Relative risk regression analysis of epidemiologic data.

Relative risk regression methods are described. These methods provide a unified approach to a range of data analysis problems in environmental risk assessment and in the study of disease risk factors more generally. Relative risk regression methods are most readily viewed as an outgrowth of Cox's regression and life model. They can also be viewed as a regression generalization of more classical epidemiologic procedures, such as that due to Mantel and Haenszel. In the context of an epidemiologic cohort study, relative risk regression methods extend conventional survival data methods and binary response (e.g., logistic) regression models by taking explicit account of the time to disease occurrence while allowing arbitrary baseline disease rates, general censorship, and time-varying risk factors. This latter feature is particularly relevant to many environmental risk assessment problems wherein one wishes to relate disease rates at a particular point in time to aspects of a preceding risk factor history. Relative risk regression methods also adapt readily to time-matched case-control studies and to certain less standard designs. The uses of relative risk regression methods are illustrated and the state of development of these procedures is discussed. It is argued that asymptotic partial likelihood estimation techniques are now well developed in the important special case in which the disease rates of interest have interpretations as counting process intensity functions. Estimation of relative risks processes corresponding to disease rates falling outside this class has, however, received limited attention. The general area of relative risk regression model criticism has, as yet, not been thoroughly studied, though a number of statistical groups are studying such features as tests of fit, residuals, diagnostics and graphical procedures. Most such studies have been restricted to exponential form relative risks as have simulation studies of relative risk estimation procedures with moderate numbers of disease events.