a single malignant cell would need to divide approximately 40 times, containing approximately 1012 cells ( =2 40 ). If the first malignant cell had, in fact, been produced by exposure to the ionizing radiation in the plant, the calculated doubling time of this tumor would have been less than 18/40 = 0.45 month. When I checked the most updated Medline database at the time he came to my clinic, the shortest doubling time of a brain tumor ever reported was about 1.5 months. Moreover, no previous research has ever reported that radiation-induced brain tumors develop within such a short period of induction time (Committee on the Biological Effects of Ionizing Radiations, BEIR V, 1990). Therefore, I could not certify that his tumor was work-related. 4.2.2 Quasi-necessary criteria For a causal criterion to be considered quasi-necessary, it is either a necessary criterion on theoretical grounds or is a confounder (an alternative explanation of the causal effect), which must be ruled out to better clarify causality. The validity of auxiliary hypotheses, invoked during one's refutation attempt, is not regarded as a necessary criterion, but is still important when evaluating causality. The quasi-necessary criteria are: 1. Consistency 2. Ruling out chance 3. Ruling out confounders (alternative explanations) 4. Coherence or consistency with other highly corroborated theories 4.2.2.1 Consistency The principle of consistency stipulates that a natural law should be universally true and that a causal relationship can be found under different times, places and settings. Strictly speaking, consistency must be a necessary criterion because if one has not invoked any false auxiliary hypotheses, the causal hypothesis should resist refutation under different settings. However, since one frequently must invoke less corroborated

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auxiliary hypotheses in human observational studies, one often ends up with a doubtful conclusion as to whether the primary causal hypothesis has, in fact, resisted refutation. For example, investigators performed an empirical study to evaluate the hypothesis that bipyridine and its isomers had caused the development of hyperpigmental and hyperkeratotic skin lesions among paraquat manufacturers. Because hyperpigmented spots or freckles are not uncommon among Caucasian or light-skinned people, researchers used the workers' close friends, of a similar age and same gender, as the non-exposed group. The results showed that a higher prevalence of freckles was not found among these workers. However, in this refutation attempt, investigators had invoked the auxiliary hypotheses of sensitive measurement, adequate induction time and at least minimal intensity of bipyridine exposure. Yet, given that the whole process was largely enclosed, the latter assumption might not have been true, i.e., workers were exposed to lower than minimal level of bipyridine (Cooper et ai, 1994). Thus, although investigators found that the hypothesis of the effects of bipyridine exposure lacked consistency, the negative findings may not necessarily refute the primary hypothesis but may in fact refute the auxiliary hypothesis. Similarly, up to 1986, only some studies of environmental tobacco smoke have shown a consistent positive association with lung cancer (Weiss, 1986). Since some studies tried to detect a small effect with low intensity of exposure and relatively large measurement error, firm conclusions could not be drawn from such studies on the effect of smoking. With potentially false auxiliary hypotheses, one should take care to determine if the data refute the primary hypothesis or, instead, refute the auxiliary hypothesis. Moreover, if we are not always looking for hypothesis that explains into detailed mechanism similar to natural law, then there can be one-time cause such as a turn-off of the electric switch producing light off. Thus, consistency may be theoretically a necessary criterion but is not easily maintained in the daily practice of epidemiological research.

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4.2.2.2 Ruling out chance For all observable phenomena, chance is always a potential alternative explanation. Consequently, one must perform some kind of statistical analysis in order to rule out chance to a certain degree. Based on the assumptions that the null hypothesis is true and that the sample was drawn in a random manner, frequentist statisticians often calculate p-value to rule out chance. However, the traditional p < 0.05 is an arbitrary decision rule set up to reject the null hypothesis. It does not necessarily mean that one has already eliminated the possibility of chance. Nor does it mean that the probability of obtaining the result is less than 0.05. Rather, it only indicates that if the null hypothesis is true and the sample is a random one, then the likelihood of obtaining a result like this one or a more extreme condition is less than 0.05. Since in observational studies, we simply assume that physical, social and behavioral processes by which people become exposed to different risk factors are close to randomization, it is not a real randomization (Greenland, 1990). Thus, it is usually more informative to write the confidence interval and exact p-value, as Rothman (1978) recommends. To better determine the extent in which chance plays a role, one should always consider the sample size of the study because p-value is also influenced by sample size. Even if the association is not strong, p-value will usually be small if the sample size of the study is large {e.g., more than 500 or 1000). Conversely, p-value is usually large if the sample size is very small {e.g., < 30). Therefore, if the sample size is large and, yet, has a large p-value (> 0.05), chance is likely the cause, and one can regard the study as a strong refutation of any association. If the sample size is moderate, and one obtains a very small p-value, e.g., < 0.01 or even smaller, then one may tentatively conclude that chance is not a probable cause and consider the study to be a failed refutation attempt of the proposed association. Nonetheless, with only a single study, one should refrain from overemphasizing the results. Finally, if the sample size is small, one should infer that no matter how small the p-value, chance cannot be ruled out as a causal factor (Miettinen, 1985a). Because of such an easy misconception on the interpretation calculating, experts in the field (Nurminen, 1997;

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Greenland, 1998) have proposed to take Bayesian viewpoints of likelihood ratio and posterior probability as an alternative. 4.2.2.3 Ruling out confounders (alternative explanations) Even if one rules out chance or displays a statistically significant association, one still cannot conclude the association to be causal. One must now consider whether there still remain any confounders or alternative hypotheses, which can explain the phenomena, and subsequently, attempt to refute such confounding. This criterion should not be confused with "specificity," (detailed in section 4.2.3.2) which was earlier proposed as a causal criterion (Hill, 1965), but is currently not considered to be necessary (Susser 1986; Weed 1986). As pointed out in Chapter 3, if all other alternative hypotheses are refuted, then one may claim that the hypothesis of interest is the one that best corresponds to fact. Otherwise, there are at least two equally valid hypotheses, which can explain the effect, i.e., confounding. One should avoid confounding right from the beginning, in the stage of study design. Since the confounder is a potential causal determinant of the outcome and is associated with the exposure of interest, one can conduct a literature search to find all other known causal factors of the effect. One should then control these factors by design or data analysis. For example, during the study for the cause of skin cancer among paraquat manufacturers, researchers asked each worker if they had ever been exposed to any known skin carcinogens such as radiotherapy, coal tars, pitch or cutting oils (Wang et ai, 1987). Since none of the 228 workers examined showed such exposures, the investigators ruled out these potential confounders. We shall return to the issue of confounding in Chapter 7. To evaluate any specific hypothesis, one should design a study (a refutation attempt) to critically test the hypothesis of interest and any equally corroborated alternative hypotheses. For example, if one observes an increased occurrence of lung cancer among people with yellow finger tips, (especially the 2nd and 3rd fingers), then one might propose a hypothesis that yellow fingertips cause lung cancer. However, there is the alternative hypothesis that smoking causes lung cancer. Thus, one should design a

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study to determine which one is more highly corroborated. In fact, recent studies have shown that yellow fingertips may also result from smoking. Furthermore, suppose that another study has demonstrated that non-smokers with yellow fingertips do not show an increase of lung cancer frequency. Such studies present a strong refutation attempt of the competing hypothesis that yellow fingertips cause lung cancer. Ruling out confounders does not conflict with the possibility of a multi-factorial hypothesis for a disease, in which a health effect may result from a variety of factors. Rather, this criterion stipulates that any alternative cause or hypothesis should not equally explain any single finding of an increased frequency of a disease. For example, while arsenic (Chen et al, 1988; Enterline et al, 1987; Hays 1997), asbestos (Selikoff et al, 1968; Stayner et al., 1996) and smoking (U.S. Department of Health, Education and Welfare, 1979) can all produce lung cancer, this criterion does not preclude a new agent such as BCME (bischloromethyl ether) from causing lung cancer (International Agency for Research on Cancer, 1987). However, if one finds evidence revealing that BCME is the cause of a specific occurrence of lung cancer; arsenic, asbestos, smoking or any other known lung carcinogens should not simultaneously explain this event. In order to corroborate the proposed hypothesis, one should rule out confounding from any alternative cause. In addition, if at least two different equally corroborated hypotheses exist, these two causal hypotheses may, in fact, act independently or synergistically to produce the effect. If current evidence cannot differentiate these two conditions, then one cannot draw any firm conclusions about the causal relationship. As a result, the fulfillment of this criterion is a quasi-necessary one. 4.2.2.4 Coherence The criterion of coherence stipulates that the hypothesis should be consistent with currently existing well-founded theories. If the hypothesis conflicts with common physical or chemical laws or theories, it is likely to

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be false. Of course, one cannot completely rule out the possibility that a new conjecture might be correct and that the status of any existing theory should be reconsidered. If this is the case, then a scientific revolution, so named by Kuhn (1970), may occur as the old paradigm is now being contested. Since such paradigm shifts rarely occur, coherence or consistency with current scientific knowledge must still be classified as quasi-necessary. 4.2.3 Other supportive criteria Some authors (Hill, 1965; Susser, 1977, 1986) have proposed other criteria, which are not necessary, but may help in determining causality from a Bayesian point of view. Namely, the existence of any of these criteria for a causal relationship may improve the subjective credibility of the hypothesis in causal decision. They are: 1. Strength of association 2. Specificity of association 3. Biological gradient or dose-response relationship 4. Biological plausibility 4.2.3.1 Strength of association Strength of association means that the magnitude of effect such as rate difference or rate ratio should be large or strong between the exposed and non-exposed. This criterion must not be confused with statistical association, such as p-value. If the exposure factor produces a very large effect, such as a rate ratio > 5, then the likelihood of a causal relationship may be high, since other known causal factor(s) usually cannot completely explain such a large magnitude. For example, suppose that asbestos workers were found to have a rate ratio of 5 for lung cancer mortality, compared with the general population who are presumed to have very low (or negligible) asbestos exposure. Further, assume that prevalence rates for smoking among asbestos workers and the general population were 90% and

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50%, respectively. This observation raises the concern that the increase of lung cancer among asbestos workers might be completely due to a high prevalence rate of smoking. If the rate ratio for lung cancer among smokers vs. nonsmokers is equal to 10, smoking alone may have caused the workers to develop lung cancer: Let Ro denote the incidence rate of lung cancer for the nonsmoking population unexposed to asbestos, and thus, lOR^ denotes that of smokers unexposed to asbestos. Assuming that asbestos does not cause lung cancer, then, the rate ratio of lung cancer for asbestos workers vs. that for the general population will be: (10R„)(90%) + Ro( 1 -90%)

9.1 Ro =

(10Ro)(50%) + Ro(l-50%)

=1.65 5.5 Ro

The rate ratio of 1.65, in which smoking is the only causal factor, cannot explain the rate ratio of 5 found in the original study. Thus, the likelihood of causal association between asbestos and lung cancer may be high. However, if the strength of association is not strong, say, a rate ratio of less than 2 or 1.5, then one may be concerned that an unknown factor, such as smoking, may confound the effect, and the causal hypothesis may not be true. However, strength of association is not a necessary criterion because even with a weak association, the relationship might still be causal. When this criterion conflicts with other criteria, how does one make a decision? There is no easy answer to this question. Instead, one must consider all the evidence and all the necessary and quasi-necessary criteria before any conclusion can be drawn. Earlier last century, Karl Pearson and Almroth Wright held conflicting opinions about whether a typhoid fever vaccine should be adopted as a routine inoculation in the army. Pearson compared the incidence and case fatality rates among the inoculated and non-inoculated. He found that the strength of association was not as high as that of smallpox vaccine, and accordingly, he opposed inoculation.

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Wright counted only autopsy cases, whose diagnoses were more definite, and showed that the different trials showed a consistent finding of 5 times more protection from typhoid mortality, which led him to support an extensive vaccination. After further studies, vaccination against typhoid was found to be effective (Susser, 1977), as Wright had believed. 4.2.3.2 Specificity of association This criterion suggests that the more specific a causal relationship is, the more likely that such an association exists. However, it is not a necessary criterion because there are already several examples demonstrating multiple causes for the same disease, even when a specific association exists between one exposure and the disease. Furthermore, one exposure factor can simultaneously produce many different diseases. For example, while exposure to asbestos, smoking or arsenic can individually produce lung cancer; asbestos can also cause mesothelioma and pleural plaque; smoking can also result in bladder cancer, chronic obstructive pulmonary disease, ischemic heart disease, etc.; and arsenic can produce bladder and liver cancer, as well. In fact, when the first committee report on smoking and health (U.S. Public Health Service, 1964) was published in 1961, Berkson, an eminent scientist, proposed that the causal hypothesis was not tenable because of the lack of specificity between smoking and lung cancer. However, it is now widely accepted that this causal hypothesis is highly corroborated and that Berkson's opinion, solely based on this criterion, was not a wise one. If specificity of association is unnecessary, why does one still consider it to be evidence supporting a causal hypothesis? By establishing a specific association between the agent and effect, one has successfully refuted other alternative hypotheses. Thus, specificity of association fulfills the quasi-necessary criterion of ruling out confounders and supports causality. 4.2.3.3 Biological gradient or dose-response relationship This criterion is derived from the rule of concomitant variation from

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Mill's rules of induction (Chapter 3). However, such a biological gradient may simply result from confounding. For example, the more yellow stained a person's finger tips are, the more likely he/she is to develop lung cancer, yet this is because smoking produces both yellow fingers and lung cancer in a dose-response manner. Moreover, observation of such a gradient generally relies on many auxiliary hypotheses. Thus, such a relationship may not be easily demonstrated in empirical studies and, therefore it is not a necessary criterion. To quantify dosage, one must clarify the detailed effect and the mechanism of effect to be produced. Therefore, an understanding of detailed PB-PK (physiologically-based pharmacokinetic) model and pathophysiologic mechanism is also helpful. In addition, the following factors must be considered in such a relationship: 1.

2. 3. 4.

5.

Intensity or concentration of exposure: For example, how many cigarettes are smoked per day, and what is the content of tar or any specific carcinogen such as bezo(a)pyrene? Similar questions should also be applied to alcohol drinking, occupational and environmental exposures, etc. Duration of exposure: For example, how long has the person been smoking? Onset of the first exposure: Is the requirement of temporality, i.e., minimal induction time and maximum latency period fulfilled? Dose rate: What was the frequency and dosage of each exposure and what was the portal of entry? Generally speaking, a high dose rate (e.g., ionizing radiation) is usually more harmful to the human body as the body's time for repair is decreased. To clarify the actual dose, one also needs to know its application method and the absorption, distribution or even excretion mechanism. For example, does the person always inhale the smoke? Or does he quickly blow it away? Host factor: The genetic susceptibility may be different for different persons. Gender, age, ethnicity and any other lifestyle factors may interact with the exposure in affecting health.

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6.

Type of dose-response relationship: Is the relationship linear or quadratic? Is there any threshold?

Because of all the complicated mechanisms and auxiliary hypotheses involved, one is frequently unable to observe a "typical" dose response relationship. If such a relationship does exist and there is no other alternative hypothesis that can explain the phenomenon, then the criterion of biological gradient may support a causal decision. This relationship, however, is not a necessary criterion. 4.2.3.4 Biological plausibility This criterion means that current biological knowledge, i.e., evidence from animal experiments or cellular and/or molecular biological research, supports the causal hypothesis. However, biological plausibility is not a necessary criterion because of inter-species differences between humans and animals. For example, at the end of the nineteenth century, when many dyestuff workers in Germany developed bladder cancer, many suspected that beta-naphthylamine might be carcinogenic,. In the 1910s, a similar tragedy occurred among dyestuff workers in the U.K. In 1921, the ILO (International Labor Office) announced beta-naphthylamine to be a bladder carcinogen without any evidence from animal models. Bladder cancer in animal experiments was not successfully induced by beta-naphthylamine until 1937, when dogs were used as the experimental model. Similar results were shown for some human carcinogens, such as benzene and arsenic. Thus, a hypothesis that fulfills this criterion can be considered as supportive evidence for a causal decision but is not absolutely necessary. Despite having discussed the criteria for causality, one still needs some kind of formal procedure or mechanism that can be applied to decision-making in public health or medicine. Such a procedure may prevent important decisions made solely based on one expert's opinion. In general, an expert committee, arriving upon some consensus under a refutational or critical attitude, may be helpful to avoid personal bias.

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Objective knowledge and consensus method

In scientific research, one performs conjectures and refutations in the effort to find the objective laws of nature. Popper termed such a collection of natural laws the "third world." As a Christian, I believe that God created the laws of our natural world. Still, no matter how these laws came into being, one should regard their discovery as based on a subjective understanding and on the method of conjectures and refutations. If a scientist can take a refutational attitude, then he or she may rise above his or her own personal biases in the discovery process, and find that the hypotheses left unrefuted are the closest approximations to the objective natural law. If everyone in a committee maintains such an attitude, then after full communication of the possible hypotheses and evidence, the group may less likely make false conclusions or recommendations. This group of experts or persons should have no conflict of interest in making such a decision and should be free from external pressure and influence. In addition to medicine and public health, such a designated consensus method has been put into practice in the jury practice of Western countries such as the U.S. and the U.K. (Fink, 1984). Specifically, every juror selected must be unrelated to both sides, the plaintiff and the defendant. After comprehensive and critical communication of all hypotheses and evidences, the jury as a group is then asked to reach a consensus conclusion. Even though every juror still makes a subjective judgment, the whole group is expected to reach a relatively objective decision. Although a critical and inter-subjective decision may still be fallacious (for example, ancient people used to believe that the sun revolves the earth), it is still the least fallible, if everyone keeps a refutational attitude, avoids outside influences and establishes a comprehensive communication. In public health and medicine, a great deal of knowledge is specialized. Thus, the relevant experts should examine the issue at hand with a critical and refutational attitude. The likelihood of reaching a fallacious decision will generally be lower, if the decision is made by a group rather than by a

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single expert. Therefore, causal decisions should be carried out by a committee of experts who understand the issue at hand. This can save time in both the communication and consensus procedure. For example, in the U.S., an advisory committee to the Surgeon General was set up to make the key decisions on the issue of smoking and health (U. S. Public Health Service, 1964). In the primitive stages of science, many different hypotheses may coexist and they are often contradictory to each other. However, the process of conjectures and refutations can eliminate some of them. The one hypothesis, which resists falsification and is recognized by a group of experts engaging in a comprehensive communication and refutational critique, will be closest to the truth for the present time being. As new evidence appears, the expert committee may revise their consensus opinion periodically to make a more informed conclusion and decision. 4.4

Summary

While the scientific research process of conjecture and refutation continues, we in public health and medicine should take action by making causal decisions to prevent morbidity and/or mortality among people. This decision should be made with a critical or refutational attitude. To facilitate such a decision, I have classified causal criteria into three levels: necessary, quasi-necessary and other. First, correct temporality is the only necessary criterion for any cause. In other words, the response or effect of exposure must occur after minimal induction time and within maximum latency period. Second, consistency should exist under different times, places and settings of observation, as long as no false auxiliary hypotheses are invoked in the study. One should also rule out chance and other alternative hypotheses to a certain extent, and the hypothesis should be coherent with current, well-founded chemical or physical laws. The category of "other" contains some criteria, which are not completely necessary, but their presence can be supportive for causal decision-making, i.e., strength and specificity of association, biological gradient and biological plausibility. To reduce the bias involved

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in causal decision-making of medicine and public health, I recommend inviting a committee of experts to critically judge all available hypotheses and evidence. After a comprehensive discussion, they can attempt to reach a consensus and make a decision.


