Efficient Estimation for Dimension Reduction with Censored Data

TL;DR

This paper introduces a flexible dimension reduction method for censored survival data using a geometric and martingale approach, providing estimators that are both feasible and statistically efficient.

Contribution

It develops a general index model for survival data that does not require covariate-independent censoring and establishes the efficiency and asymptotic properties of the estimators.

Findings

Estimators are root-n consistent and asymptotically normal.

The proposed method outperforms existing techniques in simulations.

Application to AIDS data demonstrates practical usefulness.

Abstract

We propose a general index model for survival data, which generalizes many commonly used semiparametric survival models and belongs to the framework of dimension reduction. Using a combination of geometric approach in semiparametrics and martingale treatment in survival data analysis, we devise estimation procedures that are feasible and do not require covariate-independent censoring as assumed in many dimension reduction methods for censored survival data. We establish the root-$n$ consistency and asymptotic normality of the proposed estimators and derive the most efficient estimator in this class for the general index model. Numerical experiments are carried out to demonstrate the empirical performance of the proposed estimators and an application to an AIDS data further illustrates the usefulness of the work.