A comparison of Kaplan--Meier-based inverse probability of censoring weighted regression methods

TL;DR

This paper compares three Kaplan--Meier-based inverse probability of censoring weighted regression methods, analyzing their asymptotic variances and variance estimators to determine their relative efficiency in handling censored data.

Contribution

It provides a detailed comparison of three different inverse probability of censoring weighted regression approaches using Kaplan--Meier estimators, including variance expressions and their implications.

Findings

No single method consistently outperforms others in variance.

The optimal method depends on the censoring distribution.

Standard variance estimators tend to overestimate variance.

Abstract

Weighting with the inverse probability of censoring is an approach to deal with censoring in regression analyses where the outcome may be missing due to right-censoring. In this paper, three separate approaches involving this idea in a setting where the Kaplan--Meier estimator is used for estimating the censoring probability are compared. In more detail, the three approaches involve weighted regression, regression with a weighted outcome, and regression of a jack-knife pseudo-observation based on a weighted estimator. Expressions of the asymptotic variances are given in each case and the expressions are compared to each other and to the uncensored case. In terms of low asymptotic variance, a clear winner cannot be found. Which approach will have the lowest asymptotic variance depends on the censoring distribution. Expressions of the limit of the standard sandwich variance estimator in the three cases are also provided, revealing an overestimation under the implied assumptions.