Quiz of Chapter 4 Please write down the probability (%) that the assertion is true. You will be scored according to the credibility of your subjective judgment.

Score

% 1. The only necessary criterion of causality is a correct temporal sequence. 2. Cause should be defined as something amendable. 3. HIV (human immuno-deficiency virus) is a sufficient cause for AIDS (acquired immuno-deficiency syndrome). 4. We cannot attribute the cause of a current case of AIDS to the patient's sexual contact with an infectious source occurring 3 days ago. 5. When the sample size is large (e.g. >1000), then a p-value > 0.10 is a strong refutation. 6. If the sample size is small (e.g. < 30), then chance cannot be completely ruled out. 7. Strictly speaking, the principle of consistency must be a necessary causal criterion. However, since one frequently has to use less corroborated auxiliary hypotheses in human observational studies, one often ends up with a doubtful conclusion that one has not yet refuted the primary causal hypothesis. 8. If the strength of association is low, e.g., a rate ratio of 1.5, then we can conclude that the association is not causal. 9. If one finds a dose-response relationship between an exposure and a disease, then one has established a causal association. 10. To obtain an objective decision on causality, an expert

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committee should take a refutational attitude and engage in full and comprehensive communication.

Answers: (1) T (2) T (3) F (4) T (5) T (6) T (7) T (8) F (9) F (10) T


Chapter 5 Basic Principles of Measurement 5.1 5.2 5.3

What is measurement? Why does one perform measurement? How does one measure? 5.3.1 Measurement in socio-behavioral sciences 5.4 Accuracy of measurement: validity and reliability 5.5 Scales of measurement 5.5.1 Nominal scale: A scale of qualitative measurement 5.5.2 Ordinal scale: A scale of semi-quantitative measurement 5.5.3 Interval scale: A quantitative measurement with or without an absolute zero starting point 5.5.4 Ratio scale: A quantitative measurement with an absolute zero starting point 5.6 Common evaluation method in medical diagnostic tests 5.7 Validity and reliability of physico-chemical, biological and socio-behavioral measurements from a refutationist's point of view 5.7.1 Measurement of chemicals in the environment or inside the human body 5.7.2 Conceptualization of exposure dose and its measurement in occupational and environmental medicine 5.7.3 Validity and reliability on socio-behavioral measurement 5.8 How to perform accurate measurement by questionnaire 5.8.1 Construction of a questionnaire 5.8.2 Interview procedures 5.9 Summary Introduction Observations and measurements of phenomena are a necessary part of the scientific research process. This is not surprising since all scientific research involves empirically testing hypotheses. Yet, it is usually not

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possible to make direct observations and measurements of one's primary hypothesis, especially in human observational studies. Instead, one usually deduces statements from the primary hypothesis that can be observed and measured. One then enters the field to collect the data. And finally summarizes the data by use of statistical tools to attempt to refute the various hypotheses. Since in any empirical study, one always invokes the assumption that measurements made are sufficiently accurate and sensitive, one should carefully select a valid measurement method to be used in one's study. Even in public health decision-making, which involves more than just simply testing hypotheses, people demand data from previous experiences or observations in order to make rational judgments. Therefore, measurement, a term I use to denote both observation and measurement, is one of the central issues in epidemiological research. However, most books on epidemiological methods regard measurement as an issue not unique to epidemiology and thus, decide not to discuss it (Rothman and Greenland 1998; Miettinen 1985a; Kupper et al, 1982). Others simply discuss measurement error and some of its practical aspects (Kelsey et al., 1996). In contrast, I have chosen to explore its theoretical principles and practical applications. This chapter will attempt to clarify the concept of measurement, illustrate how to make accurate measurements, explain how to set up scales of measurement and then apply such principles in the common evaluation method of medical diagnostic procedures and environmental chemical analyses. Moreover, the common validity and reliability measures in socio-behavioral science will also be discussed and explained, followed by some practical advice for the construction of questionnaires and interview procedures. 5.1

What is measurement? As Lord Kelvin pointed out: "I often say that when you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it, when you cannot express it in

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numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts advanced to the stage of science, whatever the matter may be." (Michell, 1990) The classical definition of measurement is to express a concept or characteristic of a group of objects in terms of classes (qualitative, categorical or nominal) or numbers (quantitative). This definition is very intuitive and straightforward for physical, chemical or biological objects, in which one simply finds a gold standard for comparison to obtain the class or number. It may not be sufficient, however, for the measurement of subjective preference (utility), such as health-related quality of life (HRQL) in public health or any concept involving multidimensional aspects, such as attitude, personality or cognitive ability in psychology. Thanks to the development of operationalism and representationism, Stevens (1946) has expanded the definition of measurement to "the assignment of numerals to objects or events according to rules." Thus, a measurement can be a corresponding set of operations, as long as they are precisely defined and consistently performed to assign numbers to objects. 5.2

Why does one perform measurement?

There are two major reasons for measurement. First, one attempts to form a clearer definition of the concept or object to gain a more profound understanding and to be able to perform further operations or mathematical manipulation. For example, one may want to know the current blood lead level of newborns in Taipei (Hwang and Wang, 1990). This question is descriptive, asking how one measures blood lead content and how is it distributed among newborns of Taipei. First, one must decide whether one wants to use atomic absorption spectrometry, anodic stripping voltammetry or some other method to determine blood lead level. Moreover, one must also decide from whom and how one should take blood samples. The other major reason for measurement is to empirically test a hypothesis. For example, one may want to test the hypothesis that smoking causes lung cancer. In this instance, one must consider the definitions of


smoking and lung cancer, as well as conduct actual measurements in a population. Specifically, one must decide whether to include only cases with histopathologic diagnosis or include even those cases with merely clinical evidence. Moreover, one should also measure other determinants of lung cancer, such as exposure to asbestos or arsenic. Otherwise, one will be unable to differentiate the effect of smoking from other alternative causes, resulting in confounding. Thus, a causal study always involves measurements of the major determinant and outcome of interest, as well as other determinants of outcome. Let us look at another example: an investigator wants to evaluate the preventive efficacy of taking AZT (zidovudine) after needlestick injury of HIV (human immuno-deficiency virus) contaminated blood. First, he must at least define and measure a case of such an injury, the dose schedule of taking AZT, seroconversion of HIV and other determinants of HIV infection, such as personal sexual practice, blood transfusion, etc. In fact, in the beginning of the process of conjectures and refutations (see Figure 2.1), when one attempts to propose hypotheses, it is implied that one looks for something to be measured and falsified empirically. If one cannot directly conduct measurement under the primary hypothesis, one then deduces statements that can be measured and ultimately, tested. In epidemiology, one may try to perform measurements on specific rates {e.g., lung cancer mortality rate), ratios (e.g., sex ratio) from the population under study. Moreover, when one summarizes the results in the data analysis stage with statistical methods, one may also obtain measurements of a causal effect, such as rate ratio or rate difference. Thus, measurement is the basic tool in empirical scientific research, whether it is causal or simply descriptive. 5.3

How does one measure?

Need of a gold standard As mentioned in our definition, measurement involves operational rules to express certain concepts or characteristics by different numbers or scales. For concepts that are less abstract, such as length, weight, volume, angle, etc., one simply defines the concept and establishes a gold standard for


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comparison. Then, one can measure the object by comparing it with the gold standard. Essentially, most measurements are comparative. For example, if one wants to measure the body height of a person, one must define height as the length from the top of the head to the sole of the foot, with the person standing in an erect posture. Then, one uses a large straight ruler (for comparison) to determine the height expressed in a certain unit, e.g., centimeter (cm). Because the height of an adult slightly decreases in the afternoon after working in an erect position all day (especially after heavy lifting), one may stipulate that measurements be made in the morning for consistency and accuracy. Although such a minor change {e.g., a decrease of 0.5-lcm) in measurement of height may not usually influence one's conclusion, one must still be very careful in certain occasions. Controlling all determinants of a measurement For example, one unpublished study in Taiwan tried to determine the change of body weight in a pregnant woman during her 1st, 2nd and 3rd trimesters. The results showed that there was an average loss of 0.6 kg of body weight during the 1st trimester, as compared with the early 2nd trimester. Why did a pregnant woman's weight decrease during the 1st trimester? It turned out that the investigator did not standardize his weighing operation and, consequently, maintained a systematic bias towards a heavier weight in the 1st trimester. Specifically, during the 1st prenatal visit, pregnant women were usually weighed after breakfast with a full urinary bladder. During the second prenatal visit, in the early 2nd trimester, women came in for blood tests and were often weighed with an empty stomach and bladder. As a result, the 0.6 kg decrease of body weight during the 1sl trimester was more likely due to weighing after a meal and with a full bladder during the first examination. This example illustrates the importance of understanding and controlling the determinants of measurement, and how they should explicitly be clarified in a document for comparison and future reference. Such a document is similar to the Standard Operation Procedure (SOP) of a manufacturing process, which should be carefully followed when making actual measurements.


Assisted instruments for interview When one conducts an interview, one can help subjects provide more accurate answers on their health behavior by providing devices for comparison. Let us look at another common example of using a questionnaire survey to measure the amount of alcohol intake per day. Clinicians are usually skeptical about the accuracy of measurements on alcohol intake obtained from clinical interviews. However, if one can provide a comprehensive collection of colored photographs of all brands of beers, wines and liquors, as well as different types of cups for the person to identify and determine, then one may obtain more accurate information on alcohol consumption. The photographs or assisted instruments provide the needed gold standard for comparison. Although such instruments may help to improve data collection from interviews, one is still limited by the subject's ability to measure the objects in question. For example, in a study to measure occupational exposures among workers in Taiwan, the workers were asked if they were exposed to any specific chemicals or hazards. Since most people in Taiwan were not aware of the chemicals in their work environments in 1980's (Wang, 1991), they could only identify occupational hazards through sensation. Accordingly, researchers found that the most extensive hazard at workplaces was noise, and less than 5% of workers could provide any specific chemical names. Thus, a questionnaire interview is always limited by the subject's cooperation and his/her ability to measure the items in question. 5.3.1 Measurements in socio-behavioral science In socio-behavioral science, measurement is further complicated by the need to measure the unobservable or latent concepts composed of several dimensions and domains. Under this condition, investigators usually formulate some construct or theory to express the concept and then, measure it from different dimensions and domains. After proper summarization procedures through statistical analysis, one tests the validity of the construct or theory with the results of one's measurements. Please refer to Figure 5.1. For example, the measurement of HRQL (health-related quality of life)


87

generally involves at least physical, psychological and social domains (WHO, 1948). Each domain can be measured in two dimensions: 1) an objective assessment of functioning or health status, 2) a subjective perception of health (Patrick and Erickson 1993, Testa and Simonson 1996). Since the construct of HRQL cannot be observed directly, one is actually measuring different components of HRQL, in terms of these three domains and two dimensions. The results are then summarized to yield a scaled score. This final score should be an accurate quantitative measurement of the concept of HRQL, if one has chosen the proper items and scales of measurement. The WHOQOL (WHO quality of life) generic questionnaires (WHO, 1995, 1998a, 1998b) has required all participating countries to conduct studies for descriptors first and adds cultural specific questions. Both the exploratory and confirmatory factor analyses show a consistent result of following four domains: physical, psychological, social relation, and environment. Thus, I recommend its use for general assessment of health profile and international comparison. Take another example of measuring aggressiveness in personality. One may begin by using personality theory to give this subjective characteristic an operational definition from several dimensions, followed by selection of proper measurement items and scales, as shown in Figure 5.1. After collection of the data, one still needs to summarize the different items and scales statistically to obtain results that can validate or test the original construct. A test of the theoretical construct By itself, a socio-behavioral measurement is a test of the original theoretical construct. It follows, then, that one examines the measurements to determine the existence of such a construct or theory. Moreover, one must remain wary of the fact that these measurements are subject to potential errors themselves. Thus, although one's success in refuting a hypothesis may be attributable to a false construct or theory, in some cases, it is a result of measurement errors (Blalock, 1982). Although the same statement is equally applicable to the natural sciences, one must seriously consider measurement error when dealing with measurement in the social sciences because they are based on relatively more abstract matters and subjective judgments, and rarely


remain consistent in different times, places and change of social settings.

Conceptualize Form theoretical construct (e.g., subjective quality of life)

-> into several dimensions or domains, (e.g., physical, mental)

Attempt to falsify the theoretical construct by empirically testing if it can be consistently measured.

Select suitable items to be measured in each domain.

Decide on the measurement scale for each item and weight summarization.

Collect data. Summarize the score according to the original construct.

Figure 5.1

Process of conceptualization and measurement in socio-behavioral science.

Selection of a sensitive measurement In the daily practice of public health and medicine, most measurements are relatively straightforward. One simply needs to carefully define the gold standard used for comparison and control all determinants of one's measurement. In addition, if there are several ways to make equally valid measurements, one should select the most sensitive method. For example, in our study to detect the health effect of lead exposure among kindergarten children, we found IQ (Intelligent quotient) to be more sensitive than any neurophysiological or hematological measurement, if the blood lead was below 25 ug/dl. Thus, we selected IQ as the primary indicator of health effect


89

on kindergarten children when studying possible exposure from a neighboring lead recycling factory (Wang et al., 1992; Soong et al., 1999). Similarly, since nerve conduction velocity (NCV) is usually more sensitive than clinically overt symptoms of bilateral weakness of upper and lower extremities, we used NCV in our study to detect sub-clinical polyneuropathy under different levels of n-hexane exposure (Wang et al., 1986). Throughout all kinds of measurement, one must always compare the objects one sets out to measure with a set of standards. The gold standard chosen should correspond best to the concept or fact and should be widely accepted by the scientific community. Otherwise, the accuracy of our measurement will be doubted and will be difficult to compare with other investigators' results. For example, the measurement of length is based on rulers reproduced from the ultimate standard metric ruler made from platinum-iridium alloy. In 1960, the 11th General Conference on Weights and Measures defined the standard meter to be equal to 1,650,763.73 wavelengths of orange-red radiation in a vacuum of krypton 86. Development of a gold standard In developing a new method of measurement, how does one establish a gold standard? Reaching a consensus by expert committee, as recommended in Chapter 4 for causal decision-making, is still probably the wisest choice. This expert committee must attempt to develop a gold standard, which easily performs measurement and shows consistent results under various times, places and settings. To fulfill these requirements, the measurement method must be clearly specified and all its determinants must be easily characterized and controlled in practice. With a refutational attitude and after full communication, experts may not find it too hard to reach a consensus. In general, most standard classifications or measurement systems recommended by the ISO (International Organization of Standardization), WHO or ILO (International Labor Office) are produced in this manner and are widely accepted by the scientific community. For example, the widely used International Classification of Disease (ICD) is a product of the consensus of WHO experts, who continually revise their decision every ten years.

90

5.4


Accuracy of measurement: Validity and reliability

Target shooting as an illustration The goal of measurement is to achieve high accuracy, i.e., high validity (or low systematic error) and high reliability (or low random error). If the method or instrument can actually measure what it claims to measure, then it is a valid method. If a measurement yields values that are consistent or their distributions remain close to each other, then it is reliable or "precise" as described by chemists. Of course, one always demands measurements to be both valid and reliable, namely, to have the least possible systematic and random errors (Carmines and Zeller, 1979). This concept can be illustrated by the example of target shooting. When a person shoots a clearly marked target with a gun, each bullet hits the target paper and produces a hole. After many shots, an examination of the target paper may show four types of distribution, as illustrated in Figure 5.2. The distribution of type A shows a cluster of holes near the target center, which indicates that most bullets hit very close to the target, namely, both a small systematic error and a small random error. The shots are all very accurate, i.e., valid and reliable. Type B shows a cluster of holes near the side of the target paper, which indicates a small random error but there seems to be a systematic error which directs the bullet toward the side of target instead of the center. In other words, the target line of the gun needs to be readjusted or the standard used for comparison during the measurement seems to be biased. Type C shows an even distribution of bullet holes without any clustering. This indicates a big random error (low reliability) but, seemingly, no systematic error. Type D shows no cluster but holes distributed widely over only the upper part of the target paper. This indicates a systematic error of shifting the central target to the upper portion and a large random error. If under some extreme cases, a large proportion of bullets do not produce any holes on the target paper, then one must also consider that such a large error probably also results from a combination of big systematic and random errors. Under this circumstance, one must reconsider the definition of the gold

Chapters

A

B

C

Principles of measurement

91

D

target value Type A: excellent accuracy Type B: high reliability with a low validity Type C: low reliability with a possible high validity Type D: both poor validity and poor reliability Figure 5.2 Four types of distribution of gun shots on a target paper. An accurate measurement requires high validity (or low systematic error) and high reliability (or low random error). Although systematic error appears to be smaller than random error in this figure, they are not necessarily related in this manner.

standard used in the measurement or suspect the existence and measurability of the object in question. In statistical terms, one can see how error is a combination of both random and systematic errors, or a function of variance and bias, respectively. People usually define the total variance of an estimator to be the mean squared error (MSE) of the estimator, if it is obtained from a random sample. It can be

92


derived that the MSE of an estimator is equal to the sum of variance (i.e. square of random error) plus the square of systematic error (Anderson et al., 1980). Let 9 be the target value, 9 be the estimator from a random sample, bias (6 ) be the systematic error of the estimator, and Var (9 ) be the total variance of 6 . bias(0 ) = E(0 )- 9 Var(0) = E[0 -E(0)] 2 =

E(9f-[E(9)f

MSE(

Interview Facts: subjects' memory, Subjects' technique judgment or -> -»ycoand/or operation questionnaire measurement design Perceived health or -> Facts: subjects' preference—> quality of life and/or subjective perception Lifestyle and occupational exposure data

->

Objective health data-» Facts: doctor's, nurse's measurement or -» medical laboratory and records instrumental measurement, subjects' complaints

coding, input computer data

abstracted

Figure 5.4 Determinants of measurement accuracy on health-related data obtained by questionnaire administered through self-report or interview. The flow directions of different kinds of data show the determinants or potential confounders that may lead to errors of the final codes of files.

