and (3) discusses the relevance of these data for cancer risk among Vietnam veterans.

ANALYSIS OF LATENCY IN EPIDEMIOLOGIC STUDIES

To discuss latency issues, we need to establish what is meant by the ''effect of exposure over time." First, for purposes of epidemiologic research and quantification, we are interested in the rate of disease among exposed individuals compared to the rate that would be expected if the subjects had not been exposed, which is discussed more fully below. Thus, we are interested in the relative or excess rate of disease as the measure of comparison. Because diseases such as cancer may take a long time to develop (i.e., years or even decades) an analysis of the effects of exposure must consider the "latency period," or time between the exposure and the measurement of disease. The effect of any exposure on a population, whether measured as relative or excess rates, may change with "time since exposure." Typically, after exposure to a carcinogen, no excess cancer rate will be observed for a time. Then there will be a rise in the excess until it reaches a peak, at which point it may fall back down. For exposures of short duration, time since exposure is in many cases easy to define. This situation holds for environmental exposures from industrial accidents, particularly if the exposure involves chemicals that are not retained in the body tissues. If the exposure occurred over a long period of time (a protracted exposure), as with production workers and pesticide applicators, the time since exposure is more difficult to quantify, since there were many exposure times. It is important to note that 2,3,7,8-tetrachlorodibenzo-p-dioxin (2,3,7,8-TCDD, TCDD, or dioxin) and other chlorinated herbicides are retained in some body tissues for a long time (e.g., decades), so that even after external exposure ceases, internal exposure continues. Thus, even a brief exposure such as occurred in Seveso, Italy, can involve protracted exposure of many organs of the body. Conceptually, we think of the effect of exposure at a particular time in the past as the resulting change in risk today that is ascribable to that exposure. Although this may be overly simplified, the effect of an entire exposure history can usefully be thought of as the sum of the effects from exposure at each time point in the past.

To adequately study the effects of protracted exposure, detailed exposure histories for each study subject, including the dates at which the individual was exposed and, ideally, the level of exposure, are needed. Appropriate statistical methods have been developed for investigating the effects of exposure accrued as a function of time since exposure (Thomas, 1983, 1988; Breslow and Day, 1987), but these have not been used to analyze of any of the cancer studies reviewed here.

In general, the ability to investigate the issue of timing of exposure in a given data set will depend on the quality of the exposure measure, the quality of the timing of exposure information, the number of people developing the disease,



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