5
Background for Epidemiologic Methods

INTRODUCTION

Epidemiology is the study of the distribution and determinants of disease prevalence in man (MacMahon and others 1960). Epidemiologists seek to describe the populations at risk and to discover the causes of diseases. This entails quantification of the risk of disease and its relationship to known or suspected causal factors. In radiation epidemiology, exposure to radiation is the factor of primary interest, and epidemiologists seek to relate risk of disease (primarily cancer) to different levels and patterns of radiation exposure. Epidemiologic studies have been of particular importance in assessing the potential human health risks associated with radiation exposure.1

As part of the study of the causes of disease, epidemiologists measure factors that are suspected of leading to its development. A basic comparison used in radiation epidemiology is to measure the rate of a specific disease among persons who have been exposed to radiation and among persons who have not. The two rates are compared to assess whether they are similar or are different. A logical extension of this basic mode of comparison is to stratify the exposed subjects on the basis of amount (dose) of radiation in order to assess whether disease rates vary with dose, that is, whether there is a dose-response relationship.

If the rates of a disease are essentially the same in the exposed and unexposed groups, there is said to be no association between radiation exposure and disease. This does not necessarily mean that in all populations at all times, radiation is not related to the disease, but it does mean that in this population at this time, sufficient evidence does not exist for an association between radiation and disease. If the disease rate is higher among those exposed to radiation, there is a positive association. If the disease rate is higher among the unexposed group, there is a negative (inverse) association between radiation exposure and disease.

Epidemiologists use the term “risk” in two different ways to describe the associations that are noted in data. Relative risk is the ratio of the rate of disease among groups having some risk factor, such as radiation, divided by the rate among a group not having that factor. Relative risk has no units (e.g., 75 deaths per 100,000 population per year ÷ 25 deaths per 100,000 per year = 3.0). Excess relative risk (ERR) is the relative risk minus 1.0 (e.g., 3.0 − 1.0 = 2.0). Absolute risk is the simple rate of disease among a population (e.g., 75 per 100,000 population per year among the exposed or 25 per 100,000 per year among the nonexposed). Absolute risk has the units of the rates being compared. Excess absolute risk (EAR) is the difference between two absolute risks (e.g., (75 per 100,000 per year) − (25 per 100,000 per year) = 50 per 100,000 per year). If the rates of disease differ in the exposed and unexposed groups, there is said to be an association between exposure and disease. None of these measures of risk is sufficient to infer causation. A second step in data analysis is necessary to assess whether or not the risk factor is simply a covariate of a more likely cause.

In modeling the relation between radiation exposure and disease, either the ERR or the EAR may be used. In addition, the estimated dose of radiation exposure is integrated into the models, so that estimation is made of the ERR or EAR as a function of dose. Relative risk and ERR have certain mathematical and statistical advantages and may be easier to understand for small risks, but absolute risk and EAR are more closely related to the burden of disease and to its impact on the population. Thus, each type of measure has its advantages, and each is used in this report.

Having assessed whether or not there is evidence of an association between radiation exposure and a disease in the population of interest, the next task of the epidemiologist is to assess whether noncausal factors may have contributed to the association. An association might not represent a causal link between radiation and disease, but rather could be due to chance, bias, or error. It should be noted that chance can never be ruled out as one possible explanation for an asso-

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See Glossary for definition of specific epidemiologic terms.



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5 Background for Epidemiologic Methods INTRODUCTION Epidemiologists use the term “risk” in two different ways to describe the associations that are noted in data. Relative Epidemiology is the study of the distribution and deter- risk is the ratio of the rate of disease among groups having minants of disease prevalence in man (MacMahon and oth- some risk factor, such as radiation, divided by the rate among ers 1960). Epidemiologists seek to describe the populations a group not having that factor. Relative risk has no units at risk and to discover the causes of diseases. This entails (e.g., 75 deaths per 100,000 population per year ÷ 25 deaths quantification of the risk of disease and its relationship to per 100,000 per year = 3.0). Excess relative risk (ERR) is known or suspected causal factors. In radiation epidemiol- the relative risk minus 1.0 (e.g., 3.0 – 1.0 = 2.0). Absolute ogy, exposure to radiation is the factor of primary interest, risk is the simple rate of disease among a population (e.g., 75 and epidemiologists seek to relate risk of disease (primarily per 100,000 population per year among the exposed or 25 cancer) to different levels and patterns of radiation expo- per 100,000 per year among the nonexposed). Absolute risk sure. Epidemiologic studies have been of particular impor- has the units of the rates being compared. Excess absolute tance in assessing the potential human health risks associ- risk (EAR) is the difference between two absolute risks (e.g., ated with radiation exposure.1 (75 per 100,000 per year) – (25 per 100,000 per year) = 50 As part of the study of the causes of disease, epidemiolo- per 100,000 per year). If the rates of disease differ in the gists measure factors that are suspected of leading to its de- exposed and unexposed groups, there is said to be an asso- velopment. A basic comparison used in radiation epidemiol- ciation between exposure and disease. None of these mea- ogy is to measure the rate of a specific disease among persons sures of risk is sufficient to infer causation. A second step in who have been exposed to radiation and among persons who data analysis is necessary to assess whether or not the risk have not. The two rates are compared to assess whether they factor is simply a covariate of a more likely cause. are similar or are different. A logical extension of this basic In modeling the relation between radiation exposure and mode of comparison is to stratify the exposed subjects on the disease, either the ERR or the EAR may be used. In addition, basis of amount (dose) of radiation in order to assess whether the estimated dose of radiation exposure is integrated into disease rates vary with dose, that is, whether there is a dose- the models, so that estimation is made of the ERR or EAR as response relationship. a function of dose. Relative risk and ERR have certain math- If the rates of a disease are essentially the same in the ematical and statistical advantages and may be easier to un- exposed and unexposed groups, there is said to be no asso- derstand for small risks, but absolute risk and EAR are more ciation between radiation exposure and disease. This does closely related to the burden of disease and to its impact on not necessarily mean that in all populations at all times, ra- the population. Thus, each type of measure has its advan- diation is not related to the disease, but it does mean that in tages, and each is used in this report. this population at this time, sufficient evidence does not ex- Having assessed whether or not there is evidence of an ist for an association between radiation and disease. If the association between radiation exposure and a disease in the disease rate is higher among those exposed to radiation, there population of interest, the next task of the epidemiologist is is a positive association. If the disease rate is higher among to assess whether noncausal factors may have contributed to the unexposed group, there is a negative (inverse) associa- the association. An association might not represent a causal tion between radiation exposure and disease. link between radiation and disease, but rather could be due to chance, bias, or error. It should be noted that chance can 1See Glossary for definition of specific epidemiologic terms. never be ruled out as one possible explanation for an asso- 132

