The population-based case-control study design has been widely used for studying the etiology of chronic diseases. It is well established that the Cox proportional hazards model can be adapted to the case-control study and hazard ratios can be estimated by (conditional) logistic regression model with time as either a matched set or a covariate (Prentice and Breslow, 1978). However, the baseline hazard function, a critical component in absolute risk assessment, is unidentifiable, because the ratio of cases and controls is controlled by the investigators and does not reflect the true disease incidence rate in the population. In this paper we propose a simple and innovative approach, which makes use of routinely collected family history information, to estimate the baseline hazard function for any logistic regression model that is fit to the risk factor data collected on cases and controls. We establish that the proposed baseline hazard function estimator is consistent and asymptotically normal and show via simulation that it performs well in finite samples. We illustrate the proposed method by a population-based case-control study of prostate cancer where the association of various risk factors is assessed and the family history information is used to estimate the baseline hazard function.
Keywords: Copula model; Family history; Marginal hazard function; Multivariate survival analysis.