Optimal generalized case–cohort analysis with accelerated failure time model

Case–cohort design has been widely advocated in large cohort studies when the disease rate is low. When the event is not rare, it is desirable to consider a generalized case–cohort design where the covariates are observed only for a subcohort randomly selected from the underlying cohort and a subset of additional failures outside the subcohort. In this article, we propose the smoothed weighted Gehan estimating equation for regression parameters in the accelerated failure time model under generalized case–cohort design. Asymptotic properties of the proposed estimators are developed. To demonstrate the effectiveness of the generalized case–cohort sampling, we compare it with simple random sampling in terms of asymptotic relative efficiency. Furthermore, we derive the optimal allocation of the subsamples for the proposed design. The performance of the finite sample properties are evaluated via simulation studies. A real data set is analyzed to illustrate the estimating procedure.