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BACKGROUND FOR EPIDEMIOLOGIC METHODS 133 ciation that is observed in epidemiologic data, although the investigator, the study is said to be experimental. An ex- probability may be extremely small. ample is a clinical trial designed to assess the utility of some Having judged that an association in a population under treatment (e.g., radiation therapy). When the levels of all study cannot be demonstrated to have occurred because of explanatory factors are determined by observation only, the error or bias, an investigator computes a measure of associa- study is observational. If treatment is assigned by a random tion that takes into account any relevant differences between process, the study is experimental. The majority of studies the exposed and the unexposed group. Also it is usual to relevant to the evaluation of radiation risks in human popu- quantify the uncertainty in a measured association by calcu- lations are observational. For example, in the study of lating an interval of possible values for the true measure of atomic bomb survivors, neither the conditions of exposure association. This confidence interval describes the range of nor the levels of exposure to radiation were determined by values most likely to include the true measure of association design. if the statistical model is correct. It always is possible that Two basic strategies are used to select participants in an the true association lies outside the confidence interval ei- observational epidemiologic study that assesses the associa- ther because the model is incomplete or otherwise in error or tion between exposure to radiation and disease: select ex- because a rare event has occurred (with rare defined by the posed persons and look at subsequent occurrence of disease, probability level, commonly 5%). or select diseased persons and look at their history of expo- Another step in assessing whether radiation exposure sures. A study comparing disease rates among exposed and may be the cause of some disease is to compare the results unexposed persons, in which exposure is not determined by of a number of studies that have been conducted on popula- design, is termed a “cohort” or a “follow-up” study. A study tions that have been exposed to radiation. If a general pat- comparing exposure among persons with a disease of inter- tern of a positive association between radiation exposure and est and persons without the disease of interest is termed a a disease can be demonstrated in several populations and if “case-control” or “case-referent” study. these associations are judged not to be due to confounding, bias, chance, or error, a conclusion of a causal association is Randomized Intervention Trials strengthened. However, if studies in several populations pro- vide inconsistent results and no reason for the inconsistency Intervention trials are always prospective—for example, is apparent, the data must be interpreted with caution. No subjects with some disease are enrolled into the study, and general conclusion can be made that the exposure is a cause assignment is made to some form of treatment according to of the disease. a process that is not related to the basic characteristics of the An important exercise is assessing the relation between individual patient (Fisher and others 1985). In essence, this the dose of exposure and the risk of disease. There is no assignment is made randomly so that the two groups being question that radiation exposure at relatively high doses has studied are comparable except for the treatment being evalu- caused disease and death (NRC 1990; UNSCEAR 2000b). ated. Random is not the same as haphazard; a randomizing However, at relatively low doses, there is still uncertainty as device must be used, such as a table of random numbers, a to whether there is an association between radiation and dis- coin toss, or a randomizing computer program. However, ease, and if there is an association, there is uncertainty about random assignment does not guarantee comparability. The whether it is causal or not. randomization process is a powerful means of minimizing Following is a discussion of the basic elements of how systematic differences between two groups (“confounding epidemiologists collect, analyze, and interpret data. The es- bias”) that may be related to possible differences in the out- sential feature of data collection, analysis, and interpretation come of interest such as a specific disease. Further, blinded in any science is comparability. The subpopulations under assessment of health outcome will tend to minimize bias in study must be comparable, the methods used to measure ex- assessing the utility of alternative methods of treatment. posure to radiation and to measure disease must be compa- Another important aspect of randomization is that it permits rable, the analytic techniques must ensure comparability, the assessment of uncertainty in the data, generally as p- and the interpretation of the results of several studies must values or confidence intervals. Intervention trials related to be based on comparable data. radiation exposure are conducted with the expectation that the radiation will assist in curing some disease. However, there may be the unintended side effect of increasing the COLLECTION OF EPIDEMIOLOGIC DATA risk of some other disease. Although a randomized study is generally regarded as the Types of Epidemiologic Studies ideal design to assess the possible causal relationship be- Research studies are often classified as experimental or tween radiation and some disease in a human population, observational depending on the manner in which the levels there are clearly ethical and practical limitations in its con- of the explanatory factors are determined. When the levels duct. There must be the expectation that in the population of at least one explanatory factor are under the control of the under study, radiation will lead to an improvement in health

