Regression analysis for secondary response variable in a case-cohort study

Case-cohort study design has been widely used for its cost-effectiveness. In any real study, there are always other important outcomes of interest beside the failure time that the original case-cohort study is based on. How to utilize the available case-cohort data to study the relationship of a secondary outcome with the primary exposure obtained through the case-cohort study is not well studied. In this article, we propose a non-parametric estimated likelihood approach for analyzing a secondary outcome in a case-cohort study. The estimation is based on maximizing a semiparametric likelihood function that is built jointly on both time-to-failure outcome and the secondary outcome. The proposed estimator is shown to be consistent, efficient, and asymptotically normal. Finite sample performance is evaluated via simulation studies. Data from the Sister Study is analyzed to illustrate our method.