Improving efficiency of parameter estimation in case-cohort studies with multivariate failure time data.

The case-cohort study design is an effective way to reduce cost of assembling and measuring expensive covariates in large cohort studies. Recently, several weighted estimators were proposed for the case-cohort design when multiple diseases are of interest. However, these existing weighted estimators do not make effective use of the covariate information available in the whole cohort. Furthermore, the auxiliary information for the expensive covariates, which may be available in the studies, cannot be incorporated directly. In this article, we propose a class of updated-estimators. We show that, by making effective use of the whole cohort information, the proposed updated-estimators are guaranteed to be more efficient than the existing weighted estimators asymptotically. Furthermore, they are flexible to incorporate the auxiliary information whenever available. The advantages of the proposed updated-estimators are demonstrated in simulation studies and a real data analysis.