FITTING LOGISTIC-REGRESSION MODELS IN STRATIFIED CASE-CONTROL STUDIES

Methods are developed for fitting logistic models to data in which cases and/or controls are sampled from the available cases and controls within population strata. Particular attention is paid to models in which stratum differences are modelled as well as the effects of the different risk factors experienced by individuals within strata. Maximum likelihood estimation is developed for discrete explanatory variables and is compared with the method of Fears and Brown (1986, Biometrics 42, 955-960) and Breslow and Cain (1988, Biometrika 75, 11-20), in which the prospective logistic model is fitted with a fixed offset. An example is explored in which maximum likelihood estimation proves to be substantially more efficient than the Fears-Brown method and the modelling of the stratum effects leads to much more efficient estimates of regression coefficients for the remaining variables.