Robust estimation for generalized case-cohort design under the proportional hazards model

In the large cohort study of infrequent survival event, generalized case-cohort design is a commonly used biased-sampling scheme to reduce the cost and improve the estimation efficiency. Combined with the auxiliary survival information, it has a chance to increase the efficiency further. We propose the generalized moment method for the proportional hazards model with two different weighted supplementary information under the generalized case-cohort study. If the auxiliary information is not accurate, we can use the generalized moment method by incorporating some crude information. The asymptotic properties of the proposed estimators and the Breslow estimators are established. These qualities are evaluated by some finite sample simulation studies and a real data analysis. Both theoretical and empirical analyses show that the proposed approaches are more efficient than the weighted estimating method. In the numerical studies, the proposed method with inconsistent auxiliary information is robust and even better than the full cohort estimator.