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134 BEIR VII status relative to any alternative treatment. Such studies are The information available in a prospective cohort study is usually conducted with patients who need therapeutic inter- potentially much greater than that available in a retrospec- vention; randomly selected patients may be treated with ra- tive cohort study. Exposure is contemporaneous and may be diation and some other form of treatment or with different measured forward in time, and members of the cohort may types or doses of radiation. In these trials the sample size is be contacted periodically to assess the development of any relatively small and the follow-up time is relatively short. new disease. Direct evaluation of both exposure and disease Therefore, most studies to assess the long-term adverse out- may be done on an individual basis, with less likelihood of comes of exposure to therapeutic radiation, are, of necessity missing or incomplete information due to abstracting records cohort studies. compiled for a different purpose. The follow-up of survivors of the Japanese atomic bomb explosions is largely prospective, although follow-up did not Cohort Studies begin until 1950 (Pierce and others 1996). Exposure assess- Cohort studies may be retrospective or prospective. In a ment was retrospective and was not based on any actual retrospective cohort study of a population exposed to radia- measurement of radiation exposure to individuals. Recon- tion, participants are selected on the basis of existing records struction of the dose of radiation exposure is an important such as those maintained by a company or a hospital (e.g., characteristic of this study, and improvements in dose esti- radiation badge records). These records were made out at mation continue to the present with a major revision of the the time an individual was working or treated and thus may dosimetry published in early 2005 (DS02). be used as the historical basis for classification as a member The primary advantage of a retrospective cohort study is of the exposed cohort. In a prospective cohort study, partici- that time is compressed. If one wishes to evaluate whether pants are selected on the basis of current and expected future radiation causes some disease 20–40 years after exposure, a exposure to radiation, and exposure information is measured retrospective study can be completed in several years rather and recorded as time passes. In both types of cohort study, than in several decades. The primary disadvantage of a ret- the members of the study population are followed in time rospective cohort study is that limited information is avail- for a period of years, and the occurrence of new disease is able on both radiation exposure and disease. The primary measured. In a retrospective cohort study, the follow-up has advantage of a prospective cohort study is that radiation ex- already occurred, while in a prospective cohort study, the posure and disease can be measured directly. The primary follow-up extends into the future. Many studies that are ini- disadvantage is that time must pass for disease to develop. tiated as retrospective cohort studies become prospective as This leads to delay and expense. Most studies in radiation time passes and follow-up is extended. epidemiology are retrospective cohort studies. The information available in a retrospective cohort study is usually limited to what is available from the written Case-Control Studies record. In general, members of the cohort are not contacted directly, and information on radiation exposure and disease Case-control studies may be prospective or retrospective. must come from other sources. Typically, information on The cases are those individuals with the disease being exposure comes from records that indicate the nature and studied. Cases in a retrospective case-control study are usu- amount of exposure that was accumulated by a worker or by ally selected on the basis of existing hospital or clinic records a patient. On occasion, all that is available is the fact of ex- (i.e., the cases are “prevalent”). In a prospective case-control posure, and the actual dose may be estimated based on study, the cases are “incident,” that is, they are selected at knowledge of items such as the X-ray equipment used the time their disease was first diagnosed. Controls are (Boice and others 1978). usually nondiseased members of the general population, Information on disease also must come from records such although they can be persons with other diseases, family as medical records, insurance records, or vital statistics. members, neighbors, or others. Cancer mortality is readily evaluated by retrospective co- After the cases and controls have been identified, it is hort studies, because cancer registries exist in a number of necessary to determine which members of the study popula- countries or states and death from cancer is fairly reliably tion have been exposed to radiation. Usually, this informa- recorded. tion is obtained from interviewing the cases and the controls. Most studies that have followed patients treated with However, if the case or control is deceased or unable to re- therapeutic radiation are retrospective cohort studies. Series spond, exposure information may come from a relative or of patients are assembled from medical and radiotherapy from another proxy. records, and initial follow-up is done from the date of The information available in case-control studies usually therapy until some arbitrary end of follow-up. Patients is less reliable than that collected in cohort studies. For ex- treated as long ago as the 1910s have been studied to assess ample, consider the accuracy of dietary history for the past the long-term effects of radiation therapy (Pettersson and year versus that of a year from several decades in the past. others 1985; Wong and others 1997a). Exposure information may be available only from interview

