The Analysis of Retrospective Family Studies

Case-control samples allow straightforward calculation of estimates of the association between covariates and disease status by fitting a prospective logistic regression model. In genetic studies of disease, investigators often gather additional information on response and covariate variables from family members of cases and controls. The objective is to model the responses of all the family members in terms of the covariate data. Whittemore (1995) has discussed maximum likelihood methods for fitting a special class of logistic models to family data collected according to a particular design. In the present paper, we show that we can obtain efficient semiparametric maximum likelihood estimates for an arbitrary multivariate binary regression model by fitting a modified prospective model for a wide class of retrospective designs. However, in contrast to the situation with simple case-control studies, the prospective model will differ from the original model even when the model is logistic.