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

## TL;DR

This paper compares three methods for handling censored data in regression using the Kaplan-Meier estimator, focusing on their asymptotic variances and performance.

## Contribution

The paper provides a novel comparison of three inverse probability of censoring weighted regression methods using asymptotic variance expressions.

## Key findings

- No single method consistently has the lowest asymptotic variance across all censoring distributions.
- The standard sandwich variance estimator overestimates variance under the implied assumptions for all three methods.
- Expressions for asymptotic variances are derived and compared for each method.

## 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.