5.9

Summary

All empirical science involves measurement, and all refutation attempts invoke the auxiliary hypothesis that their measurements are accurate and sensitive enough to detect an effect. Thus measurement is one of the central issues in scientific research. In most biomedical measurement, one can obtain accurate data simply by defining a widely accepted gold standard for comparison and controlling all determinants during the actual measurement. However, in socio-behavioral science one must first conceptualize the

Chapter 5 Principles of measurement 117

theoretical construct and find an operational procedure to measure it. The data are then summarized statistically and feedback to test the original construct. Accuracy of measurement can be achieved through minimizing systematic error and random error (high validity and reliability). In clinical medicine, a diagnostic test is usually evaluated by the indices of sensitivity and specificity, which is based on the assumption that cases and normal persons are randomly drawn. To apply such a test on clinical grounds for positive predictive value, one also needs to know the total prevalence of a particular disease. Dose in environmental and occupational exposure should be sampled and measured according to the pathophysiology and PB-PK model for a meaningful interpretation. In the actual measurement of dose at the target organ, one often needs to invoke some assumptions that may not be highly corroborated. To obtain accurate information by questionnaire, one must be clear and straightforward and insert some dummy questions, as well as develop standardized interview procedures. Nonetheless, the information collected by questionnaire is always limited by the subjects' cooperation and ability to measure the items in question.


Quiz of Chapter 5 Please write down the probability (%) that the assertion is true. You will be scored according to the credibility of your subjective judgment. Score

% 1. An accurate and sensitive measurement is always one of the auxiliary hypotheses that one invokes during a refutation attempt. 2. Since questionnaires and interviews ask subjects to measure something by themselves, investigators are always limited by the subjects' cooperation and ability to measure these items. 3. Throughout all kinds of measurement, one always needs to compare a set of gold standards with the objects one sets out to measure. 4. For ordinal scales, one should try to find or set up a relatively objective standard for comparison, which makes each ordinal scale more easily identifiable. 5. An interval scale has an absolute 0 starting point. 6. A reduction of ratio-scale variable to an ordinal or nominal variable is prohibited because there will be some loss of information. 7. If a diagnostic test happens to be related to the severity of a patient, then the sensitivity result obtained from a medical center is usually an overestimate if one wants to apply it in a community hospital. 8. In an interview questionnaire, standardization is particularly important to avoid any systematic error if the interviewer is also asked to measure some of the subjects' responses.

Chapter 5 Principles of measurement 119

9. Measurement is one of the central issues in scientific research. 10. A socio-behavioral measurement is by itself a test of the original theoretical construct. Thus, a successful falsification in an empirical study can be attributed to either error in measurement or the substantive theory.

Answers: (1) T (2) T (3) T (4) T (5) F (6) F (7) T (8) T (9) T (10) T


Chapter 6 Basic Measurements in Epidemiological Research 6.1 6.2

6.3

6.4 6.5

6.6

6.7

Evolving trends in epidemiological measurement Basic measurements of outcome in epidemiology 6.2.1 Outcome measurement: Counting of events and states, rate, proportion and ratio 6.2.2 Determinants of measurement indices or parameters Incidence rate, cumulative incidence rate, risk and their determinants 6.3.1 Incidence rate and density 6.3.2 Cumulative incidence rate(CIR) and risk 6.3.3 Determinants of incidence rate (IR) Prevalence or prevalence rate Measurement of effect: rate difference, rate ratio, etiologic fraction and expected number of prevented cases 6.5.1 Rate difference and rate ratio 6.5.2 Excess fraction (EF) and etiologic fraction 6.5.3 Odds ratio 6.5.4 Expected number of prevented cases Measurement of utility of health: Quality-adjusted survival 6.6.1 Concept of QALY and its potential application 6.6.2 Life table method for estimating the QAS 6.6.3 Estimation of HRQL (health-related quality of life) Summary

Introduction A scientific discipline is usually considered a function of its substantive matters. In epidemiology, one is concerned with the occurrence and determinants of diseases and health-related events and states in human populations. Therefore, the science of epidemiology can be expressed as

121


P = f {D}, where P is the parameter of interest one wants to measure, and D are the determinants of such parameters. In this chapter, different parameters of measurements will be considered. Starting with the traditional counting of events and states in populations to obtain rate, proportion and ratio. Measurement of effect, in terms of rate ratio, rate difference and etiologic fraction, will also be discussed. Principles and applications of epidemiological research have recently been extended to assist health policy decision-making. As a result, the measurement of utility of health has also extended from counting the number of lives saved to measuring the functions of health-related quality of life (HRQL) and survival, and combining them with a common unit of quality-adjusted life year (QALY). Let us review some of the developing trends in epidemiological measurement. 6.1

Evolving trends in epidemiological measurement

Since the development of this discipline, early epidemiologists sought to calculate mortality rates, birth rates, etc., from demographic data obtained from death and birth certificates, regularly collected by governmental agencies. Since these rates were known to possibly change with different places, times, and population characteristics, such as age and sex, epidemiologists attempted to propose hypotheses which could interpret and predict such trends. Later, they found that such countings could also be performed for different health events (or diseases) to obtain morbidity rates, such as incidence rates for acute diseases: food poisoning, measles, polio, etc.; and chronic diseases: cancer, diabetes mellitus, stroke, etc. Moreover, if one clearly specifies the observation period of patients (for comparison), then cure rate, recurrency rate, case fatality rate, etc. can also be calculated. MacMahon and Pugh (1970) summarized epidemiological measurements into three types: rate, proportional rate, and ratio; and pointed out the importance of considering determinants, such as time, place, person, and other differences. In the beginning, counting the occurrence of a health event {e.g., cholera) was considered similar to counting the frequency of positive responses of Bernoulli trials. There was no distinction between relative risk and rate ratio,

Chapter 6 Measurements in epidemiology 123

as they were both regarded as a ratio of two proportions. More will be discussed on their differences later in this chapter. Neither was there differentiation between density sampling and cumulative incidence sampling for case-control study (Cornfield, 1951). This will be further explained in Chapter 11. Finally, time factor was dealt with by only specifying the presumed duration. As epidemiologists increasingly began to deal with chronic diseases, the concept of time as a denominator for incidence rate became more and more obvious (Elandt-Johnson, 1975). Because events (diseases) occur with the passage of time, some members in the cohort would be lost to follow-up or censored if observation time was prolonged. Statisticians, thus, could analyze incidence rate if they regarded it as a hazard rate of survival function (Breslow and Day, 1980). The concept of density sampling in case-control study developed by Miettinen (1976) further clarified that such a design neither requires the assumption of rare disease nor a constant exposure proportion(Greenland and Thomas, 1982). Again, case-control study will be discussed in further detail in Chapter 11. With its primary goal of prevention, epidemiological research, specifically etiologic studies, have been applied to health policy decision-making ever since the birth of epidemiology. Simple calculation of mortality and/or morbidity rates, and expected number of prevented cases may have been sufficient in the past. However, with the discovery of more and more etiologic agents, many of which are multi-factorial and cause both morbidity and mortality; it has become even more difficult to decide which action or policy will provide the greatest amount of utility of health and which should be taken first. Thus, combining the consideration of quality of life and length of survival, which is accomplished by the common unit of QALY (quality-adjusted life year) (Weinstein and Stason, 1977; Beauchamp and Childress, 1994; Gold et ah, 1996), can help in this decision-making process. However, there are so many different health states for each disease to be conceptualized in assessing quality of life, and survival status can possibly change with the passage of time. Therefore, developing a calculation of QALY by quality-adjusted survival (QAS) is crucial for a more accurate


quantification of utility of health (Hwang et al, 1996, 1999). 6.2

Basic measurements of outcome in epidemiology

6.2.1 Outcome measurement: Counting of events and states, rate, proportion, and ratio Distinction between events and states The epidemiological measurement for outcome, i.e., diseases or health-related objects, can generally be classified into 2 types: event and state. Occurrence of an event always involves a change of state with the passage of time. A state or status denotes a characteristic or feature that is present at a certain time point or period. For example, a person may develop the common cold today. This means that he (or she) did not have the symptoms of a common cold yesterday. This change in condition is regarded as the event of a common cold, while displaying or not displaying symptoms of a cold on a particular day is called one's state of health. Similarly, if a patient's tuberculosis (TB) is cured, then the event of cure has occurred, namely, one's health state has changed from affliction with TB to recovery. Ratio scales: Proportion and rate Time, health-related state, and event are the elementary measurements in epidemiological studies. As pointed out in Chapter 5, the simple counting of such elements possesses the characteristic of extensiveness of measurement, i.e., a o a = 2a. For example, 20 students who wear eyeglasses are equal to 10 times 2 students with glasses. One can create a proportion by dividing one counting with another counting of the same category. If the duration of time is also considered in the denominator, then such a proportion becomes a rate. Both proportion and rate are ratio scales. For example, 20 out of 40 college students wear eyeglasses, and 10 out of 40 high school students are of the same state. Then, the proportion of eyeglass-wearing in college is 2 times that in high school. Take another example: If within the last 3 months, 20 out of 100 students in public health develop a common cold, then the incidence


rate, or rate of catching a cold, is 0.2 during this period. If 20 out of 50 medical students develop a common cold in the same period, then the incidence rate is 0.4, which is 2 times that of students majoring in public health. Time in the denominator Initially, there was no need to put time into the denominator of rate, with specification of the duration of observation being sufficient. However, as epidemiologists came across more and more events of a chronic nature, it became more likely that two rates might be obtained from different durations of observations. If the two rates have different time units in their denominators, they cannot be directly compared. Moreover, if a rate is unspecified, one generally takes the average rate during the time period involved. When calculating incidence rate, one must also take care to differentiate an event from a state in the numerator because only the development of an event involves the passage of time. However, there may be some instances where the division of two countings of the same state (i.e., a proportion) may also be called a "rate" because the collection of data involves a period of time in the denominator (Miettinen, 1985a). When one divides the count of a particular event or state with another count of a different event or state, the result is called a ratio. Usually the events involved are related in some manner to obtain a meaningful index of ratio. For example, the sex ratio of a graduate class is 10/10= 1,which may be compared with another class with a different sex ratio, say 10/5 = 2, etc. 6.2.2 Determinants of measurement indices or parameters Demand for an index with fewer determinants A determinant of an index (or parameter) is a factor that is influential or predictive of the change in index. To examine a rate, proportion, or ratio, one needs to consider its determinants, which include accuracy of measurement of both numerator and denominator, and determinants of the related events or states. One prefers to explore an index with a fewer number


Table 6.1

Common indices or measurements involving health-related event, state, and time.

Proportion = (No. of a specific state or event) / (all possible states or events) e.g., The proportion of graduate students wearing eyeglasses among the entire class is: 10/20 = 0.5 The proportion of gastrointestinal disease among all diseases contracted in the past year is: 4/16 = 0.25 Ratio = (No. of a specific state or event) / (No. of another specific state or event) e.g., The sex ratio in a graduate class is: 10 (female)/10 (male) = 1 Rate = (No. of a specific event) / (Total amount of observed person-time) (Unit = time"') e.g., The incidence rate of gastrointestinal (GI) disease during the past year is: 4 (GI disease) /20 (total persons observed in one year) = 0.2(year"') Duration = (Total amount of person-time) / (No. of a specific event) e.g., It is the inverse of rate or the average duration of waiting time to develop gastrointestinal disease: 20/4 = 5 (year)

of determinants because of the ease in testing its determinants and etiologic agents individually. For example, the etiologic agents of an age-, sex- and cause-specific mortality rate are more easily determined than those for an overall crude death rate, because for the latter one must also falsify each possible etiologic role for age, sex, and different causes of death. Determinants of rate vs. proportion Proportion is generally more complicated than incidence rate because the denominator of the former is usually composed of different events or states, each with its own determinants. Let us examine a hypothetical example of the proportional mortality rate of motorcycle injuries, a proportion, as shown on Table 6.2.


Table 6.2

Frequencies of different traffic injuries in May, 1996 of city X.

Types of traffic injuries Motorcycle Car Bicycle Pedestrian Total

No. of death 15 8 2 2 27

Proportion (%) 56 30 7 7 100

Can one conclude that motorcycles are the most dangerous? Since one has no information on the population-time at-risk for the different types of traffic injuries, one can only conclude that motorcycle mortality is the highest proportion among them. Some may suggest that counting how many of each type of registered vehicles there are in city X is a good approximation of the number of people using each one of them, and might help judge the danger in using each vehicle. However, many people, who own bicycles and/or motorcycles, may not frequently use them for commuting, and the number of people riding on each vehicle may also be different. Thus, using the number of registered vehicles as the approximation of total observed person-time in the denominator only results in an erroneous conclusion. Let us take another example. If the outpatient clinic of hospital Y has the following summary statistics (as in Table 6.3), can one conclude that the most common disease is gastrointestinal (GI) disease? If the main purpose is for administrative consideration, of whether they need to increase specialists in a GI clinic to match market demand, then the answer is straightforward. However, if one wants to interpret it as a higher occurrence rate among local people, then the evidence does not seem to be adequate. There are still other determinants that may explain the higher proportion of GI disease found in hospital Y. For example, the GI specialists in hospital Y may be more outstanding and famous, and thus, attract more people with GI disease from city X to this hospital. Another alternative explanation may be that patients with non-GI diseases visit other hospitals more often than hospital Y, which produces the effect that the proportion of visits with GI disease at hospital Y


increases. In other words, proportions are less suitable for refutation because using the total number of diseases as the denominator invokes the auxiliary assumption that occurrence of every kind of non-GI diseases should be constantly stable. Therefore, one needs to find the correct denominator, population-time at-risk, in order to figure out which explanation is more plausible. Thus, determinants of an incidence rate are generally simpler than those of a proportion. Table 6.3

Frequencies of patients who visit hospital Y stratified by main categories of disease on a particular day.

Main types of disease Chest disease Gastrointestinal disease Hypertension disease Heart disease Kidney disease Endocrinologic problems Others Total

No. of patients 150 250 150 100 100 50 200 1000

Proportions (%) 15 25 15 10 10 5 20 100

Determinants of crude vs. specific rates Let us examine some rates and proportions used in medicine and public health, by first looking at the mortality rates listed in Table 6.4:

Table 6.4

Mortality rates with total population no. in one year as the denominator.

Total no. of deaths in one year (a) crude death rate = Total population no. during mid-year x 1 year


Total no. of live newborns in one year (b) crude birth rate = Total population no. during mid-year x 1 year

Total no. of deaths of a specific age stratum in one year (c) age-specific mortality rate = Total population no. during mid-year x 1 year

Total no. of deaths due to a specific cause in one year (d) cause-specific mortality rate = Total population no. during mid-year x 1 year

(e) sex-, age-, causespecific mortality rate =

Total no. of deaths of a specific sex, age stratum due to a specific cause in one year Total population no. during mid-year x 1 year

Consider four different rates, (a), (c), (d), and (e) in Table 6.4, and judge which one has fewer determinants, making it more suitable for studying etiologic agents. Of course, (e) sex-, age-, cause-specific mortality rate is the most suitable because it has the smallest number of determinants, where death rate is clearly specified for each and every cause, age strata, and gender. On the other hand, (a) crude death rate lacks this specificity, and thus, a change in this rate can arise from any number of determinants singly or in combination. Falsification of the numerous possibilities becomes an overwhelming task. Similarly, an age-specific mortality rate has taken care of the age factor but not of different genders and causes; a cause-specific mortality rate has focused on a specified cause of death, but has left gender and age strata ambiguous. Thus, the more specific a rate, the fewer determinants one must analyze for its falsification. Take another example of the measurement of indices involving newborns, in Table 6.5:


Table 6.5

Rates or ratios with no. of live births in one year as the denominator.

Total no. of infants who died within one year after birth in one year (a) Infant mortality rate = No. of live births in one year x 1 year

Total no. of infants who died within 4 weeks after birth in one year (b) Neonatal mortality rate = No. of live births in one year x 1 year

Total no. of fetal deaths (pregnant > 20 weeks) in one year (c) Fetal mortality ratio = No. of live births in one year

Strictly speaking, the number of live births is the correct denominator for (a) and (b) of Table 6.5; however, it is not the correct denominator for (c). Fetal mortality rate requires counting all pregnancies longer than 20 weeks during the year, which may not be feasible. Thus, people may simply take the number of live births as a surrogate, and interpret this fetal mortality ratio as the odds between fetal death and live birth. Rate with a specified time unit With such examples of rates as shown in Tables 6.4 and 6.5, one may understand why many earlier books of epidemiology left out the time unit of one year in the denominator, and simply assumed the observation period of one year. However, if unexpected problems develop and induce significant changes within several weeks or months, such as the enforcement of a helmet law, one may want to look at the change of such rates in a shorter period of time for comparison. Since two rates with different observation periods


cannot be compared, the use of a specified time unit in the denominator is a fundamental solution. In clinical medicine, people sometimes still use case fatality rate, remission rate, recurrency rate, etc., which also indicate occurrences of specific events but lack a time unit. In fact, such rates usually imply certain observation periods for the occurrence of each event, and people simply assume that those who use it know the duration of observation for a specific index. However, for long-term observation, such as the follow-up for cancer, one generally specifies the duration of follow-up, such as 3-year survival rate or 5-year survival rate, etc. Consequently, I recommend that clinical medicine also use a time unit to allow for fair comparisons. Similarly, the same concept can be applied to health policy studies, as well as other (health- related) events and rates in a population. For example, the following rates are often used to evaluate the effectiveness of an emergency medical service system, as shown in Table 6.6. Table 6.6

Indices of effectiveness of an emergency medical service system.

