🤖 AI Summary
This paper addresses the bias in variance estimation for the inverse probability weighted Kaplan–Meier (IPTW-KM) estimator in observational survival analysis. We show that the classical “XL” method neglects variability induced by propensity score estimation, leading to upwardly biased variance estimates. To resolve this, we establish the first rigorous asymptotic theory for the IPTW-KM estimator under data-driven propensity score estimation—revealing that propensity score estimation actually reduces the asymptotic variance. Building on this insight, we propose a consistent plug-in variance estimator that explicitly accounts for uncertainty from propensity score estimation. Through theoretical derivation and extensive simulation studies, our method achieves substantially improved variance estimation accuracy, eliminates upward bias, and enhances the reliability of causal effect inference in survival analysis.
📝 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.