ASYMPTOTIC THEORY FOR THE SEMIPARAMETRIC ACCELERATED FAILURE TIME MODEL WITH MISSING DATA

We consider a class of doubly weighted rank-based estimating methods for the transformation (or accelerated failure time) model with missing. data as arise, for example, in case-cohort studies. The weights considered may not be predictable its required in a martingale stochastic process formulation. We treat the general problem as a semi parametric estimating equation problem and provide proofs of asymptotic properties for the weighted estimators, with either true weights or estimated Weights. by using empirical process theory where martingale theory may fail. Simulations show that the outcome-dependent weighted method works well for finite samples in case-cohort studies and improves efficiency compared to methods based oil predictable weights. Further. it is seen that the method is even more efficient when estimated Weights are used, as is commonly the case in the missing data literature. The Gehan censored data Wilcoxon weights are found to lie surprisingly efficient in a wide class of problems.