Joint Semiparametric Regression Models for Secondary Responses in Case-Cohort Studies

Music City Center 

Case-cohort studies are widely used as a cost-effective sampling strategy. It is often of interest to analyze the association between the secondary responses and the main exposures in a case-cohort study. The analysis of the secondary responses using the case-cohort data is not well studied. We propose a joint model of the time-to-event survival outcome, the continuous secondary responses, and the multivariate mix-type expensive exposures. Specifically, a Cox proportional hazards model, a multivariate linear regression model, and a semiparametric density ratio model are assumed for the failure time, the secondary responses, and the expensive exposures, respectively. The density ratio model is flexible in modeling multivariate mixed-type data without specifying the baseline distribution function. We develop nonparametric maximum likelihood-based estimation and inference procedures. The resulting nonparametric maximum likelihood estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Extensive simulation studies demonstrate that the asymptotic approximations are accurate under practical settings. The proposed methods are also shown to be reasonably robust to some model misspecifications. We apply the proposed methods to the National Wilms Tumor Study data.