(a) Mortality rate before arrival at the hospital

Total no. of deaths occurring before arrival at the hospital during a certain time period = Total no. of emergency runs by ambulances during this period

Total no. of deaths occurring on ambulances during a certain time period

(b) Mortality rate during transportation =

Total no. of emergency runs by ambulances during this period Total no. of deaths occurring before arrival of ambulance during a certain time period (c) Mortality rate on the scene = Total no. of emergency runs by ambulances during this period


Again, one tries to incorporate a time unit, such as month"', in the denominator for comparison of such rates in the health services. Since the determinants of (a) in Table 6.6 include all determinants of (b) and (c), one ought to obtain information on (b) and (c) for a more detailed evaluation of an emergency medical service system. 6.3

Incidence rate, cumulative incidence rate, risk and their determinants

6.3.1 Incidence rate or density Incidence rate is a fundamental measurement in epidemiology. It is defined as the number of new occurrences of a specified event in a population during a period of time. The population should only include candidates who may develop the event, namely population-at-risk. For example, the population-at-risk and incidence rate of cervical cancer should not include any males. Thus, the denominator of an incidence rate is the total amount of observation of population-time at-risk. It is written as follows: Number of new cases of a specific event Incidence rate = Total amount of population-time at-risk In a dynamic population, where some extent of turnover among people may occur, one simply assumes that it is in a steady state. In other words, the rate of new people joining the population per unit of time is the same as the rate of those leaving. Thus, one may obtain the incidence rate very easily. For example, if 50 new cases of an event occur in a stable candidate population of 100,000 during a year, then the average incidence rate is 50/100,000 = 5 x 10"4 year"1. A cohort population is usually defined as a group of people followed up throughout a certain period of time without replenishment. The total person-time is accumulated for each member until one develops the event or dies, or is censored due to a failure to follow up or cessation in observation.


Let us look at the example of following 5 persons for 7 years, as shown in Figure 6.1.

case i

1

C\ \J

9

T.

• indicates follow-up stop X indicates ccurrence of the event O indicates loss to follow-up or death

V

iSh

A

v9

2

r\

< i

1 2

i

-2

= 8.9x10

year

22.5

i

i

i

>

Follow up time (year) Figure 6.1

Calculation of incidence rate from following 5 persons for 7 years.

In Figure 6.1, there are 2 persons (cases 3 and 4), who develop the health events of interest during the follow-up person-time. The denominator is accumulated as follows: 7 (no. l) + 2(no. 2)+ 4.5 (no. 3)+ 3 (no. 4)+ 6 (no. 5) = 22.5 person-years. The contribution of person-years for person no.3 is 4.5 person years because he/she no longer contributes any person-year at-risk after the occurrence of the health event. Thus, the average incidence rate is 2/22.5 (year) = 8.9 x 10"2 year"1. Such a calculation is similar to the life table method. When the population is large, which is usually the case, incidence rate can be viewed as the proportion of people developing the event among the population followed in a short period of time, as shown in Figure 6.2. (Rothman, 1986) Incidence rate is also called "hazard rate" or "failure rate" by statisticians,


(e.g., Cox, 1972; Kalbfleisch and Prentice, 1980; Lee, 1992), because it is similar to the occurrence of a specific hazard in a certain proportion of a population (human or non-human objects). It has been also known as "force of morbidity" (MasMahon and Pugh, 1970), because it indicates a tendency within a specified time period for a certain proportion of the population to succumb to the disease. Miettinen (1976) gave it another name, "incidence density," because it is similar to measuring the density of an event occurring in a population followed across time. To illustrate why incidence rate should be given a time unit, let us examine the following example. Suppose that one has followed up 200 cases with myocardial infarction for 1.5 years and obtained the data as follows: 10 cases died within one week; the next 15 died before one month; an additional 20 cases died within 6 months; and another 25 cases died by the end of the follow-up period. Assuming that there are no losses to follow-up or censorship (withdrawal of living cases), one might calculate the mortality rates of different periods: 1st week 8-30 days 2nd - 6th months 0.5-1.5 years

10/200 = .05 (per week or week-1) 15/(23 x (200-10)) = .0034 (per day or day-') 20/(5 x (190-15)) = .0229 (per month or month"') 25/(175-20) = .1613 (per year or year -1 )

Since these numbers were observed under different durations of observation time or units, they cannot be compared. Furthermore, one cannot determine when the highest mortality rate occurred. However, if one uses the same unit, e.g., per week or week"1, then, one can obtain a new set of figures: 1st week 8-30 days 2nd-6th months 0.5-1.5 years

10/[(200)(lwk)] = .05 week"1 or wk"1 15/[(190)(3.3wk)] = .0239 wk"1 20/[(175)(21wk)] = .0054 wk"1 25/[(155)(52 wk)] = .0031 wk"1

After transforming all mortality rates to the same unit, one can then


compare and state that the 1 st week was the most dangerous, with the highest mortality rate.

Population At Risk N(t) A N

Time

Figure 6.2

A cohort of population (N(t)) followed through time. Within At time period, a proportion (AN) of the population develops the event. The incidence rate AN IR= When At-»0, one may obtain the instantaneous incidence (N(t))(At) rate (modified from Rothman, 1986).

6.3.2 Cumulative incidence rate (CIR) and risk While incidence rate represents the tendency or proportion of a population who will develop the health event, it does not delineate the risk of a single individual. Assuming that risk is defined as the probability that a particular event occurs during a stated period of time or results from a particular challenge, then risk can be estimated by CIR or proportion after the specified time period. Let incidence rate (IR) at time t be the rate of new cases developed from the population (N(t)) at risk after a small period (t) of observation time, as shown in Figure 6.2.


K- -^t

3, , (IR)At

N(t)At

*N N(t)

Take the integration, - } o (IR)dt = In (N(t)) - In (N(o)) = In

Take the antilogs, exp (- fo (IR)dt)

CIR t =

N(t) N(o)

_N(t) N(o)

N(0)

~ N ( t ) = 1 - ^ - = l-exp(- J f' V(IR)dt)= l-exp(-Y (IRi)(Ati)) n N(o) N(o) ° f

Alternatively, the risk can be estimated by the life-table method. Let us construct a life table after j years of follow-up. Let R(j) be the risk of contracting the disease by the end of the j t h year. Then, the risk of developing the event by the end of the 1st year can be estimated by the average incidence rate IR(1): R(1)=1-(1-R(1))=1-(1-IR(1)) Similarly, the j , h year will be as follows: R0) = i - n O - R 0 ) ) = i - ( i - R ( i ) ) ( i - R ( 2 ) )

(i-R(j))

j

= 1-(1-IR(1))(1-IR(2))

(l-IR(j))

So, one must obtain the data of particular incidence rates during the specified period of time in order to assess the risk. For an individual, one must assume that if the person has not died of other competing causes, then his probability of getting the disease is R(t): When R(t) < 0.1, e x = 1 + X;, thus, R(t) = K l R ^ t , . ) . i

For example, the incidence rate of stomach cancer for an American


white male in 1975 was 12.4x 10"5, and his life expectancy at birth was 69.4. Thus, his lifetime risk of developing stomach cancer (conditional that he does not die of other diseases) is: Ro-«.4= 1-e-(l2'4xl0"5)x69-4 = 0.012, which is approximately equal to (12.4 x 10"5) x 69.4 = 0.009 In other words, when incidence rate is very small, the CIR is almost equivalent to the sum of age specific rate (IR,) multiplied with the interval of age stratum (t|). This method is also recommended by IARC (International Agency for Research on Cancer) for the calculation of cumulative cancer incidence for international comparison (Davis, 1978), as it not only indicates personal risk, but also can be directly compared as long as the cumulative time period remains the same, e.g., 0-7'4 years of age. When the cumulative time period is prolonged, CIR is equal to 1 because almost every one at risk develops the event. When the specified time interval is short, t-»0, then CIR is equal to incidence rate. If one wants to apply risk interpretation for an individual, however, one needs to assume that the person has not died of some other disease during the observation time period. The assumption may not be true because of competing causes of death, and the CIR often over-estimates the life time risk as demonstrated by Schouten et al (1994). 6.3.3 Determinants of incidence rate (IR) After identifying the calculation method for IR, one should also be familiar with all of its determinants so that whenever one finds a change of IR, one can immediately think of all the determinants, which may contribute to this change. Determinants of IR can largely be classified as follows: 1. Because the numerator of IR is the counting of a particular (health) event, it follows that all the determinants of the event are also determinants of IR. For example, if the event is bladder cancer, then all of its determinants,


such as smoking, exposures to aromatic amines, diagnostic criteria, etc., should also be determinants of the IR of bladder cancer. Similarly, if the event is head injury, then all of its determinants, such as the wearing of a helmet or seat belt, diagnostic criteria, etc., should also be determinants of the IR of head injury. In fact, the definition and measurement accuracy of the health event should always be considered as one of the possible determinants. 2. Accurate counting of both the numerator and the denominator, including how the information is obtained and the accuracy of the data, is always a major determinant. For example, if one uses death certificate data as an approximation to estimate the IR of lung cancer, the error may not be too large because most cases with lung cancer die within 1-3 years. If the same set of data is used to estimate IRs of skin cancer and glaucoma, then one is bound to make an underestimation because patients with either disease rarely die of them, and such diagnoses, especially glaucoma, often do not appear on the death certificate. In a cross-sectional survey of occupational diseases, workers with diseases are often hospitalized and absent from their jobs, leading to a frequent underestimation of the data in the numerator. For example, in a study of the prevalence of hepatitis among workers exposed to dimethyl formamide (Wang et al, 1991), we found that two workers did not come in for their physical examinations because they were hospitalized with hepatitis. In another investigation, we studied lead poisoning among lead battery recycling workers and found a 48% prevalence of lead poisoning. However, we underestimated the IR because those who did not come in for physical examination actually worked for significantly longer hours and experienced a higher exposure (Jang et al, 1994). Similarly, if the reason for loss of follow-up in a cohort study is related to the outcome or exposure of interest, then we should be careful about either over- or under-estimation. For example, in a follow up study of workers exposed to vinyl chloride monomer (Du and Wang, 1998), if workers suffering from ill health were more likely to take early retirement and become lost to follow up, then there might be an

Chapter 6

Measurements in epidemiology 139

underestimation of the effect. 3. Induction time is always a determinant of the occurrence of the health event. Induction time is defined as the minimal time period required for an etiologic agent to produce the event. It should be differentiated with the latency period that denotes the time period from exposure to the agent to the time when the disease is detected (Rothman, 1981). Latency period will generally vary according to the development of clinical technology for early detection, while induction time is supposed to stay constant. For example, one will not attribute the brain tumor of a patient to his radiation exposure that occurred only two months ago, an inadequate induction period. Similarly, one will never attribute a painless, fever-less diarrhea to some food consumed one month ago, either. Therefore, for calculation of IR of any health event with long induction time, one should not include those cases and population-at-risk with inadequate induction time or exceeding maximum latency period in the numerator and denominator, respectively. (See also cases 1-3 in Chapter 4.) 4. Constitutional factors or any genetic predisposing factor related to the event. For example, anyone with a family history of breast cancer or colon cancer is more likely to develop such an event than those without such a history (Neuhausen, 1999). Ethnically, Caucasian people are more likely to develop skin cancer. As our understanding of human genetics and genomic medicine increases, such factors should always be kept in mind, and an extensive search into the literature is crucial to the inclusion of these factors. 5. Environmental or occupational factors. For example, people with occupational and/or environmental asbestos exposure are more likely to develop lung cancer and mesothelioma (Chang et


ai, 1999). Children living or employees working next to a heavily contaminated factory may be under a danger of increased lead absorption (Wang et ai, 1998). Again, a comprehensive literature search is needed to avoid overlooking important determinants. 6. Lifestyle and soeio-behavioral factors. One must consider any lifestyle practices that may have been reported as determinants of the heath event. For example, cigarette smoking is a major determinant for lung cancer and chronic obstructive lung disease. Homosexual practice and intravenous drug abuse are major determinants for HIV (human immunodeficiency virus) infection, etc. The above classification system is relatively arbitrary, but can help epidemiologists easily remember and avoid overlooking any major determinant. Overall, a comprehensive literature search for the health outcome and its determinants should be performed before conducting the study. 6.4

Prevalence or prevalence rate (PR)

Prevalence is defined as the proportion with a specified state in the population at a particular time point or period. Strictly speaking, it is a proportion rather than a rate because there is no inherent time involved in the denominator. However, since the collection of such data often involves an observation time, it is often called a prevalence rate by many epidemiologists. No. of people with the specified state PR= Total no. of population who may have such a state It can be derived that prevalence is connected to incidence rate through the duration of health state under a stationary population and without migration. To simplify interpretation, I shall use a disease to represent the

Chapter 6

Measurements in epidemiology 141

health event. Let us use the following notations: Nt: Total no. of population at time t IR: Incidence rate of the disease TR: Termination rate of the disease (i.e., incidence rate of patients recovered back to normal) D: Mean duration of the disease If the population is in a steady state, then the number of new cases developed is equal to the number of patients who died or recovered back to normal. N, (1-PR)(IR) = N, (PR)(TR) 1 Because the inverse of TR is equal to D, i.e. TR = D 1 (1-PR)(IR) = ( P R ) ( — — ) D (IR)D Thus, PR = 1 + (IR) D

If IR and D are both very small, then PR = (IR) D . PR is a proportion generally applied to describe a population rather than an individual. It can be used for a time point or during a period of our observation. Because PR depends on both incidence rate and mean duration of the diseased state ( D ), its determinants include all determinants of IR plus D . If D is unrelated to the exposure of interest or any other etiologic agent, then PR actually changes with all determinants of IR. Thus, epidemiologists sometimes conduct cross-sectional studies, which usually obtain PR only, for causal inference. Under this condition, one should always be aware that one invokes an


assumption of mean duration being unrelated to any etiologic agent of interest. If the disease is not a highly fatal one, then one may collect information about duration-to-date on each prevalent cases and estimate IR (Freeman and Hutchinson, 1980). 6.5

Measurement of effects: rate difference, rate ratio, etiologic fraction, odds ratio, and expected number of prevented cases.

In general, an effect is the end result produced by a change or modification on the cause. In epidemiology, such an effect is usually expressed as the change of occurrence of health events or states, and the cause is usually construed as exposure to an etiologic agent. Because a disease or health event generally has many different determinants, one should pay attention to alternative causes (or other determinants), to try to control potential confounding. By analyzing other alternatives, one can conclude with more validity that the effect, i.e., the change of occurrence frequencies of a disease, is attributable to the change of specific exposure states. 6.5.1 Rate difference and rate ratio When one compares one or more rates with the baseline rate (the non-exposed rate), the comparison is generally expressed in two ways: Rate difference (Ri-R0) and rate ratio (R,/R0), assuming that RQ denotes the baseline rate and R, denotes the rate among the exposed. One can produce such comparisons from the data for incidence rate, cumulative incidence rate, or prevalence rate to imply measurements of effect. For example, if the (40-50) age-specific lung cancer incidence rate for smokers and non-smokers in city X were 10 x 10"5 year"' and 1 x 10"5 year"1, respectively, then the rate difference and rate ratio resulting from smoking are (10-l)x 10 s year"1 and (lOx 10"5 year"')/(l x 10"5 year"1) = 10, respectively, assuming that there is no exposure to other alternative etiologic agents. In the study of acute infectious disease, people previously called incidence rate ratio (IRR) "relative risk" (RR) because IRR is almost equal to cumulative incidence rate ratio (CIRR), which is an estimate of RR, if the observed time duration is short and clearly


specified. If one is studying chronic diseases, however, then CIRR or RR can approximate IRR only under two assumptions: one, the disease is rare; two, the exposure proportion is constant during the observation period (Greenland and Thomas, 1982). Because both assumptions may be violated in studies of chronic disease, and since IRR can cover both acute and chronic diseases, I recommend that future epidemiologists should use IRR or rate ratio more often. Even for acute disease, if one divides time into smaller intervals, one may obtain different estimates for IRR and RR. For example, suppose that there was an outbreak of food poisoning after a banquet, attended by 100 people. Guests began to develop painless diarrhea 3 hours after the banquet. The numbers of patients each hour thereafter were 3, 6, 14, 10, 8, 4, respectively, as shown on Table 6.7. Table 6.7

Calculation of incidence rates and cumulative incidence rates (estimate of risk) from a hypothetical example of acute disease (e.g., food poisoning), showing how they are interrelated: Incidence rate is a first order derivative of cumulative incidence rate when the time interval approaches 0.

Time No. of persons (hr) at risk 0-2 100 2-3 100 3-4 97 4-5 91 5-6 77 67 6-7 7-8 59 8-24 55

No. of new cases Incidence rate (IR) Cumulative incidence with diarrhea during the hour (hr"1) rate (Risk Q.Q 0 0 0 3 3/100 3/100(Risk0.3) 6 6/97 9/100(Risko.4) 14 14/91 23/100(Risko.5) 10 10/77 33/100(Risko_6) 8 8/67 41/100(Risko.7) 4 4/59 45/100(Risko-8) 0 0 45/100(Risko.24)

Because of the small time interval for observing food poisoning, a common disease, the IRs and CIRs (risks) are quite different. Thus, the ratio of two IRs may also differ from the ratio of two risks.