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BACKGROUND FOR EPIDEMIOLOGIC METHODS 135 of the study subjects and therefore be less reliable than reli- various forms of treatment being evaluated. Random assign- ance on contemporary records. There may be differential ment prevents selection on the basis of outcome and pro- recall of exposure to radiation depending on case or control vides the optimum strategy for minimizing differences be- status, which leads to a lack of comparability in the informa- tween the two groups being studied. Comparability in a tion available. It is rare to be able to quantify the amount of cohort study means that subjects exposed to radiation and past exposure in a case-control study. However, in some situ- unexposed subjects are enrolled without knowledge of dis- ations related to radiation exposure, only data from case- ease status, that information on disease is obtained without control studies are available. knowledge of exposure status, and that other factors related The critical differences between a retrospective cohort to disease occurrence are not related to exposure status. study and a case-control study are that subjects in the former Lack of comparability in any of these epidemiologic study are selected on the basis of exposure category at the start of designs may lead to one or another form of bias, which in the follow-up period and exposure measures are concurrent turn may minimize or invalidate any information contained with the actual exposure. Conversely, in a case-control study, in the data from the study. Three common and potentially subjects and controls are selected on the basis of disease serious forms of bias are selection bias, when enrollment outcome, and past exposures must be reconstructed. into a study is dependent on both radiation exposure and On occasion in epidemiology, a hybrid study is per- disease status; information bias, when information on dis- formed: the “nested” case-control study. A cohort study is ease or on radiation exposure is obtained differentially from conducted, and subsequently, additional information on ex- exposed or from diseased persons; and confounding bias, posure is collected for persons with disease and for a sample when a third factor exists that is related to both radiation of persons without disease. For example, radiation exposure exposure and disease effects. among persons with a second cancer may be compared to Selection bias is generally a minor issue in clinical trials that among a sample of those without a second cancer. and cohort studies, including retrospective cohort studies. In Nested case-control studies are best thought of as a form of a prospective cohort study, disease has not yet occurred, so retrospective cohort study, in that the study population is there is little possibility of selecting exposed persons on the initially defined on the basis of exposure rather than of basis of their future disease status. Exceptions are rare and disease. limited to situations in which some preclinical sign or symp- In evaluation of the possible health effects of exposure to tom affects selection—for example, when persons volunteer ionizing radiation, many of the informative case-control for one or another intervention because they know that they studies have been nested within cohorts. Exposure measures are at special risk. in these studies are generally not based on interview data, By contrast, selection bias can be a major issue in case- but rather on review of available records, sometimes supple- control studies, because both exposure and disease already mented by extensive modeling and calculations. In some have occurred when the study subjects are enrolled; there is nested studies, the objective is to obtain information on dose the danger that persons who are both exposed and diseased or other factors that would be too expensive to obtain for the will be overselected to participate in the study. If this occurs, entire cohort. Examples are a case-control study of selected the data contain invalid information on the true relation be- cancers in women irradiated for cervical cancer to obtain tween exposure and disease. Self-selection (volunteering) for individual dose estimates (Boice and others 1985); a breast a nonexperimental study can be a particularly potent source cancer study of A-bomb survivors to obtain data on repro- of bias. ductive factors through interview (Land and others 1994b); An example of selection bias occurred in a study of leu- and a study of lung cancer in Hanford workers to extract kemia among workers at the Portsmouth, New Hampshire, smoking histories from medical records (Petersen and others Naval Shipyard (Najarian and Colton 1978). In an initial 1990). case-control study, persons with leukemia who had been occupationally exposed to radiation were widely known and hence more likely to be located and enrolled than were unex- Comparability in Study Design posed workers with leukemia, and a positive association be- The design of an epidemiologic study must assume com- tween radiation and leukemia was reported. Subsequently, parability in the selection of study participants, comparabil- after an extensive follow-up of all members of the workforce, ity in the collection of exposure and disease information rel- no association between radiation exposure and leukemia was evant to each study subject, and comparability of the basic found (Greenberg and others 1985). The initial preferential characteristics of the study subjects. Any lack of comparabil- selection of diseased workers who were exposed to radiation ity may undermine inferences about an association between led to an erroneous appearance of a positive association be- exposure and disease, so that interpretation is ambiguous or tween radiation and leukemia. impossible. Information bias may occur in a clinical trial or a cohort Comparability in a clinical trial ordinarily is straightfor- study if knowledge of exposure is available when informa- ward, because study subjects are assigned randomly to the tion on disease is being obtained; there is the possibility that

