General Relative Risk Regression Models for Epidemiologic Studies1

Three parametric families of relative risk functions for the analysis of case-control data are discussed. A desirable feature for any general relative risk function is that inference based on it be independent of the coding of a binary covariate. Only one of the three families considered has this property. Additionally, when the relative risk is not multiplicative, methods of inference based on the asymptotic covariance matrix are likely to be seriously misleading unless the sample size is very large, as has been noted previously in other papers. This is illustrated by means of examples. Likelihood-based procedures should routinely be employed when nonmultiplicative relative risk functions are used for analysis of case-control data.