6.5.2 Excess fraction (EF) and etiologic fraction If the incidence rate ratio (IRR) is larger than 1, then one may obtain an excess fraction (Greenland and Robins, 1998), which was called attributable risk percent, or attributable proportion in the past. Let IR] and IR0 denote incidence rate among the exposed and nonexposed, respectively. Then, EF = (IR, - IR0)/( IR,) = 1 - (1/(IRR)). For example, if the age-specific lung cancer incidence rates for smokers and nonsmokers were lOx 10"5 year "' and lxlO" 5 year "', respectively, then the EF = [(10-1) x 10"5 year "'] / (lOx 10"5 year"') = 90%. This excess fraction was once interpreted as the etiologic fraction (Miettinen, 1974a), if there is no alternative cause in the estimate of incidence rate of lung cancer among smokers. However, if the etiologic fraction is defined as these individuals for whom exposure was a contributory cause, then there may be cases accelerated by exposure (Greenland, 1999). If the number of such accelerated cases is substantial, then the excess fraction may underestimate the etiologic fraction. The assumption of no competing risk further complicates the interpretation. Thus, an epidemiologist must recognize that rate ratios and rate fractions only reflect the overall impact of exposure on a population, rather than the total number of persons affected by exposure (Greenland and Robins, 1986), and one should always consider biologic model and mechanism of how exposure produces effect on interpreting an epidemiologic measure. 6.5.3 Odds ratio One will often come across data on cases of the disease (numerator data), and will not find available data on population-time at-risk (denominator data). Accordingly, epidemiologists have designed a method termed "case control study" to sample a population-at-risk over a defined time period. Essentially one attempts to sample a control series to estimate the exposure odds of the controls (exposed vs. non-exposed). One also utilizes the data from the case studies (numerator data) to estimate the exposure odds for case series. Thus, an odds ratio or estimate of the incidence rate ratio for the


exposed and non-exposed population can be obtained by dividing the exposure odds of the case series by that of the control series. One can then further model an odds ratio with multiple logistic regression to control possible confounding by other variables. Such modeling can be performed easily on currently available computer packages such as BMDP (Biomedical Data Processing), SAS (Statistical Analysis System), SPSS (Statistical Process of Social Science). Thus, odds ratio has become a fashionable name in epidemiology and people sometimes forget that it had better be interpreted as a measurement of effect under the case control study design (Greenland, 1987a). Readers who desire to model odds ratio in statistical packages should be familiar with case-control study design (chapter 11) first and then decide whether it is the correct measurement of effect. 6.5.4 Expected number of prevented cases (Tsauo et ah, 1999) To estimate the effect of a prevention program, one can also try to calculate the expected number of prevented cases. To perform such a calculation, one must first assume that the excess fraction is equal to the etiologic fraction. One should also first consider the simplest case of a prevention program, involving the elimination of one particular exposure, and further assume that such an exposure can only result in one particular disease di.

Suppose that the activity of the prevention program begins at time to, and the proportion of exposure also begins to decrease at the same time because of this activity. Moreover, assume that the prevention program completes at time tj, and the reduction of proportion of exposure also becomes stabilized after t]. Then, after a period of induction I 35 IU) were compared for different intensities of exposure to DMF. Since chronic hepatitis B infection, as indicated by a positive carrier status of its surface antigen (HBsAg), may increase the frequency of abnormal liver function, one should compare workers with the same carrier state in the same stratum. Such stratification can eliminate the mixing of effect from DMF and HBsAg, as shown in the upper panel of Table 7.3. Essentially, it provides us an opportunity to look at the effect of DMF while holding that of hepatitis B constant. The concept of modeling is similar to stratification. In modeling, one holds all other determinants in the model constant, while singularly examining the change of outcome under changing exposures of interest. Modeling had the added advantage that one can explore the quantitative interaction among different determinants, while stratification only provides an intuitive appeal through displaying actual frequencies in individual strata. In the lower panel of Table 7.3, the frequencies of workers with abnormal liver function were compared by modeling analysis for an independent effect of each determinant: HBsAg, DMF, and exposure indices 1 and 2. A 95% confidence level that includes an odds ratio of 1 is usually not considered to be


a statistically significant effect. As both stratification and modeling hold stratified and modeled determinants constant, they are useful in controlling confounding. To perform modeling and stratification, one needs to measure or collect information on all other determinants of the outcome. Moreover, a causal inference usually involves a hypothesis of a natural law, which should be universal in different time and spatial settings. Thus, one should try to draw conclusions beyond the statistical association obtained from one study. Furthermore, one should consider evidence outside of the study to see which hypotheses are falsified and which remain unrefuted. The characteristics of descriptive and causal inferences in epidemiological studies are summarized in Table 7.4. 7.1.3 More about distinctions between descriptive and causal inferences The general and primary goal of statistical analysis in epidemiological research is to summarize the data, which is often expressed as the estimation of parameters, tests of significance or both. In a descriptive study, parameters describing characteristics of a population, such as rate, are estimated from a random or quasi-random sample. Statistical inferences are made mainly based on the representativeness of the sample, meaning that one must determine to which specific population one can infer characteristics from the sample under study. In a causal study, the statistical summarization of data is used to rule out chance as an alternative explanation or to estimate the magnitude of the causal effect while holding other determinants constant. After estimating parameters of effect (rate ratio or rate difference) and performing tests of significance from the sample; investigators often consider evidence and alternative hypotheses outside of the study, in order to falsify hypotheses. Because causal hypotheses are proposed natural laws that should not be limited by different times, places or particular settings, one must take outside hypotheses and evidence into consideration before reaching a conclusion. In fact, this process involves conjecture and refutation. In other texts, causal inferences have been

Chapter 7 Study design 169

Table 7.3

Stratification of workers with abnormal liver function,* by index of exposure to dimethylformamide (DMF) and hepatitis B surface antigen (HBsAg) (Wang, et al, 1991). DMF Exposure Index

Liver Function (ALT level)

Status

HBsAg (-)

S 35 O

All other determinants of outcome should a priori be known and under strict experimental control so that the two groups have the same distribution of such determinants. This condition is more readily achievable in animal experimentation, in which one utilizes inbred strain animals to control


constitutional factors and set up a totally controlled environment. However, due to ethical concerns, one cannot experimentally control a human population, but can only make observations or at most set up double-blind random trials. Thus, if any major determinant of outcome is differentially distributed between the two groups, confounding may result. 7.3.2 Characteristics of confounders and their control A confounder is, a priori, a causal determinant of the outcome under study. Furthermore, it is associated with the exposure of interest, meaning that it is differentially distributed among the exposed and non-exposed populations. In Example 7.10, cases of occupational or hereditary asthma might produce confounding if they also reside in the area with high S0 2 concentration, the exposure under study. Likewise, people who developed asthma elsewhere and then moved into the study community produced confounding because they chose to live in the exposed area. In Example 7.11, since distributions of age and sex of residents near the airport were significantly different from the entire Los Angeles area, these factors were mixed with the exposure to jet noise, resulting in confounding. Thus, in the detection of potential confounding in a study, one should list all causal determinants of the outcome of interest, and examine them one by one to see if any one of them is associated with the exposure. On the other hand, non-causal determinants do not produce any confounding. In Example 7.10, the investigators worried neither about the color of clothing people wore nor about body heights, as these are not causal determinants of asthma. Similarly, the researchers in Example 7.11, studying the association of high mortality rate and exposure to jet noise, did not worry about the above characteristics either, since they were not determinants of mortality. Even in physical or chemical experiments, one is only concerned with known determinants of outcome and seeks to control them during the experiment. Moreover, a determinant of exposure that happens to be associated with the outcome of interest, still cannot be viewed as an alternative explanation


because the association may be indirectly linked through the exposure (Rothman and Greenland, 1998). For example, socio-economic status is a determinant of smoking and happens to be associated with the incidence of lung cancer. However, because socio-economic status first affects smoking rates, which then leads to lung cancer rates, socio-economic status cannot be considered a potential confounder, if smoking rates were under control. So, one should only examine and control for the causal determinants of outcome, to save time and resources, instead of also considering all determinants of exposure. One should prevent alternative causal determinants from linking with the exposure by restricting them in the design stage, or control them by stratification or modeling in the analysis stage. The latter involves one's attempts to comparably distribute the causal determinants between the exposed and non-exposed populations. Thus, strategies for controlling confounding can be summarized as follows: Strategy 1. Restriction of enrollment of subjects (See also Section 11.4) Restrict the selection of exposed and non-exposed groups during the design stage so that they are comparable in alternative causal determinants. Suppose one wants to study whether smoking causes lung cancer, one may restrict the study to only the white male population, to avoid potential confounding from mixing female and/or nonwhite people. Moreover, one needs to select a comparable non-exposed group (placebo/sham group in clinical trials or animal experiments), to rule out other causal determinants. Conceptually, such a non-exposed group should possess the same distribution or pattern of all causal determinants of outcome as the exposed group, all except for the exposure of interest, as summarized in Table 7.8. Therefore, an investigator should first perform a comprehensive literature search to find all causal determinants of outcome.


Table 7.8

How to select suitable nonexposed groups to prevent or control confounding, as demonstrated through various types of causal research. This is generally accomplished by comparably distributing all alternative causal determinants of outcome. i —

Clinical trials

Follow-up or Cohort

Types of

Animal

causal research

experiment

studies

Examples

Painting rabbit ears Treating peptic ulcer with tar to produce patients with cimetidine skin cancer

Determining the association between asbestos and lung cancer

Comparability of effects

Tar group vs. non-tar group (painted with solvent to dissolve the tar)

Cimetidine group vs. placebo group (contains everything used to formulate cimetidine tablet but does not contain cimetidine molecule itself)

Asbestos workers vs. nonasbestos workers (e.g., cotton workers exposed to fibers that do not cause lung cancer)

Comparability of contrasted populations: constitutional, life style, socio-behavioral, occupational and environmental

Selecting inbred strains

Randomizing then comparing causal determinants between the two groups.

Factors affecting job entry and exit should be unrelated to lung cancer, or at least comparable between the two groups. The non-asbestos workers should not possess any characteristics which are causal determinants of lung cancer, e.g., greater number of smokers.

Comparability of Measurements

Double blind measurement

Double blind measurement

Measurement of outcome and collection of data should be unrelated to the exposure.

■

■


I have reclassified the determinants of outcome (See also Chapter 6) into 3 categories (Wang and Miettinen, 1982): (1) Effect(s) caused by the exposure of interest. (2) Characteristics of the population (constitutional, life style, socio-behavioral, occupational and environmental factors) that may influence the outcome. Obviously, the selection procedures for study subjects have a direct impact on these characteristics. (3) Measurement or data collection methods. In order to avoid missing any important determinant, one should thoroughly search for causal determinants among these 3 categories. Moreover, such considerations help one to recognize that the ideal "reference" group is not simply characterized by non-exposure but is also comparable with the exposed in terms of all other alternative causal determinants. Strategy 2. Standardization, stratification or modeling Apply standardization (adjustment), stratification or modeling in the data analysis. Conceptually, in all of these processes, one attempts to divide or stratify the population into several or more smaller groups or strata, according to different causal determinants. Within each specific group or strata, the exposed and non-exposed groups should then be comparable. The standardization procedure involves the summarization of the different strata into an overall figure, which can also be achieved by other procedures such as Mantel-Haenszel (1959; Mantel, 1963) or maximum likelihood estimation. Modeling involves a similar concept of holding all other factors equal to see how much the outcome will change according to a change of exposure status. In a study to determine kerosene as the major cause of dermatitis among ball-bearing workers (Example 7.12, Jee et ai, 1985), other causal determinants of dermatitis (gender, age, use of protective cream and hand gloves, habits of hand-washing, dish-washing and laundry; etc.) and occupational exposures were evaluated. Because all 79 ball-bearing workers were young females, we restricted our non-exposed group to females of a similar age, educational backgrounds and salaries, by selecting 263


zipper-manufacturing workers, unexposed to kerosene. Thus, we chose a non-exposed group comparable in effect, contrasted populations and measurements, as summarized in Table 7.9. In Example 7.4, we found that paraquat manufacturers in Taiwan developed hyper-pigmentation or freckles in sunlight exposed areas of their bilateral forearms. To control the possible confounding effect of sunlight and age, we stratified the exposed and non-exposed populations according to these two determinants, in addition to the duration of exposure to centrifugation and crystallization, as shown on Table 7.10. The data indicated that the longer the exposure duration during the centrifugation and crystallization processes, the more likely the development of hyper-pigmentation. A logistic regression analysis of the same data showed a similar result. Because the stratified analysis allows the reader to visualize the analysis and is more intuitively appealing, I recommend such a tabulation. However, a multivariate analysis, which simultaneously considers many determinants of outcome to measure the individual magnitude of each determinant's effect, can help explore how these factors interact. The bottom half of Table 7.3 is one example of a multivariate analysis by modeling. (See also Tables 11.5 and 11.6.) In fact, both strategies 1 and 2 can be combined and applied in the same study, just as one can have both descriptive and causal inferences in a single study. In the study to determine whether higher levels of lead absorption occurred among workers in an iron-forging factory near a lead recycling factory, we (Chao and Wang, 1994; Example 7.13) deliberately chose workers from another iron-forging factory, 20 km away, as a reference or non-exposed group. Since the two groups performed the same job, the requirement of comparability of effects was satisfied. We excluded truck drivers and workers on the job for less than 2 months because of smaller exposure dose and likelihood that their blood lead level had not yet achieved a steady state in such a short period of time. Furthermore, we stratified the two samples into outdoor and indoor workers because by being outdoors raised the likelihood of exposure to lead dusts from the nearby factory and local traffic. In our analysis, blood lead was randomly measured without knowledge of the exposure status. Thus, comparability of effects, contrasted populations and


measurements were achieved.

Table 7.9

Characteristics of the exposed (ball-bearing factory) and reference (zipper manufacturing company) groups (Jee et ai, 1985).

Number of workers Sex Age(years) Range Mean SD Monthly income Educational level Major contactantsb Minor contactantsc a. b. c.

Exposed group 79 Female 16-26 18.9 1.9 NTS 7,000a Elementary school only, in most cases Kerosene, steel Antirust oil

Reference group 263 Female 15-29 20.2 3.7 NT $ 7,000a Elementary school only, in most cases Plastics, textiles Scissors, lubricants

NT $ stands for new Taiwan dollars. NT $ 7,000 is equivalent to USD 200. Any substances to which the workers were heavily exposed daily. Substances to which the workers were lightly and only occasionally exposed.

We also needed to address one more potential confounder, the possibility of lead contamination from the iron-forging process itself. During our study, we found a higher proportion of smokers among reference workers than among the exposed. Thus, if there was any risk of lead contamination in the iron-forging process, the non-exposed might show a higher lead content due to the picking up and inhaling of cigarette butts resting on possibly contaminated surfaces. However, the statistical summary of the data, in Table 7.11, showed conversely that there were higher blood lead levels among the exposed workers. By taking care of potential confounders and sampling two groups of workers comparable in effects, population characteristics and measurements, we were able to conclude that exposure to a nearby lead recycling factory increased the risk of lead contamination. Similarly, in a


study exploring the effect on liver function by mixtures of solvents, we apply two modeling techniques to control potential confounding by viral hepatitis infection, alcoholism, and body mass index. Because both general linear model and logistic model showed a consistent trend, we concluded that exposure to mixtures of solvent would mildly impair liver function, evidenced by elevated total bile acid in serum(Chen, et al, 1997). 7.3.3 How to detect confounding or systematic bias in a study In the literature {e.g., Michael et al, 1984; Sacket, 1979) on systematic bias or confounding, one may frequently encounter many terms, such as selection bias, recall bias, diagnostic accuracy bias, ecological fallacy, Hawthorne effect, etc. Although each bias has its own definition and may evolve from different conditions, all of them can be viewed as one type of mixing of effect, i.e. confounding. Since only causal determinants of outcome have the potential to become confounders, one can try to detect bias by first listing all causal determinants. As discussed in the previous section, one can look for alternative determinants by analyzing the effect of exposure, population characteristics (including constitutional, lifestyle, social, occupational and environmental differences), and measurement methods, as in Table 7.8. Namely, one can examine each causal determinant to see if it is associated with the exposure. During the study design stage, one should conduct a comprehensive literature search and consult experts in the field to list all major causal determinants ever reported. Then consider strategies to control confounding either by restrictive selection of subjects or by stratification and modeling in the data analysis. The basic principles for control of confounding in both follow-up and case-control studies are essentially the same, with some added features for the latter, which will be discussed in Chapter 11.


Table 7.10 Number of workers with hyper-pigmented macules stratified by duration of exposure to centrifugation and crystallization processes, sunlight and age (Wang et al, 1987). Exposure to sunlight (hours per week) 12

Duration of exposure to crystallization and

Age

60

Total

centrifugation processes (months) >6 Total t 1-6 0 1 1 0 0 18 10 12 1 0 23 2 7 12 1 1 4 19 1 1 0 0 1 0

Yes No Yes No Yes No Yes No

0 0 18 1 21 4 14 0 1


2 15 3 20 4 24 2 1

0 2 3 0 0 4 0 0

1 0 4 0 3 0 0 0

3 17 10 20 7 28 2 1


2 5 1 11 3 9 0 1

2 2 3 0 1 1 0 0

0 0 5 1 2 1 2 0

4 7 9 12 6 11 2 1

Yes No

22 140

12 15

35 3

69 158


%2( 1 )(Mantel-Haenszel) X2(l)(Mantel extension for the trend) Odds ratio: Point estimate (Mantel-Haenszel) 95% Confidence interval (test based) 6.7 : p < 0.001 t Does not include one worker with unclassified lesion.