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136 BEIR VII disease will be diagnosed more among exposed persons than exposed to radiation, one interpretation would be that radia- among nonexposed persons. For this reason, in obtaining tion reduces the risk of death. information on disease among participants, information on In a clinical trial, assignment to a type of specific expo- exposure is kept hidden (blinded), so that any error in dis- sure is ordinarily a random process so that, on average, the ease ascertainment occurs equally among exposed and unex- two groups being compared are comparable with respect to posed persons. possible confounding factors. Thus, in a randomized trial, Information bias is a major threat in a case-control study confounding—although possible—is less of a concern than if knowledge of disease is available when information on in a cohort or a case-control study. exposure is being obtained; there is a possibility that expo- sure will be ascertained more among diseased persons than Statistical Power among nondiseased persons. For this reason, in obtaining information on exposure among participants, information on An important part of any epidemiologic study is its statis- disease is kept hidden from the interviewer and, if possible, tical power (i.e., the probability that under the assumptions from the respondent (blinded), so that any error in exposure and conditions implicit in the model, it will detect a given ascertainment occurs equally among diseased and non- level of elevated risk with a specific degree of significance). diseased persons. Further protection against information bias The power of a cohort study will depend on the size of the may come from blinding subjects and/or interviewers to the cohort, the length of follow-up, the baseline rates for the hypothesis under study. disease under investigation, and the distribution of doses Information bias as well as selection bias affected the within the cohort, as well as the magnitude of the elevated Portsmouth Shipyard Study (Najarian and Colton 1978). In risk. Similarly, statistical power in a case-control study de- the initial case-control study, information on radiation expo- pends on the number of cases, the number of controls per sure was obtained by interview of relatives of workers with case, the frequency and level of exposure, and the magnitude and without leukemia. Subsequently, it was found that rela- of the exposure effect. Statistical power is generally evalu- tives of those with leukemia tended to overreport radiation ated before a study is conducted. Afterwards it is more use- exposure, whereas relatives of those without leukemia ful to refer to statistical precision, which is reflected in the tended to underreport exposure (Greenberg and others 1985). width of the confidence intervals for risk estimates Confounding bias is a basic issue in all epidemiologic (UNSCEAR 2000b). studies where no random assignment of exposure has oc- curred; this is the usual situation except for randomized clini- ANALYSIS OF EPIDEMIOLOGIC DATA cal trials. No one type of nonexperimental epidemiologic study is inherently more subject to confounding bias. If in- The basic data collected in an epidemiologic study are formation is available on each factor that is suspected of data on exposure and data on disease. In the simplest form, being a confounder, confounding bias may be minimized in an individual may be exposed or not and may be diseased or a study design by matching on the relevant factors or in data not. Thus, there are four possibilities: exposed and diseased, analysis by stratification or statistical adjustment. However, exposed and not diseased, not exposed and diseased, or not if some confounding factor has not been measured, the data exposed and not diseased. Typically, these data are entered may be wrong. Thus, interpretation of the data must take into a “fourfold table” (Table 5-1). into account the possible influence of potential confounding. It can be seen that in a study of N individuals, a + b are Confounding bias is especially troublesome when the asso- exposed, a + c are diseased, and a are both exposed and ciation under investigation is weak. In this case, a confounder diseased. Interest is generally focused on whether a is larger has the potential to mask an association completely or to than expected in relation to the other entries. Mathemati- create an apparent effect. Because the risks associated with cally this is the same as asking whether d is larger than ex- low levels of ionizing radiation are small, confounding bias pected, or whether b or c are smaller than expected. Accu- is potentially important in low-level radiation studies. rate counts in all four cells are necessary for valid inferences A third factor (other than exposure and disease) can be confounding only when it is associated with both the expo- sure and the disease. Association only with exposure or only TABLE 5-1 The Fourfold Table with disease is not sufficient for a factor to be confounding. The so-called healthy worker effect is an example of con- Disease founding in studies of mortality among occupational groups, including those employed in the nuclear industry (Monson Exposure Yes No Total 1990). Ordinarily, persons who enter the workforce are Yes a b a+b healthy, and if mortality among workers is compared to that No c d c+d among the general population, the workers are found to be at Total a+c b+d N a relatively low risk. If all members of the workforce were

