Variance Estimation for the Inverse Probability of Treatment Weighted Kaplan Meier Estimator

TL;DR

This paper develops a new variance estimator for the IPTW Kaplan-Meier estimator in survival analysis, accounting for estimated propensity scores, and demonstrates its improved accuracy over previous methods through simulations.

Contribution

It provides a rigorous asymptotic variance analysis for the IPTW KM estimator with estimated propensity scores and introduces a consistent plug-in variance estimator.

Findings

The proposed variance estimator is more accurate than XL's over-estimating method.

Estimating the propensity score reduces the asymptotic variance of the IPTW KM estimator.

Simulation results confirm the superiority of the new variance estimator.

Abstract

In a widely cited paper, Xie and Liu (henceforth XL) proposed to use inverse probability of treatment weighting (IPTW) to account for possible confounding in observational studies with survival endpoints subject to right censoring. Their proposal includes an IPTW Kaplan-Meier (KM) estimator for the survival function of a treatment-specific potential failure time, which can be used to evaluate the causal effect of one treatment versus another. The IPTW KM estimator is remarkably simple and highly effective for confounding bias correction. The method has been implemented in SAS's popular procedure LIFETEST for analyzing survival data and has seen widespread use. This letter is concerned with variance estimation for the IPTW KM estimator. The variance estimator provided by XL does not account for the variability of the IPTW weight when the propensity score is estimated from data, as is usually the case in observational studies. In this letter, we provide a rigorous asymptotic analysis of the IPTW KM estimator based on an estimated propensity score. Our analysis indicates that estimating the propensity score does tend to result in a smaller asymptotic variance, which can be estimated consistently using a plug-in variance estimator. We also present a simulation study comparing the variance estimator we propose with the XL variance estimator. Our simulation results confirm that the proposed variance estimator is more accurate than the XL variance estimator, which tends to over-estimate the sampling variance of the IPTW KM estimator.