Asymptotic theory for the semiparametric accelerated failure time model with missing data

TL;DR

This paper develops a semiparametric asymptotic theory for weighted rank-based estimators in accelerated failure time models with missing data, demonstrating improved efficiency and practical performance through simulations.

Contribution

It introduces a novel asymptotic framework for doubly weighted estimators in AFT models with missing data, accommodating non-predictable weights and empirical process techniques.

Findings

Weighted estimators perform well in finite samples.

Estimated weights increase efficiency.

Gehan weights are highly effective across various scenarios.

Abstract

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 as required in a martingale stochastic process formulation. We treat the general problem as a semiparametric 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 on 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 be surprisingly efficient in a wide class of problems.