74.32* 61.9* 12.5 -23.4

Table 7.11 Comparison of blood lead and general characteristics of workers in two iron-forging factories by Wilcoxon Rank sum test (Chao et al., 1994). Reference factory

Exposed factory No. of

Median

Range

Male Female Working outdoors(total) Male Female Total No. Age (years) Duration of work (years ) % Male % Male smoker

Median Range

workers

workers Working indoors(total)

No. of

11

,ja,b

21-6

11

5C

5-4

6

15

21-6

4

5

5-4

5

11

14-9

7

4

5-4

25

24a

49-10

36

5.5

20-4

24

23

49-10

31

6

20-4

1

40

5

4

5-4

36 33 ±9.6

47 35.1+11.5 6.7 ±5.4

3.011.7

74.5

83.3 43

57

a pO.001, if compared with the reference factory. b p0.1, if compared with working outdoors and stratified by sex. d p = 0.003, if compared with workers employed for more than 2 months by the same factory.


7.4

Summary

Based on the inferences made, empirical research can be classified into two types: descriptive and causal. In descriptive studies, one defines the objectives, chooses accurate and sensitive measurement methods, selects representative population through proper sampling methods, and then goes to the field to measure and collect the data. If the response rate is very low, then one may try to perform random sampling of the non-respondents to determine if non-response is related to the effect or items of measurement. If all determinants involved in the measurement process and all determinants of outcome are similar for respondents and non-respondents, then one can draw conclusions about the source population from the small group of respondents. Otherwise, one should only draw inferences about the respondent population, which must be specified or characterized. For causal studies, one should prevent or control confounding during the study design stage. Confounding occurs if there are any alternative causal determinants, which can partially or totally explain the effect of exposure. Since a confounder is inherently a causal determinant of outcome, one should search for all such determinants through a comprehensive literature search and consultation with experts. Then, one should examine the distribution of each causal determinant among the exposed and non-exposed populations, in order to determine if any determinants are associated with the exposure of interest. After uncovering the potential confounders in one's study, one can prevent confounding by restrictive selection of subjects, or control it by stratification and/or modeling in the data analysis. The main theme of this chapter is also summarized in Figure 7.1.


Define the objectives

i Perform a Descriptive studies

literature search

Causal studies

and consult experts. ^ List all causal determinants of List all determinants of

outcome and all determinants of

measurement and its contents.

the measurement

Choose accurate, sensitive and

Choose accurate, sensitive and feasible measurement methods for exposure, outcome and other causal determinants of outcome.

feasible measurement methods.

i

I

Select the exposed and non-exposed groups, according to strategies for controlling potential confounders.

Select the population to be measured.

I Decide on a sampling method for the exposed and non-exposed populations, based on the strategies: restriction of the sampling population or stratification and/or modeling in the data analysis.

I Decide on a sampling method.

Decide on methods for data analysis.

Go to the field to carry out the study. Figure 7.1

Diagram on how to design descriptive and causal empirical studies.


Quiz of Chapter 7 1-5 300 cases were collected and followed up for stroke every 3 months for 1.5 years, and the following life table data were obtained. Please fill in all the blanks of the table. Interval

No. lost to

No.

No. deaths No. entering No. at risk

(month)

follow-up

withdrawn

interval

rate

alive

per month

1-3

10

4-6

10

5

15

7-9

10

10

10

10

mortality

20

10-12

15

10

5

13-15

25

10

5

300

290

0.023

Please write down the probability (%) that the assertion is true. You will be scored according to the credibility of your subjective judgment. Score % 6. When the response rate is not high, e.g., 42%, then the result cannot be generalized to the entire population. 7. In a study of lung cancer among asbestos workers, if one has not collected data on smoking, one cannot rule out the possibility of smoking as an alternative cause. Thus, one may have difficulty in drawing a conclusion. 8. Even if the response rate exceeds 85% or even 90%, one still cannot draw a definite inference on a divorce rate of 5% because many people who are divorced may not have responded. 9. If all other determinants of outcome for the exposed and


non-exposed are comparable, there will be no confounding in the conclusion. 10. In causal studies, we are always looking for alternative hypotheses that have not yet been refuted.

Answers:(6) F (7) T (8) T (9) T (10) T

(l)-(5) Please see Table 6.8 for details: No. at risk = No. entering interval - 1/2 (No. censored=No. withdrawn alive +No. lost to follow-up) Mortality rate per month =

No. death Total No. of person - months No. death 3 monthx(No. a trisk-l/2(No.

Interval (months')

No. lost to follow-up

No. withdrawn alive

No. death

No. entering interval

1-3 4-6 7-9

10 10 10 15 25

10 5 10 10 10

20 15 10 5 5

300 260 230 200 170

10-12 13-15

death))

No. at risk

Rate per months

290

0.0238

252.5

0.0204

220

0.0155

187.5

0.0090

152.5

0.0111


Chapter 8

8.1 8.2 8.3 8.4 8.5 8.6

Adjustment and Standardization of Rates

Components of crude rates Adjustment or standardization of rates Standardized mortality or morbidity ratio (SMR) and indirect standardization Precision maximizing weight SMR computed from a case-control study Summary

Introduction As discussed in Chapter 6, the basic measurements of epidemiology include rate, incidence rate, and prevalence rate. Their purpose is to measure the characteristics (states or events) of a population. Since a population is generally heterogeneous, in which people possess a variety of characteristics (different age, gender, and occupation), there are many determinants which can explain an overall crude rate. In contrast, age-, sex-, and ethnic-specific rates are simpler because certain determinants have been ruled out in the etiologic study. However, oftentimes for mostly administrative purposes, a crude rate, such as the crude mortality rate of a country, may provide a simple summary of a heterogeneous group. Each crude rate is a summary of different component rates weighted by some population distribution. When looking at two or more different rates, epidemiologists must pay careful attention to how crude rates are weighted to make valid comparisons. In this chapter, we will first discuss the components of crude rates and their adjustment or standardization. Then, we will consider the special case of standardized mortality ratio (SMR) and indirect standardization, which actually utilizes a set of weights closely approximating the precision maximizing weight. Finally, we will look at how to obtain SMR through a

197


case-control study design. Throughout the discussion, incidence rate will be used in our examples, but these examples can also be generalized for other types of rates such as prevalence rates. 8.1

Components of crude rates (Miettinen, 1972a)

According to the definition of a crude incidence rate (See Section 6.3), it is the total number of new cases divided by the total number of population-time at-risk. Assume that a, is the number of new cases and Nj is the number of population-time at-risk in the i"1 stratum, then the crude incidence rate can be expressed as:

Crude incidence rate = I

In fact, crude incidence rate can also be viewed as a summarization or summation of a group of individual specific rates of each ilh stratum (a: / Nj) weighted by its corresponding population-time at-risk (Nj), i.e.,

Sa,

INK—)

;

Nj

I Nj /

IN; i

For example, in Table 8.1, the crude mortality rate of employees in financial institution X is the total number deaths divided by total population-time at-risk, 50/(29,335 x 1) year"1 = 1.70 x 10"3year"'. This crude rate can be rewritten as an expression of component age-specific mortality rates, as follows:

Chapter 8 Adjustment and standardization of rates 199

[(9399 x 1) x

+(7402 x 1) x 9399x1

+...+ 7402x1

( 5 3 x l ) x - i — ] ^[(9399 + 7402+...+53) x 1 year] = 53x1 1.70 x 10"3year"' Similarly, one can use the strata-specific component rates to calculate the crude rates of a teacher's association, a hypothetical occupational group, and the general population of Taiwan as 1.57 x 10"3 year"1, 3.25 x 10"3 year"1, and 5.86 x 10"3 year"1, respectively. Here, the population distributions for each age-specific group serve as the corresponding weights (namely, Nj = W;) needed to obtain the crude rates. If one applies a population distribution outside of the group in question, such as the general population of Taiwan, as weights for the set of component rates, then these rates have undergone an adjustment. 8.2

Adjustment or standardization of rates

Because each crude rate has its own individual set of component rates and weights, the comparison between two or more crude rates may be confounded by the different weighting schemes. For example, in Table 8.1, all age-specific mortality rates (see columns labeled ASMR) of the teacher's association are the same as those of another hypothetical occupational population. However, their crude rates are very different: 1.57 vs. 3.25 x 10"3 year"1. This variance results from different population counts for each individual rate. For instance, there are more people in the age bracket from 30-34 in the teacher's association than there are in the same age group for the hypothetical occupational population. Thus, even though the two groups have the same age-specific rates for each age strata, these rates are weighted differently. The crude mortality rate of the teacher's association is as follows: [(26,627 x 0.30 x 10"3 year"1 + 31,897 x 0.44 x I0"3 year"'+ ... + 748 x 4.01 x 10-3year-')]-H [(26,627 + 31,897 + ...+748)] = 1.57 x 10"3year"'


The crude rate of the hypothetical occupational population is as follows: [(6,667 x 0.30 x 10"3 year1 + 9,091 x 0.44 x 10"3 yeaf' + ... + 27,181 x 4.01 x 10"3 yeaf')]-H (6,667 + 9,091 + ... + 27,181) = 3.25 x lO^yeaf1 Thus, if one wants to compare two or more crude rates, one needs to apply the same set of weights to their component rates. Such a procedure is called adjustment or standardization of rates, and the set of weights is usually chosen from a "standard" population distribution (Miettinen, 1972b). The formula of adjustment can then be written as:

IW,. A ) TV. , where W, is the weight chosen for stratum i. /

In Table 8.1, if we apply the national population distribution as the standard set of weights, then the age-standardized mortality rate of the financial institution X becomes as follows: [[(1,768,454 x 1 x 0.53) + (1,430,984 x 1 x 0.54) + ... + (467,117x1 x 18.88)] xl0-3]-^(l,768,454 + 1,430,984 + ... + 467,117)x 1 year = 3.20x 10'3 year"' Similarly, one can calculate the age-standardized mortality rates for the teacher's association, hypothetical occupational population, and general population as 1.87 x 10"3 year "', 1.87 x 10 3 year"1, and 5.86 x 10"3 year "', respectively. It turns out that the standardized mortality rate of the teacher's association is the same as that of the hypothetical occupational population, because the same set of weights, the general population distribution of

Table 8.1

Age

Comparison of age-specific mortality rates (ASMR), cumulative mortality rates (CMR30.69), age-standardized mortality rates, and standardized mortality ratios (SMR) for employees of a public financial institution X, members of a teacher association, a hypothetical occupational population, and the general population (GP) of Taiwan, 1987. Employees of a

Members of a

A hypothetical

financial institution X

teacher association

occupational population

No. of Pop. ASMR No. of deaths count 10"3 year"1 deaths

30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 30-69 CMR3OJ»

Age-standardized mortality rate (GP of Taiwan as standard weights) SMR (GP of Taiwan as reference population)

5 4 6 4 7 12 11 1

9,399 7,402 4,200 2,801 1,965 1,926 1,589 53

0.53 0.54 1.43 1.43 3.56 6.23 6.92 18.88 crude rate 50 29,335 1.70 179.14X10"3

3.2 X 10"3 year"1

0.47

8 14 25 31 35 57 44 3

Pop. count 26,627 31,897 23,548 20,735 13,808 11,838 8,754 748

217 137,955 W.76 X

ASMR No. of Pop. ASMR 10-3 deaths count lO"3 year"1 year"1 0.30 2 6,667 0.30 0.44 4 0.44 9,091 1.06 11 1.06 10,377 1.50 18 11,989 1.50 2.53 56 22,135 2.53 4.82 117 24,272 4.82 5.03 132 26,243 5.03 4.01 109 27,181 4.01 crude rate crude rate 1.57 449 137,955 3.25 93.76 X 10"3 0"3

1.87 X 10"3 year"'

0.42

1.87 X 10"3 year'1

0.16

General population of Taiwan No. of deaths

Pop. count

ASMR lO"3 year"1 1.38 1.84 2.84 4.17 6.30 9.53 15.04 24.32 crude rate 5.86

2,444 2,635 2,558 3,772 5,056 7,494 9,860 11,362

1,768,454 1,430,984 901,802 903,857 802,202 786,726 655,426 467,117

45,181

7,716,568 278.99X10"3

5.86 X 10'year 1

1


Taiwan, are applied to both. Thus, adjusting the age-specific mortality rates to obtain age-standardized mortality rates eliminates the confounding factor of different population distributions, and one can then make more valid comparisons between the two groups. Adjustment or standardization of rates can be regarded as one way to control confounding and has been widely used in the comparison of two or more populations or sets of component rates. 8.3 Standardized mortality or morbidity ratio (SMR) and indirect standardization When one wants to compare the mortality rates of two populations, adjustment with the same set of weights or population distributions is usually necessary to control confounding. The population of interest is often a cohort population with a particular exposure. It is called the index or exposed population, while the comparison group is a population without the exposure and is called the reference or non-exposed population. Here, the reference population will not be referred to as the "control" population, in order to prevent any confusion with the control group of a case-control study. In fact, one can rarely perform a "control" experiment in observational human studies. One of the most commonly used rate ratios for comparing mortality between the index and reference populations is the SMR, originally defined as an observed-to-expected ratio. The observed is the sum of the number of observed deaths for each stratum i of the index population (a;), while the expected is the sum of the expected stratum-specific mortality rates of the reference population, adjusted by the population-time distributions of each stratum i from the index population. Namely,


lai '

observed SMR =

£N,i(

= expected

—) Nn

=

XN,i(

bj N0i

)

ZNn( '

bj

)

N0i

where aj = no. of deaths for stratum i of the index population bj = no. of deaths for stratum i of the reference population Nn= no. of person-years observed for stratum i of the index population Noi=no. of person-years observed for stratum i of the reference population. In fact, SMR can be regarded as the overall weighted rate ratio of the two sets of component rates, in which the stratum-specific population-time distributions of the index population are used to weight both rates. However, to calculate SMR, one does not need to adjust the stratum-specific rates of the index population to calculate this ratio. Accordingly, calculating SMR has been labeled "indirect standardization" to distinguish it from direct standardization. As discussed earlier in Section 8.2, direct standardization involves directly multiplying the stratum-specific rates of two or more index populations with the weights of a reference population distribution. SMR, however, is a special case for the more general case of the comparison of overall rates for two populations, in which the same set of stratum specific weights are applied to the component rates of index and reference populations. Assume the same notations as before, the general comparison of two sets of rates can be expressed as:


iw,.(^)/zw ;

?W*(-S-)

iw, A / z w ,

£w;(-^-)

#0/

'

'■

N

0i

When Wj= N n , this rate ratio becomes the SMR, or observed-to-expected ratio. Because the weights taken for each SMR study are the specific index population distributions of that study, the SMRs obtained for different index populations cannot be directly compared. For example, if one employs the general population as the common reference population for the index populations of the teacher's association and the hypothetical occupation, then the SMRs calculated for each one of them cannot be directly compared because the set of weights assigned are different. The SMRs of the two occupations are 0.42 and 0.16, respectively. They are obtained by the following calculations: 217 /[(26,627 x 1 x 1.38 + 31,897 x 1 x 1.84 + ... + 748xlx24.32)xl0 - 3 ] = 0.42 449 /[(6,667 x 1 x 1.38 + 9,091 x 1 x 1.84 + ... + 27,181 xlx24.32xl0" 3 ] = 0.16 As shown in previous sections and in Table 8.1, these two index populations share exactly the same age-specific mortality rate, but possess different SMRs and crude rates because of different weights employed in the calculation. Similarly, one cannot directly compare the SMR of the financial institution, which is 0.47, with the other two occupational populations for the same reason. Therefore, two or more SMRs can only be compared if they use the same set of weights and reference component rates. If not, then the results are confounded by either one of these two factors. Because epidemiologists from different


countries still debate the validity of using a universal set of weights for standardization (Doll, 1976), some have recommended using the cumulative incidence rate (CIR, Davis, 1978; Miettinen, 1985a). CIRs can be directly compared if the cumulative age period is the same. The CIR30-69S of each population in Table 8.1 are calculated as follows: -X (Age-specific rates) t CIRrfl-r, = 1-e Since t = 5 for each age stratum, then, CIR30-69 of employees in the financial institution -(0.53 + 0.54 + ... + 18.88) X 10"3 X 5 = 1-e = 179.1 x 10"3 CIR30-69 of the teacher's association -(0.30 +0.44+ ...+4.01) X 10'3 X 5 = 1-e = 93.8 x 10"3 CIR30-69 of the hypothetical occupational population -(0.30 +0.44+...+4.01) x 10"3 X 5 = 1-e = 93.8 x 10"3 CIR30.69 of the general population -(1.38 + 1.84 + 2.84 + ... +24.32) X 10"3 X 5 = 1-e = 279.0 x 10"3 The above CIRs can be directly compared and interpreted because every year is uniformly weighted. When CIR « 0.1, then a; CIR,i_,2 = X(stratum-specific rates) t, = £ ( ) tj.

'

H

For cancer incidence rate, the above assumption is generally acceptable. Thus, Davis (1976) has recommended this simple formula for the international


comparison of cancer incidence rates. 8.4

Precision maximizing weight

From a statistical point of view, to maximize precision, one may choose a set of standard weights, which considers the variances of both populations. Under the null hypothesis, the precision maximizing weight depends on the population distributions of both index and reference populations for stratum i, Nu and Noi, respectively. W-

'

=

] =

1/N ]i+ 1/N 0i

(N,,)(N oi ) N„+N0|

If Noi » Nu, then Wj = Na. Conceptually, this means that when the index population is much smaller than the reference population, the precision maximizing weight is approximately equal to the index population. Thus, the SMR calculation, which is commonly used to explore a particular occupational population, is very close to the precision maximizing weight because a specific occupational group is generally much smaller compared to the general population. SMR can also be calculated from a case-control study design, but this will be discussed in the next section. The CIR calculation, however, assumes uniform age-specific rates, which sometimes overweighs the older age strata because these strata usually possess small numbers of population-time-at-risk. As a result, epidemiologists can still use both SMRs and CIRs, but they need to be careful about their limitations. 8.5

SMR computed from a case-control study

Although case-control study design is discussed more fully in chapter 11, it deserves some discussion here to give readers a broader understanding of SMR. Because SMR is an observed-to-expected ratio, it can be obtained by a


case-control study without collecting the actual information of population-time at-risk. Consider the example of determining the causal relationship between blackfoot disease and drinking artesian well water (Chen et ai, 1988). Blackfoot disease is a peripheral vascular disease involving gangrene of the feet and toes, which was prevalent in four towns of Southern Taiwan. For age stratum i, we collected (a, + bi) cases of blackfoot disease and inquired their histories on drinking water from artesian wells. It turned out that a; cases were exposed and bi cases were non-exposed to artesian well water. We also randomly collected (c; +di) local residents without the disease but of similar ages and sexes, and asked their histories of exposure. The numbers of exposed to non-exposed were C| and dj, respectively. Then, without obtaining the population-time at-risk for the exposed (Nil) and non-exposed (Na), we could calculate the SMR, as shown in Table 8.2.