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BACKGROUND FOR EPIDEMIOLOGIC METHODS 137 about whether the disease is associated with the exposure. Instead of categorizing persons with radiation exposure The rate of disease among the exposed subjects (Re) is equal as simply being exposed or not, subjects may be categorized to a/(a + b), and the rate of disease among the unexposed as having high, medium, or no exposure. In this case, there subjects (Rn) is equal to c/(c + d). would be a sixfold table—three rows and two columns. Such data are of value in assessing whether or not there is a dose- response relationship between radiation exposure and dis- Measures of Association ease. If the rate of disease is highest among the most ex- Two measures are commonly used to compare the dis- posed, intermediate in the middle exposure group, and lowest ease rates between exposed and unexposed subjects. The among those with no exposure, a dose-response relationship relative risk (RR) is the ratio of the two rates; that is, exists. In this report, only data that are of utility to a quanti- RR = R e/R n. The ERR is given by ERR = RR – 1 = tative assessment of a dose-response relationship between Re/Rn – 1 = (Re – Rn)/Rn. These ratios are dimensionless. The radiation exposure and disease are included. rates can also be subtracted rather than divided. The differ- For radiation, we are generally interested in going be- ence between Re and Rn, that is, Re – Rn, is termed the “attrib- yond just deciding if there is a causal relationship. An im- utable risk,” or “risk difference.” It is also referred to as the portant strength of radiation epidemiology is the availability excess risk (ER) or the EAR, with the latter terminology of quantitative information on dose. Only by relating effects commonly used in radiation epidemiology. The ER and EAR to dose can results be compared across studies or used to are often expressed as the number of excess cases or deaths predict risks from exposures in other settings. per person-year (PY) or, for convenience, per 1000 PY. In radiation studies, information on radiation dose is of- Tools of Statistical Inference ten available. Either of the measures, ERR or EAR, can be expressed per unit of radiation dose. In the simplest situa- The second task in data analysis is assessing the statisti- tion, one has exposed and unexposed groups and informa- cal precision of an ERR or other measure of association cal- tion on the average dose D received by exposed subjects. culated from data. Statistical estimates calculated from data The ERR coefficient is then defined as are imprecise, or variable, in the sense that replication of the study (with identical conditions of exposure and levels of ERR = (Re – Rn)/(RnD), exposure, but with a different random sample of subjects) would likely result in a different estimate of risk. Thus, it is and absolute risk coefficient is defined as important to determine whether the actual observed associa- tion (e.g., an RR different from 1.0) can be explained by EAR = (Re – Rn)/PY·D, chance (random variation) alone. In epidemiologic studies the assessment of precision is usually accomplished via the where PY is the number of person-years of follow-up. calculation of p-values or confidence intervals. Both measures may depend on variables such as sex, age The validity of both p-values and confidence limits rests at exposure, time since exposure, and age at risk (attained on many assumptions about the study design and the data. age). The ERR expresses risk and its dependencies relative Statistical results are often most correct when deviations to risk in the unexposed, whereas the EAR expresses risk from the assumptions are small, that is, the procedures are and its dependencies independent of risk in the unexposed. “robust.” It is the task of the investigator and any subsequent The RR (or ERR) has certain statistical advantages and is the analyst to know the assumptions and to ensure that they are more commonly used measure for epidemiologic studies, sufficiently close to reality. especially etiologic studies. The EAR is a useful measure for Consider a hypothetical replication of the study in which estimating the burden of risk in a population, including the the true RR is 1.0 (i.e., disease outcome is not related to dependence of this burden on various factors. Both measures exposure). The ERR from the hypothetical replication will can be used to estimate absolute lifetime risk as discussed in not equal 1.0 exactly, but will vary randomly around the true Chapters 11 and 12. value of 1.0. The p-value of the actual study is the probability In some of the more informative radiation studies, dose that the RR estimated from the hypothetical data is more estimates for individual subjects are available. In this case, extreme in its difference from 1.0 (in either direction) than more complex statistical regression methods are used to es- the RR estimated from the actual sample. A small p-value timate the ERR and EAR per unit of radiation dose based on means that it is unlikely that the actual RR was calculated the assumption of a linear dose-response. These methods from data having a true RR of 1.0. In other words, a small have been used in analyses of data on Japanese A-bomb sur- p-value provides evidence that the true RR is different from vivors and on some medically exposed populations. The 1.0; the smaller the p-value, the stronger is the evidence. reader should consult Chapters 6 and 7 for further discussion The confidence interval and p-value are based on the same of this approach. theory; they use the theory in slightly different ways to an- swer slightly different questions. A p-value is appropriate

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138 BEIR VII for answering a confirmatory question such as, Is 1.0 a be- confounders and summarizing results in a standardized RR lievable value of RR? A confidence interval is appropriate with associated confidence interval. for answering an exploratory question, such as, What are the believable values of RR? Obviously, a confidence interval Linear Relative Risk Model lends partial information to the confirmatory question since values not in the 95% confidence interval are “rejected” at A model that plays a prominent role in radiation epide- the significance level of 0.05. The p-value does add addi- miology studies is one in which the RR is a linear function tional information, however, since it provides a degree of of dose. In its simplest form, evidence. For example, p-values of .049 and .00000049 pro- vide quite different measures of the believability of the hy- RR(D) = 1 + βD, pothesis (of RR equal to 1.0, say), even though the 95% con- fidence interval excludes 1.0 in both cases. where D is dose, RR(D) is the relative risk at dose D, and β Statistical precision is determined largely by study size is the ERR per unit of dose, which is usually expressed in (number of subjects). Larger studies generally result in more grays or sieverts. In more complex forms, β is allowed to precise estimates. Small effects (RRs near 1.0) are generally depend on gender, age at diagnosis, and other variables. more difficult to detect than large effects, because a confi- This linear RR model has been used extensively in radia- dence interval centered close to 1.0 is likely to include 1.0 tion epidemiology, including studies of A-bomb survivors unless the sampling variance is small. One consequence is (Chapter 6), persons exposed for medical reasons (Chap- that very large studies are required to estimate small effects ter 7), and nuclear workers (Chapter 8). The model has precisely. This explains in part why risk models cannot be served as the basis of cancer risk estimation by three BEIR based exclusively on low-dose studies. The RRs associated committees (NRC 1988, 1990, 1999), by the 2000 with low doses are close to 1.0 and thus can be estimated UNSCEAR committee (2000b), and by the National Insti- precisely only in very large studies. tutes of Health (NIH 2003). It also plays an important role in developing the BEIR VII committee’s cancer risk esti- mates (Chapter 12). The linear model has been chosen be- Control of Confounding cause it is supported by radiobiological models (Chapter 2) The third task in data analysis is to assess whether or not and because it fits the data from most studies (although in the crude association that is observed in a study is due to many studies, statistical power is inadequate to distinguish confounding by one or more other factors. For example, in among different dose-response functions). assessing the relation between radiation and lung cancer, one In the simplest situation, in which one has exposed and should consider whether cigarette smoking is a confounding unexposed groups and information on the average dose D factor. Cigarette smoking is a recognized cause of lung can- received by exposed subjects, β is estimated by (Re – Rn)/ cer, and thus there is an association between smoking and (RnD) as discussed earlier. In many radiation studies, how- lung cancer. If persons who are exposed to radiation, such as ever, doses for individual subjects are available and more uranium miners, smoke more than persons who are not ex- complex estimation procedures are required to make use of posed, they may have an increased risk of lung cancer just this information. Preston and colleagues (1991) have devel- from the smoking. Thus, unless the analysis deals with smok- oped the EPICURE software that allows for flexible model- ing as well as radiation, it is possible that an association ing of both relative and absolute risks, including the fitting between radiation and lung cancer seen in data only reflects of linear RR models. the confounding influence of cigarette smoking. Prentice and Mason (1986) and Moolgavkar and Venzon In data analysis, the simplest way to assess whether or not (1987) discuss inferences based on the linear RR model and confounding is present is to stratify on the confounding fac- note that the distribution of the maximum likelihood tor. That is, two fourfold tables are set up that relate the estimate of β may be highly skewed, and that confidence exposure (radiation) to the disease (lung cancer). If it is as- intervals based on the estimates of the asymptotic standard sumed that all smokers smoke the same, one table contains error (Wald method) can be seriously misleading. Re-–pa- data only for smokers and a second table contains data only rameterizing the model as β = exp(α) is sometimes helpful for nonsmokers. Within each of these two tables, no con- but does not allow for the possibility that β or its lower con- founding by smoking is possible. fidence bound may be negative. Another difficulty is that, If it is necessary to control more than one confounding to ensure that the RR is nonnegative, it is necessary to con- factor in the analysis of epidemiologic data, it is usual to strain the parameter β to be larger than –1/DMAX, where construct a multivariate model relating exposure to disease DMAX is the maximum dose in the study. These problems and controlling for the potential confounding effect of a may be particularly severe in studies of nuclear workers, number of other factors. For example, sex and age are two where dose distributions are highly skewed and estimates of factors that are commonly included in multivariate models. β are often very imprecise. For this reason, tests and confi- Such modeling is similar to stratification on a number of dence intervals in nuclear worker studies have sometimes

