Semiparametric mixtures in case-controlstudies

We consider likelihood based inference in a class of logistic models for case-control studies with a partially observed covariate. The likelihood is a combination of a nonparametric mixture, a parametric likelihood, and an empirical likelihood. We prove the asymptotic normality of the maximum likelihood estimator for the regression slope, the asymptotic chi-squared distribution of the likelihood ratio statistic, and the consistency of the observed information, in both the prospective and the retrospective model. © 2001 Academic Press.