Table 8.2

SMR (standardized morbidity ratio) can be obtained by a case-control study design, as illustrated by the study on drinking water from artesian wells and blackfoot disease in four endemic towns of Taiwan (Chen et ai, 1988). Drinking artesian well water Yes

Blackfoot disease Population-time at-risk

Yes No

Ci

N,i

No b,

Total

di

ai+bj q + di

N0j

N.j + Noi

Because sampling procedures for (aj + bi) and (Ci + di) are both unrelated to the exposure of artesian well water, the ratio, ai / bi, estimates exposure odds for drinking well water of people with blackfoot disease, Ai / Bi; while q / dj estimates


the exposure odds of the population-time at-risk, N u / Noi. Then, SMR can be calculated by summarizing them across the i,h strata in a case-control study:

SMR =

'ZNB(btINu)

=

i Z(N H /N 0i ) i

5X _

i

i

8.6

Summary

A crude rate can be viewed as a summary of a weighted set of component rates. Therefore, two crude rates cannot be compared unless the set of weights are the same or similar, which requires an adjustment or standardization procedure. SMR is an observed-to-expected ratio, which is actually standardized with weights taken from the index population for both the numerator and the denominator. Two or more SMRs cannot be directly compared unless both sets of reference rates and weights are the same. CIRs, however, can be directly compared if the cumulative period is the same. For statistical efficiency, one may choose to use precision maximization weights as the standard weights, which can be obtained through SMR calculation. Moreover, SMR can also be obtained through a case-control study design when one does not have information on the population-at-risk or any other denominator data.


Quiz of Chapter 8 Please write down the probability (%) that the assertion is true. You will be scored according to the credibility of your subjective judgment. Items 6-10 will be scored according to the exact correct answer instead of judgmental scores. Score % 1. A crude rate is a summarization of individual specific rates weighted by population-time at-risk. 2. There were 3 SMR studies of lung cancer among asbestos workers. The first one, reported from Sweden, had an SMR of 7, the second and third from the U.S. reported SMRs of 4 and 5, respectively. One can say that Swedish workers were exposed to a higher concentration of asbestos than that of Americans' because the SMR of Swedish asbestos workers was higher. 3. A confounder must be a causal risk determinant. 4. SMR is usually using a set of precision maximization weights because an industrial cohort is usually much smaller compared with the general population. 5. Data from case-control study can be used to calculate SMR. 6-10. There are 4 reports with different follow-up periods and recurrences of breast cancer. (A) 10 cases recur out of 100 cases within 6 months; (B) 20 recur out of 100 cases within 1.5 years; (C) 30 recur out of 100 cases within 2 years; (D) 50 recur out of 100 cases within 3 years. Please calculate the average recurrence rates for each study. A recurrence of cancer is an event, so please


6. 7. 8. 9. 10.

use the same unit for comparison. (A) (B) (C) (D) Please arrange the above rates in the ascending order. < <
is related to the standard deviation S.D. of the sample:


oy - \S IV n jy/l - (j)

where <j> = n / N (N is the population size). If the population has a limited number of units or subjects, then the sampling fraction, i.e., (j>, must be corrected. However, most texts assume that, N, the population number, is close to infinity, then -> 0, and the correction factor 1 - <j> can be ignored. For example, if the size of population is 200,000, 20,000 or 2,000, a sample of 100 or less makes little difference in the correction factor 1 - ^ . In fact, when < 0.10, ^j\- is usually close to 1. If one samples a population to inquire about a positive health event or state, then one may rewrite the formula as follows: Let p denote the proportion of members with the event or state in the population, and q be that without the event or state, so that q = 1 - p; then the standard deviation (S.D.) of p is

For example, in a survey conducted among a community of 432 families to determine how many of them regularly watch CNN news, one randomly samples 50 families and finds that 10 out of 50, i.e., p = 0.2, watch CNN news regularly. The standard deviation of the sampled proportion is then:

l(0-2X0-8) j - J O . .Q.Q53 V 50 V 432 If one omits the correction factor, then it becomes 0.057.

Chapter 9 Sampling method and practical applications 219

9.4

Stratified random sampling

To achieve a higher efficiency, one may divide the population into several sub-populations or strata according to the determinants of outcome so that there is small variation within the sub-population but large variations between or among sub-populations. Then, one may reduce the sample size within each sub-population or strata. 9.4.1 Principles of stratification In order to perform stratified random sampling, one needs to obtain prior information about the determinants of outcome in order to form the basis for stratification. Let us examine the following examples. Example 9.5

HIV infection in Bangkok

If one wants to study the prevalence rate of HIV (human immuno-deficiency virus) infection among the adult population of Bangkok, one attempts to select a random sample. Since the prevalence rate may be around < 5%, one probably needs a big sample size, say 1000 or more. However, if one possesses information of a higher carrier rate among a younger age group, then one can probably stratify the whole population into 3 - 4 age strata {e.g., >60, 45-59, 30-44, 15-29) and perform random sampling within each stratum with a reduced sample size for the younger age strata. For example, if the prevalence rates for old and young age groups are around 1-2%, 3-4%, respectively, then one may allocate more samples to the old age group because their prevalence rates are smaller and variance is larger than those of the younger age groups. In other words, one may improve sampling efficiency by stratifying the population into several relatively homogeneous sub-populations. Example 9.6

Disease patterns and frequency of use of Taipei's emergency medical services

To determine the disease patterns and frequency of use of the emergency


medical services in Taipei, one might perform simple random sampling of 11 hospitals providing such services. However, each hospital may have different characteristics and/or emphases on providing services. For example, some hospitals have neurosurgical or burn units; some have a team for extracorporeal circulation; while others have MRI (magnetic resonance imaging) instruments; some focus on psychiatric patients, etc. Because the demand for emergency visits for certain diseases, e.g., ophthalmic or psychiatric emergency, only occupied a small proportion (as previously shown on Table 7.2), investigators decided to treat each hospital as a separate strata to avoid missing important diseases, which make up only a small proportion (Chiang et al., 1986). Thus, the stratified random sampling may improve sampling efficiency, when compared with simple random sampling. The basis for stratification is generally based on prior information or prior studies, so that small variations exist within each stratum, but large differences exist between or among individual strata, which may be rechecked after empirical samples are obtained. 9.4.2 Estimation of the mean and standard deviation of stratified random samplings Once sampling is finished, one needs to calculate the overall mean and/or standard deviation by appropriately weighting the original proportion of each stratum. Let Nj denote the total number of sub-population or stratum i, y{ indicate the mean of stratum i, and N represent the total sum of all sub-populations. Then, the overall mean of the population (y"st) is calculated as follows: y * = X N& /N = YJ Wtyt , (where W, = N, / N) i

I

i

Namely, the sample in each sub-population should be weighted by Wb which is determined by the proportion of each sub-population, N; / N.

Chapter 9 Sampling method and practical applications 221

The variance or standard deviation is as follows: Assume that sample size and S.D. in the ith stratum are n; and Si, respectively. Let ^jdenote the sampling fraction of stratum i, i.e., 0,- = nj/Ni, then: Var(y;) = S i 2 (l- '

J

JJlR0(t)dt

£/i?iWA' =±

£IRomt

= IRR

'0

Thus, IRR is an approximation of risk ratio when the disease is rare and the observation time is short. Alternatively, if we reconsider risk ratio approximation from Cornfield's concept and assume that the disease is rare and no change of exposure proportion during the study period, then Riskratio= ™L = ^ CIR 0

« MN.-A)

B/N 0

=

B/(N0-B)

MN,-A) = B/(N0-B)

i/f. b/d

Again, one can calculate a / b from a sample of cases (a + b) to estimate A/B, and one can calculate c/d from a sample of controls (c + d) to estimate (N, A)/(N 0 -B). Based on the above concept, if one obtains both cases and controls in a cross-sectional survey, then one has obtained prevalent cases and controls, and one can then calculate the prevalence odds ratio (POR), which is the ratio of the prevalence odds of cases (a/b) and the prevalence odds of controls (c/d). The POR value can be an estimate of risk ratio, as well. P0R =

£d = (,/N,xd/N0) be

(b/N0)(c/N,)

=

crc,(i-crc 0 ) = a* C7R0(1-CK,)

= Rjsk

^

CIR0

Therefore, Miettinen's concept of density sampling, which does not require any assumptions, revolutionized case-control study design and can be applied to all kinds of diseases. Specifically, one can now apply case-control studies to other non-rare acute diseases, such as injury-related health problems (Tsai et ah, 1995). One can also carry out case-control studies concurrently within a cohort to save resources-(e.g., as in a cohort study of vinyl chloride monomer exposure and liver cancer (Du and Wang, 1998). Moreover, with density sampling, one can now conduct case-control studies initiated by the


control group (Greenland, 1985), multiple control groups (Fairweather, 1987; Liang and Stewart, 1987), etc., in addition to initiation by case series. Essentially, as statistical methods advance, the applications for case-control studies grow ever larger. Case-control design can be regarded as a general solution for calculating incidence rate ratio, when one lacks data on population at risk because the random sample of controls can consistently estimate the odds of population-time at risk between the exposed and the non-exposed ([N.Ct.-gj/fNoCtrto)]). 11.2.4

The proportional hazard model

Cox (1972) proposed a mathematical model to represent the risk of developing a particular disease based on the concept of proportional hazard. This concept is the same as incidence rate under the condition that the person has survived up to the specified time. In other words, one has successfully dealt with time and expressed the incidence rate through a probability model. Prentice and Breslow (1978) applied the proportional hazard model to case-control studies and reached the same conclusion as that obtained from density sampling. Moreover, the direct development of statistical methods from this model have facilitated its practical use (Breslow and Day, 1980; Liang and Stewart, 1987). Finally, it also provides flexibility for modeling the change of exposure as a function of time, further enlarging the potential applications for case-control studies. For those familiar with the concept of modeling, this approach can be very powerful and versatile. However, it may not be easily understandable for most physicians and lay people, who in general are unfamiliar with statistical models. I recommend that beginners in epidemiology understand the concept of density sampling first when utilizing case-control studies. Later, one can study modeling for data analysis or simply consult a statistician.

Chapter 11 Case-control study 271

11.3 Practical selection of cases and controls based on the principle of density sampling (Miettinen, 1985b; Wacholder et al. 1992a, 1992b, 1992c; Rothman and Greenland, 1998) In practice, one can usually perform in either one of the following two ways: The first approach is tc define the population at risk, and then try to collect every new case that occurs during the period of study. For every case, one tries to sample one to several controls matched in time of occurrence and/or age. A second method is to define where one can collect new cases (numerator data). Then, define who the population at risk are and perform sampling amolfg them. Let us examine several examples for illustration: Example 11.5

Preventive effect of helmets - An example of density sampling

In a study to determine the preventive effect of different types of helmets for head injury, Tsai et al. (1995) decided to use all Taipei City residents as the population at risk. Therefore, eligible cases were all new case0 of motorcycle accidents occurring between Aug. 1 and Oct. 15, 1990 from 16 hospitals governmentally approved for emergency care. The investigators sampled two controls groups, emergency room and street, by density sampling. The emergency room control group consisted of motorcyclists who sought emergency care other than head injuries at one of the 16 hospitals. The street controls were matched with cases in time and place of accident. Sampling of the street controls occurred one week after each case, by simply taking four consecutive photos of passing motorcyclists. Investigators used the first motorcyclist appearing in each of the four pictures as the street control and determined his/her helmet-wearing state, age, sex and type of motorcycle. All cases and controls were sampled without any preference to helmet use. After controlling potential confounders by multiple logistic regression analysis, Tsai et al. found that both groups showed relatively consistent protective effects for different types of helmets, as summarized in Table 11.5. Specifically, a full-face helmet showed a protection factor of 3, while a partial coverage helmet provided a doubtful 25% protective effect.


Example 11.6 Etiology of bJackfoot disease - An example of cumulative sampling Chen et al. (1988) conducted a case-control study to examine multiple etiologic agents for blackfoot disease (BFD), an endemic peripheral vascular disease in southern Taiwan. They recruited";!!1 living cases of BFD residing in the 4 townships within the endemic area as case scries. Since all individuals within the endemic township were at risk, they randomly sampled three controls matched for age, sex and residence for every case. A total' of 24.1 BFD patients and 759 matched healthy controls were identified and interviewed. Multiple logistic regression analysis showed that ttie duration of artesian well water consumption was positively associated with the development of BFD in a dose-response relationship, as summarized in Table 11.6. Both arsenic poisoning and family history of BFD were also found to be significantly associated with the disease. Returning back to the examples introduced earlier in this chapter, we will now discus^ now to select cases and controls for each of them. In Example 11J, all Taipei residents were identified as the population at risk. The odds of population-time at risk for different methods of commuting can then be estimated by taking samples from the street. This approach is similar to the method of sampling street controls in Example 11.5. In Example 11.2, since NTUH is a medical center or a tertiary care center, patients may come from all over Taiwan. Thus, one may find it difficult to determine the population at risk, which here consist of people who will go to NTUH if they develop lung cancer. However, one may use NTUH patients with diseases unrelated to the exposure (smoking) as controls because these patients would probably enter NTUH if they had developed lung cancer instead. Diseases known to be related to smoking, such as chronic obstructive pulmonary diseases, laryngeal cancer, bladder cancer, ischemic heart disease, etc., must be excluded as candidates for control samples. Moreover, due to reasons of accessibility or connections, one may want to sample another group of controls from people living in a nearby neighborhood, workers from the same factory, and/or friends or relatives of hospital employees. These people

Chapter 11 Case-control study 273

Table 11.5

Adjusted odds ratios of different risk predictors of head injury computed from multiple logistic regression analysis (Tsai et al., 1995).

Risk predictors

Helmet type Full face vs. no helmet Partial coverage or full vs. no helmet Weather Rainy vs. Sunny Cloudy vs. Sunny Place At intersection vs. not at intersection Motorcycle type RS vs. STI* UB vs. STI* STIII vs. STI* STII vs. STI* Riding position Driver vs. passenger Age (years) < 29 vs. > 65 30-64 vs. >65 Sex Male vs. female

Unconditional logistic regression analysis; emergency room (cases,, n=562; controlss, n=789) Odds ratio 95% confidence interval

Conditional logistic regression analysis; (daytime cases, n=224; matched street controls, n= 1,094) Odds ratio 95% confidence interval

0.26 0.72

0.14-0.47 0.38-1.37

0.36 0.73

0.13-0.98 0.36-1.47

1.31 1.31

0.91-1.87 0.96-1.79

3.32 0.72

1.60-6.86 0.35-1.50

0.99

0.79-1.24

0.86 1.09 0.92 1.03

0.56-1.32 0.76-1.56 0.65-1.29 0.76-1.39

1.55 0.83 0.53 3.71

0.81-2.97 0.50-1.37 0.34-0.83 2.31-5.95

1.10

0.83-1.47

1.22

0.76-1.96

0.68 0.63

0.50-0.92 0.44-0.89

0.68 0.69

0.26-1.81 0.25-1.87

1.02

0.78-1.33

0.64

0.43-0.95

RS, racing sport type; UB, utility bike; STI, STII and STIII, step-through types with a stroke volume of < 50, 51-99, and > 100 cc, respectively.


Table 11.6

Multiple logistic regression analysis of risk factors associated with blackfoot disease (Chen et al., 1988).

Variables Artesian well water consumption (yrs) 0 1-29 >30 Arsenic poisoning No Yes Familial blackfoot disease history No Yes Staple food consumed Rice Rice + sweet potato Sweet potato Vegetable consumption frequency (days wk) 7 4 1 to 3 4 1 to 3 l _ , 2 A 2 J \ 2 A 2 / 1 2 A 2

,

In real numbers, the QASn - QASap is equal to 16.68 - 5.36 = 11.32

Chapter 13 Health Policy Application 317

QALYs, which can be regarded as the utility gained from the successful prevention of an average case of angina pectoris. If one takes an annual discount rate into consideration (e.g., r = 0.03)(The World Bank, 1993), then the expected utility loss from getting angina pectoris is 12.69 - 4.62 = 8.07 QALY. patients with angina general population

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 Years After Diagnosis

Figure 13.3 Survival curves of patients with angina pectoris and for the population during the thirty years after diagnosis (Wang et al., 2000).

In addition, one can multiply the QALYs gained with the number of affected cases to obtain the expected total utility gained. In practical terms, one can first establish a cohort by enrolling all patients (say, 500 or more) diagnosed with a specific disease X( from a specific hospital during the last 10 years, which can be followed and compared with the death certificate database composed by the Department of Health to obtain the survival function. Then, a stratified random sample of 50-100 patients with different durations-to-date were surveyed with the QOL questionnaire (e.g., WHOQOL-BREF) and utility measurement, which can estimate the QOL function of the disease X;.


patients with angina general

1.2 $

l

°

0.8

\ _

population

0.6 0.2 0

J

I

0

I

2

I

4

I

I

I

6

l__l

8

!

L_l

10

I

12

L

14

16

Years After Diagnosis Figure 13.4 QOL curves of patients with angina pectoris and for the population during the thirty years after diagnosis (Wang et al., 2000).

■ patients with angina general population

0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 Years After Diagnosis

Figure 13.5 QAS curves for patients with angina pectoris and for the general population during the thirty years after diagnosis (Wang et al., 2000).


