A pseudolikelihood approach to analysis of nested case-control studies

In nested case-control studies the controls are sampled from the risk set at the failure times of the cases. The analytical basis for such studies has been limited to semiparametric estimators under proportional-hazard models. In this paper it is observed that conditional inclusion probabilities of ever being included in the nested case-control study can be obtained, where conditioning is on the information needed to carry out a nested case-control study. The inclusion probabilities are used in pseudolikelihoods by weighting the individual log-likelihood contributions by their inverse. This makes it possible to fit parametric regression models. Also a new semiparametric estimator is obtained under the proportional-hazard model. The methods are illustrated by simulation experiments and by application to a dataset.