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BACKGROUND FOR EPIDEMIOLOGIC METHODS 139 been based on the likelihood ratio, or on score statistic ap- The p-value or confidence interval that is computed esti- proximations, or on computer simulations (Gilbert 1989), mates only the likelihood that chance alone could have ac- which can lead to intervals that are not symmetric on either counted for the observed association. The p-value does not a linear or a logarithmic scale. In some situations, especially distinguish between a true association and one that is due to in studies with sparse data, the estimate and/or the lower bias or error. Also, interpretation of the likely range of an confidence bound for β may be negative; some investiga- association based on its confidence interval reflects only the tors report such findings simply as <0. play of chance, not of error or bias. In addition, rare events do happen. Each p-value of the confidence interval should be examined with some care to determine whether a rare INTERPRETATION OF EPIDEMIOLOGIC DATA event is a plausible explanation for the statistical findings. Interpretation of the results of statistical analysis is as much Assessment of Associations an art as a science. After epidemiologic data have been collected and ana- In all epidemiologic studies, measures of exposure and lyzed, the associations noted in the data must be interpreted. measures of disease are imprecise. This imprecision is not The measures of association and of statistical precision that considered an error in methodology, but rather an inevitable have been computed have no inherent meaning; they reflect occurrence associated with the assessment of observational only the data that have been accumulated in the study. It is data. When errors in measuring disease or exposure are ran- possible that these data have resulted from bias, error, or dom, unrelated to true disease and exposure, and indepen- chance and thus have no interpretive meaning. A formal dent among subjects, it is usually the case that measures of evaluation of the study design and of the methods used to association are attenuated. That is, RRs are biased toward collect and analyze the data is needed to assess the meaning 1.0, the case of no association. In radiation epidemiology, of the data. errors in measuring disease (e.g., misdiagnosing cancer) are The first step in the interpretation of data is to assess the not different from disease misclassification problems in methods used in the study itself. The following questions other epidemiology studies. Thus, the effect of disease must be considered: misclassification is reasonably well understood. However, exposure measurement error problems in radiation epidemi- • Is there evidence that selection bias has been avoided ology are often unique to radiation studies, and the effect of in enrolling the study subjects? such errors generally is less well understood. • Is there evidence that information bias has been mini- For most radiation epidemiology studies, measurements mized in assessing exposure or disease? of exposure were not made at the time of exposure, but • Is there evidence that the potential confounding influ- rather have been reconstructed some time after exposure us- ence of other factors has been addressed? ing available information. For example, exposures for A- • Is there evidence for sufficient precision in the mea- bomb survivors are calculated using sophisticated models sure of exposure or of disease to permit a reasonable basis for the spatial intensity of radiation and information about a for interpretation? subject’s location and local shielding at the time of expo- sure. It is likely that such measurements contain both ran- The possible occurrence of selection bias or of informa- dom and nonrandom components. The effects of random tion bias may be assessed only by evaluation of the meth- errors in exposure measurements are reasonably well un- ods used in data collection. If either of these biases is judged derstood and include, in general, attenuation of estimated to have an appreciable likelihood of being important, no associations, underestimation of linear risk coefficients, and analyses can be conducted to adjust for the error that may possible distortion of the shape of the dose-response rela- have been introduced. The data must be regarded as unsuit- tionship. The severity of these effects generally depends on able for the purpose at hand. In contrast, potential con- the magnitude of the measurement errors (as measured by founding bias can be assessed and usually controlled by their variance) relative to the variability in true exposures. analytic strategies for factors on which information has The effects of nonrandom errors in exposure measurements been collected. There will always remain factors that have are specific to the nature of the error. For example, if a do- the potential for confounding but for which no information simetry system systematically overestimated exposures by is available, including factors that are not even suspected of 10%, the dose-response relationship would erroneously be being confounders. This does not mean that no interpreta- stretched over a greater range of doses, the slope of the fit- tion is possible, but it does mean that some degree of cau- ted line would be reduced, and linear risk coefficients would tion is needed in interpreting any association between radia- be underestimated by approximately 10%. tion exposure and disease. A second step in evaluating whether some exposure Chance is always a possible explanation for any associa- causes some disease is to assemble all of the relevant litera- tion (or lack of association) in a scientific study, no matter ture and to display all of the data that are regarded as rel- how strong or how statistically significant the association. evant and of adequate quality. On occasion, a so-called meta-

