have been proposed and reviewed by various authors (for example, Little and others 1992, 1994; Moolgavkar and others 1993; Crump 1994a,b; Moolgavkar 1994; Goddard and Krewski 1995; Little 1995).

This committee did not pursue biologically motivated cancer-risk models for several reasons. First, the mechanisms of radon-induced carcinogenesis must be known with sufficient certainty before an appropriate biologically motivated model can be constructed. Despite the considerable amount of information summarized in chapter 2, the committee recognized that current knowledge of radiation cancer mechanisms remains incomplete and any postulated model would necessarily be an oversimplification of a complex process. Second, application of a fully biologically motivated model requires information on fundamental biologic events, such as mutation rates and cell kinetics, that is not readily available in the present application. Third, a comprehensive biologically motivated model involving many parameters, such as the 2-stage clonal-expansion model used by Moolgavkar and others (1993) to describe the Colorado miner data, cannot be fruitfully applied without comprehensive longitudinal data on personal exposures to both radon progeny and tobacco. When the various steps in radon-induced carcinogenesis are more fully understood, the biologically motivated approach might become the preferred approach. However, the committee considered an empirical approach to be preferable at present.

Empirical Approach

Statistical methods for the analysis of epidemiologic data, particularly cohort data, have evolved rapidly since the 1970s. These statistical methods can be used to estimate lung-cancer risks directly from epidemiologic data, as done by the BEIR IV committee. To implement the now-common empirical approach, it is assumed that disease rates in narrow time intervals are constant, or at least can be accurately approximated by mean disease rates in the time intervals. Epidemiologic cohort data are summarized in a multidimensional table, in which each cell contains information on person-years at risk, number of events (lung-cancer deaths) occurring within the cell, and variables that identify the cell, such as age, cumulative exposure, and exposure rate. For each cell, the observed number of events is assumed to follow a Poisson distribution, with a mean equal to the underlying disease rate for the cell multiplied by the person-years at risk. Poisson events are assumed to be infrequent and have a distribution in which the variance equals the mean.

In the development of an empirical risk model to describe rates of radon-induced lung-cancer in miners, several a priori assumptions are needed about either the shape of the exposure-response function or the factors that influence risk. In its most general implementation, empirical modeling is sufficiently flexible to offer some degree of biological plausibility with only minimal assumptions needed about the structure of the model. That generality, as well as the



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