The expected value of QOL is multiplied with the corresponding survival rate at time t to obtain the QAS curve for the disease X;. Moreover, Hwang et al (1999) further showed that the curve can be extrapolated throughout life, if the cohort population has been followed up for about 3-5 years. The break-through has made the estimation of QALE (quality-adjusted life expectancy) for most chronic diseases possible. Hwang and Wang (2001) have recently demonstrated that similar results can be obtained if we replace utility values by psychometric scores for each health profile items or facets, of which the meaning can be interpreted as survival-weighted psychometric scores. Let us use Example 13.3 for a more detailed illustration of how one can estimate the total utility gained in the first 12 months of the implementation of a helmet law for motorcyclists in Taipei. Example 13.3

Helmet regulation

First, investigators randomly selected 400 out of 8221 registered head injury cases in Taipei during 1989-94, of which they successfully assessed 99 current health profiles (Tsauo et al., 1999). They converted these profiles to corresponding utility values of IHRL (index of health-related quality of life, proposed by Rosser et al., 1992) and constructed the survival function, HRQL, and quality-adjusted survival of head injury from 7 years of follow-up of 400 cases, as shown in Figures 13.6 - 13.8. Head injury is one of the main causes of death from motor vehicle injury in Taipei, of which the estimated annual incidence rate was 1.82*10"3 year"1 (Ding et al., 1993). 64.6% of all motor vehicle injuries involved head injuries and 80% of these injuries involved motorcyclists (Ding et al., 1994). The incidence rate of head injury among motorcyclists was 9.41 * 10"4 year"1, as shown on Table 13.2. According to Tsai et al. (1995), the odds ratios (OR) of head injury with no helmet, full-face helmet and partial coverage helmet were 1.0, 0.31 and 0.73, respectively. At the time, the proportions (Pe) of no helmet (Pe,), full-face (Pe2) and partial coverage helmets (Pe3) were 88%, 8.5% and 3.4%,


1.2

0.4 0.2

0

_L.._J

16

J

11 16 21 26 31 36 41 46 51 56 61 66 71 76 81

Axis of abscissas: month Axis of ordinates: survival probability reference population head injury cases Figure 13.6 The survival function of head injury cases and the reference population in the 80 months after onset (Reprinted from Accident Analysis & Prevention, 31, Tsauo JY, et al. Estimation of utility gain from the helmet law in Taiwan by quality adjusted survival time, 253-63, Copyright (1999), with permission from Elservier Science).


1.2 '

0.8 0.6 0.4 " 0.2 0 '

' 1 6

' 11

' 16

' 21

' 26

' 31

' ' 36 41

' 46

' 51

' 56

' 61

' 66

' 71

' ' 76 81

Axis of abscissa: time after onset of head injury in month Axis of ordinates: health-related quality of life reference population head injury cases Figure 13.7

The health-related quality of life (HRQL) of head injury cases and the reference population in the 80 months after onset (Reprinted from Accident Analysis & Prevention, 31, Tsauo JY, et al. Estimation of utility gain from the helmet law in Taiwan by quality adjusted survival time, 253-63, Copyright (1999), with permission from Elservier Science).

respectively (Tsai et al., 1995). Thus, the incidence rate (IRi) of head injury for cyclists without helmets can be obtained by solving the following equation: (IRhi indicates incidence rate of head injury; IR2 and IR3 indicate incidence rates of head injury with full-face helmet and partial coverage helmets, respectively) Pe,(IR,) + Pe2(IR2) + Pe3(IR3) = IRM

322 Basic Principles and Practical Applications in Epidemiologica) Research

Pe,(IR,) + Pe2(OR2)(IR,) + Pe3(OR3)(IR,) = IRhi (0.88)(IR,)+ (0.085)(0.31)(IR,)+ (0.034X0.73XIR,) = 9.41 *10"4 year"1 IR, = 1.01*10"3 year1 The incidence rates of head injury for cyclists with full-face and partial coverage helmets could also be derived as 3.44x 10'4 and 8.10x 10"4 year"1, respectively. To estimate the number of prevented cases one year after enforcement of the helmet law, Tsauo et al. assumed that the proportion of motorcyclists with no helmet dropped from 88% to 5%, as reported by the traffic police department of Taipei. They also assumed that the ratio of full-face to partial coverage helmet remained at 8.5:3.4, so that the proportion of cyclists with full-face helmet would be 67.3% and partial coverage helmet would be 26.9%. The number of head injury cases before enforcement of the helmet law in one year was calculated to be 2541 cases, as shown in Table 13.2. The number of cases after one year of enforcement of the law was estimated to be 1241. (See Table 13.2.) Thus, the number of prevented cases was shown to be 1300 cases. Since the expected loss of utility per case of head injury (without consideration of an annual discount rate) is 4.8 QALYs, then the total utility gained by the intervention during the first year would be 4.8x (2541-1241) = 6,240 QALYs. The above calculation still does not take into account the potential utility gained from reduced severity and improved survival and HRQL from the protective effect of a full-face and partial coverage helmet in cases of head injury.


1.2

0.8

0.6 0.4 0.2 0

1

6

11 16

21 26

31

36

41

46

51

56

61

66

71

76

Axis of abscissas: month after onset Axis of ordinates: quality-adjusted survival reference population head injury cases Figure 13.8

The quality-adjusted survival of head injury cases and the reference population in the 80 months after onset (Reprinted from Accident Analysis & Prevention, 31, Tsauo JY, et al. Estimation of utility gain from the helmet law in Taiwan by quality adjusted survival time, 253-63, Copyright (1999), with permission from Elservier Science).


Table 13.2

Estimation of the expected number of prevented head injuries and QALYs (quality-adjusted life-years) gained under a helmet law enforced for one year. Assumption: the induction time for prevention of head injury is 0. (Prevention becomes effective when a person begins wearing a helmet while riding a motorcycle.) (Reprinted from Accident Analysis & Prevention, 31, Tsauo JY, et al. Estimation of utility gain from the helmet law in Taiwan by quality adjusted survival time, 253-63, Copyright (1999), with permission from Elservier Science).

No. of Taipei residents

2.7xl0 6

Incidence rate of head injury in Taipei

1.82x 103 year'1

Proportion of traffic injuries in head injury

64.6%

Proportion of motorcycle injury in traffic injury

80%

Incidence rate of head injury of motorcyclists

9.41X10"4 year"' (=1.82xl0"3x64.6%x80%)

Odds ratio of head injury for cyclists with

no helmet full-face helmet partial coverage helmet

Proportion of cyclists with no helmet before intervention

88%

Proportion of cyclists with a full-face helmet

8.5%

Proportion of cyclists with a partial coverage helmet

3.4%

Incidence rate of head injury for cyclists with no helmet

1.01 xlO"3 year"1

Proportion of cyclists with no helmet, after execution of law, reduced to: 5% Proportion of full face helmet

(1-5%) x (8.5/12) = 67.3%

Proportion of partial coverage helmet

(1-5%) * (3.4/12) = 26.9%

Number of cases before regulation in 1 year 2.7xl0 6 x9.41 xio-4(year"') x 1 year = 2541 Number of cases with head injury after enforcement of law for 1 year 2.7x 106 x 1.01 x lO"3 x (0.05+67.3%x0.3 l+26.9%x0.73) =1241 Total utility gained from the enforcement of the helmet law in 1 year 4.8x(2541-1241)= 6240 QALYs


In short conclusion, the effectiveness of health services can be evaluated by QAS method (for utility) and survival-weighted psychometric assessment (for health profile), which can be used in both the national health service resource allocation and clinical decision, as shown by Figure 13.9. 13.3 Risk assessment: Public health and individual viewpoints Another major contribution to health policy and management by epidemiologists is risk assessment. Although the definition of risk may not be universal, it is useful to discern the definitions of hazard, risk and detriment. Hazard is considered to be the intrinsic property or potential of causing harm. Some examples of objects, which can pose a hazard to people's health, are work material, equipment, work methods and practices. Risk is usually defined as the probability that an adverse event occurs during a stated period of time (or results from a particular challenge.) Detriment is a numerical measure of the expected harm or loss associated with an adverse event and is generally the integrated product of risk and harm, which is often expressed in terms of cost (such as US $, sterling, loss in utility of health or loss of productivity). In modern management system of occupational safety and health, however, risk is defined as a combination of the likelihood of the adverse event and its consequence, as proposed in the British Standard (BS) 8800 (British Standard Institute. 1996), which is also the common notion recognized among toxicologists in their risk assessment (Fan and Chang, 1996). Thus, readers should be aware of such a possible confusion. As this book focuses on methods of epidemiological research, I take the epidemiological tradition to delineate risk as the probability only in chapter 6.


Clinical decision making

National resource allocation Maximize utility of all people (No. of QALY)

Maximize individual patient's utility

under the constraint of National Health

under resource constraint

Insurance System (NHIS)

based on: psychometric theory

based on: expected utility theory

WHOQOL health profile

standard gamble (utility, e.g. E u r o Q o l )

(multi-dimensions) +

+

survival function

survival function

Summarize to only one dimension survival weighted psychometric scores for each facets

QAS (QALY)= J E{Qol(t I xi ))S(t i xi)

E[FAS}=jS(t\xi)Esub[Q(t\xi)]dt

Each patient participates in clinical decision to maximize no. of QALY/per given cost How much is the patient willing to pay for a QALY ?

quality adjusted survival Cost/QALY(or DALY)

How much will NHIS pay per QALY under the constraint of distributive justice?

Figure 13.9 Utility and psychometric assessment weighted by survival for national resource allocation and clinical decision (modified from Wang et al, 2000).


13.3.1 Risk assessment from a public health point of view In epidemiology and public health, we usually consider disease or death as the adverse event. Risk can then be estimated by cumulative incidence rate (cumulative proportion) after the specified period of time. In fact, such a risk estimate is commonly based on historical data. Its calculation was discussed earlier in Chapter 6 and can be briefly summarized as follows: Let incidence rate (IR) at time (t) be the rate of new cases developing during the person-time observation. The risk of developing the health event during the period of t0 to ti is estimated by: CIRto_t, = 1 - exp(-J;; (IR)dt) = 1 - exp(-I (IR; )(A t i )) i

Assume that t; is any small interval during t0 and t,, and assume that the person has not died of other competing causes of death. Or, construct a life table after the j , h year of follow-up and apply the Kaplan-Meier method to estimate the risk during 0 - j years. Let R(j) be the risk of contracting the disease by the end of the jth year and IR(j) be the average incidence rate of the jth year, then RG)=i

- n a - ^ ( y ) ) = i -(i -IR(I)XI -iR(2))---(i-iR(j)) j

Thus, one needs to obtain the data of particular incidence rates during the specified period of time in order to assess the risk. Furthermore, R(t) represents an individual's probability of getting the disease, only if one first assumes that this person has not died of other competing causes. Because incidence rates may change according to the variation of different determinants, one needs to assess these determinants in order to characterize the risk. Moreover, an identification of the population at risk from these hazards is also needed in an empirical assessment. For example, an occupational and environmental risk assessment usually involves the following four steps, as recommended by the U.S. NRC (National Research


Council) (NRC, 1983): 1. Hazard identification: What health effects will result from the toxicant? 2. Dose response assessment: Draw a figure or develop a formula to express what proportion in a population will suffer from the effect of different doses. Namely, actual doses of the agent at the target organ are considered in estimating incidence rates of a population. 3. Exposure assessment: Evaluate or measure the exposure dose for the particular situation. 4. Risk characterization: Determine the risk or probability of occurrence of the health effect. If the information on the population at risk is available, one can estimate the number of expected cases during the specified period of time. Let us consider Example 13.4 again. Example 13.4 Regulation of asbestos factories Chang et al. (1999) tried to quantify the risk of increased mortality of lung cancer and mesothelioma among people living near asbestos factories. Detrimental health effect could potentially result from exposure to asbestos, which would lead to mesothelioma and lung cancer cases among the exposed. After reviewing the literature, investigators selected a dose-response model for asbestos-related lung cancer, as follows: D = O-E = E*(b/100)*X*w D: excess death of lung cancer = observed (O) - expected (E) b: slope (fiber- year /cc)"1: dependent on type of asbestos factory, asbestos cement: 0.5 asbestos textile: 3 X: cumulative exposure dose of asbestos (fiber- year/cc) w: weighting factor; conversion due to situation offset from the original equation. The original assumption for this model was that workers work 40 hours


per week and 48 weeks per year. Accordingly, this model needed to be adjusted for ambient exposure of community people who usually stay 16 hours at home, 7 days per week and about 50 weeks per year. Thus, the weighting factor was adjusted to (50 x x 16 x 7)/(40 x 48) = 2.92. In addition to performing air measurement, the investigators also counted the number of people actually living near the factory with help from local policemen and obtained the population sizes for residences 100m, 200m and 300m away from (or diameter distances 200m, 400m, and 600m of) the factories. Similarly, the investigators selected the following dose-response model for asbestos-related mesothelioma: Although there were only 5 asbestos textile factories, which accounted for more risk of lung cancer among residents if compared with cement factories. The EPA of Taiwan issued an order to relocate textile factories and implement a more effective control technology. I(t) = K*C*(T3-2 - (T - D)32), if 0 < t =d I(t) = K*C*T32, if t > d I(t): Incidence rate of mesothelioma C: asbestos concentration during exposure (f / c.c.) T: interval of first exposure starting from the present (year) D: exposure duration (year) t > d, ever exposure 0 < t = d, current exposure K: constant, 0.04 * 10"8for chrysotile exposure. Tables 13.3 and 13.4 summarize the exposure concentration and risk of developing mesothelioma and lung cancer in areas near cement and textile asbestos factories.


Table 13.3

Diameter Distance

Estimated number of excess deaths from lung cancer and mesothelioma, resulting from 74-year exposure to air-borne asbestos among residents near asbestos-cement factories in Taiwan. Population size Concentration (person)

in air (f/cc)

200 m

1221

0.006

400 m

4221

600 m

9101

Table 13.4

Dose (f*yr /cc)

Excess death

mesothelioma

lung cancer

1.30

0.177

0.007

1.51

0.714

0.011

0.006

1.30

1.320

0.021

0.003

Estimated number of excess deaths from lung cancer resulting from 74-year exposure of air-borne asbestos among residents near asbestos-textile factories in Taiwan.

Diameter

Population size Concentration

Distance

(person)

in air (f/cc)

Dose (f * yr /cc)

Excess death lung cancer

mesothelioma

200 m

228

0.012

2.59

0.40

0.001

400 m

552

0.02

4.32

1.60

0.004

600 m

960

0.006

1.30

0.84

0.002

Question: How much risk is acceptable? Everyday, people face the question of how much risk is acceptable or unacceptable. Although there is no universal consensus, one can use the numbers provided by the OSHA (Occupational Safety and Health Administration, 1997) and EPA (Environmental Protection Agency, 1991) of the U.S. as references. For example, the U.S. OSHA uses an acceptable working lifetime (45 years) of 10"3 as a guide in determining permissible

Chapter] 3 Health Policy Application 331

exposure levels for carcinogens. Thus, they have classified different occupations according to their individual lifetime risks of mortality: High risk occupations'.

fire fighting mining / quarrying Average risk occupations: all manufacturing all service Low risk occupations: electrical equipment retail clothing

=27.45 x 10"3 =20.16 x 10"3 = 2.7 x 10"3 = 1.62 x 10"3 = 0.48 x 10"3 =0.07 x 10"3

The U.S. EPA (National Research Council, 1994) and FDA (Food and Drug Administration) consider a lifetime risk of 10"6 for each contaminant to be acceptable. From animal to human: Can we obtain a reference value from animal experimentation ? In most situations, human epidemiological data may not be available. In such cases, we may need to extrapolate the potential risk from animal data. However, interspecies differences need to be considered and adjusted for: including body weight, body surface area, life span, pharmacokinetics, metabolism, genetic constitution, repair mechanism, rate of intake, nutritional conditions, bacterial flora, mode/route of exposure, exposure schedule and competing causes of death. While there is no universal method to account for such differences, we usually employ a mg/kg/day or a mg/m2/day dose rate scale. The U.S. federal agencies have used some standard reference values for such an adjustment, as shown in Tables 13.5 and 13.6.


Table 13.5

Species Human Mouse Rat

Table 13.6

Reference values for dose calculations: lifespan, body weight, food and water intake, and nominal air intake for adults.

Sex M F M F M F

Lifespan (yr) 70 78 2 2 2 2

Body Weight (kg) 75 60 0.03 0.025 0.5 0.35

Food Intake (Wet Weight) (g /day) 1500 1500 5 5 20 18

Water Intake (ml/day) 2500 2500 5 5 25 20

Air Intake (m3/day) 20 20 0.04 0.04 0.2 0.2

Reference values for cdose calculations: selected lung ventilation values for humans (m3 per time period). Light

Light

Heavy

Resting

Activity

Activity

Activity

Total

(m3 / 8 hr)

(m 3 /16hr)

(m 3 /8hr)

(m 3 /8hr)

. (m 3 /24hr)

19.2 9.6

20.6

33.8

9.1

12

Male (adult)

3.6

Male (adult)

3.6

Female (adult)

2.9

Female (adult)

2.9

22.8 21.1

18.2

24

Moreover, the following abbreviations are useful: NOEL (mg/kg body weight/day) = no-observed effect level NOAEL (mg/kg body weight/day) = no-observed adverse effect level LOAEL (mg/kg body weight/day) = lowest-observed adverse-effect level

(statistically or '

biologically significant)

These levels can be calculated from animal and human studies after adjusting for safety factors: (NOEL, NOAEL, LOAEL) =

G-h


C = concentration in mg per unit of contaminated media (air, water, or food) Ij = intake in units of contaminated media per day (Tables 13.7 & 13.8) Wj = adult body weight in kg j

= 1 ,refers to data from an animal study

j

=

2, refers to data from a human study

F; (safety factors) F, = 1-10 intraspecies variation in sensitivity F2 = 1-10 potential synergism F3 = 1-10 less appropriate route F4 = same factor mediate of interest (e.g., if drinking water only accounts for 20% of total intake of a compound, then F4 = 5) F5 = 1 or 10, OR F5 = 1 in risk analysis, OR F5 = 10 if LO AEL is used instead of NOEL or NO AEL F6 = lor 10, OR F6 = 1 for human data, OR F6 = 10 for animal data After allowing for lifetime dose and latency period, the data from animal studies is: D, =

(Ci)(/i)

(70)(

J]

)(74 - L)(365)

i

The data from human studies is: D2 = (

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