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140 BEIR VII analysis is conducted in which there is a quantitative sum- • Coherence—The association is believable based on in- marization of the data. Such an analysis is not a necessary formation from other scientific disciplines. step and in fact may not be indicated. Only data from valid • Statistical significance—The association is statistically studies may be included in a meta-analysis, and among valid significant or not. studies, all studies must contain similar information. In es- sence, a meta-analysis is a formal rather than an informal Each of these criteria should be considered in assessing summarization of the epidemiologic literature. whether an association between exposure and disease can be A pooled analysis of data from similar studies is not the judged to be causal. Except for temporal relationship, there same procedure as a meta-analysis, but rather a useful exten- need not be evidence for each of these criteria. sion of basic data analysis. An important tool for obtaining a With respect to the use of the Hill criteria in assessing the broad assessment of the evidence from several studies is to association between exposure to ionizing radiation and conduct combined analyses of data from groups of similar health outcome, they are of limited current value for human studies. Analyses based on combined data provide tighter cancer. Ionizing radiation at high doses is acknowledged to confidence limits on risk estimates than analyses based on be a cause of most relatively common human cancers (IARC data from any single study population. To the extent that 2000). The presence of a dose-response relationship for biases found in individual studies tend to cancel out, com- many cancers is considered strong evidence for a causal re- bined analyses may help to reduce bias that results from con- lationship. For less common cancers and for diseases other founding and other potential sources of bias. Such analyses than cancer, there are not sufficient data to apply the Hill also help to determine if differences in findings among stud- criteria. IARC (2000) notes: “A number of cancers, such as ies are truly inconsistent or are simply the result of chance chronic lymphocytic leukaemia, have not been linked to ex- fluctuations. The application of similar methodology to data posure to x or γ rays.” from all populations, in addition to the presentation of re- sults in a comparable format, facilitates comparison of re- Assessment of Dose-Response Relationships sults from different studies. A third step in interpretating epidemiologic data is to As noted above, evaluation of a dose-response relation- compare the results of an individual study with those of simi- ship is one of the Hill criteria to be applied in assessing lar studies. The goal of such an exercise is to reach a judg- whether or not an association is judged to be causal. With ment about whether, in general, it may be concluded that respect to providing a risk estimate for low-dose, low-linear under certain conditions, an exposure causes a disease. energy transfer radiation in human subjects, other informa- The so-called Bradford Hill criteria are the standard crite- tion is necessary. Specifically, one needs relatively accurate ria used to assess whether the general epidemiologic litera- information for individuals on dose from ionizing radiation, ture on some exposure or some disease provides sufficient as well as a relatively complete measure of the incidence of information to judge causality (Hill 1966). These criteria or mortality from diseases. To date, the data from the survi- have been expanded, reduced, revised, and reinterpreted by vors of the atomic bomb in 1945 in Hiroshima and Nagasaki countless authors to meet their special needs, but the core have been the primary source of such information. The Ra- idea remains—use rational operational criteria to judge evi- diation Effects Research Foundation has been responsible dence from observational studies. A revised version of the for estimating the exposure of individuals and for measuring Hill criteria follows: the incidence and mortality of cancer and other diseases. One of the primary tasks of this committee has been to • Consistency—An association is seen in a variety of set- evaluate the data that are available from studies of popula- tings. tions exposed to medical radiation, occupational radiation, • Specificity—The association is well defined rather than and environmental radiation so as to assess whether infor- general. mation on dose-response associations from these data • Strength—The association is high or low rather than sources can be assembled and to evaluate whether such in- close to 1.0. formation can be compared to that obtained from the popula- • Dose-response—The higher the exposure, the higher is tions exposed to radiation from the atomic bombs. Chapters the rate of disease. 7, 8, and 9 address these studies. • Temporal relationship—The exposure occurs before the disease.