Case-control survival analysis with a general semiparametric shared frailty model--a pseudo full likelihood approach

In this work we deal with correlated failure time (age at onset) data arising from population-based case-control studies, where case and control probands are selected by population-based sampling and an array of risk factor measures is collected for both cases and con- trols and their relatives. Parameters of interest are e?ects of risk factors on the failure time hazard function and within-family depen- dencies among failure times after adjusting for the risk factors. Due to the retrospective sampling scheme, large sample theory for existing methods has not been established. We develop a novel technique for estimating the parameters of interest under a general semiparamet- ric shared frailty model. We also present a simple, easily computed, and non-iterative nonparametric estimator for the cumulative base- line hazard function. We provide rigorous large sample theory for the proposed method. We also present simulation results and a real data example for illustrating the utility of the proposed method.