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 controls and their relatives. Parameters of interest are effects of risk factors on the failure time hazard function and within-family dependencies 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 semiparametric shared frailty model. We also present a simple, easily computed, and noniterative nonparametric estimator for the cumulative baseline 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.
"Case-control survival analysis with a general semiparametric shared frailty model: A pseudo full likelihood approach." Ann. Statist. 37 (3) 1489 - 1517, June 2009. https://doi.org/10.1214/08-AOS615