An Extension of Greenwood's Formula to Variances

TL;DR

This paper extends Greenwood's formula to estimate the variance of the Greenwood variance estimator, demonstrating its smaller asymptotic variance and robustness compared to the Kaplan-Meier estimator.

Contribution

It introduces a new estimator for the asymptotic variance of Greenwood's estimator, enhancing variance assessment in survival analysis.

Findings

The asymptotic variance of the Greenwood estimator is smaller than that of the Kaplan-Meier estimator.

The new estimator improves the robustness of variance estimation in survival analysis.

Greenwood's estimator shows reduced variability, leading to more reliable confidence intervals.

Abstract

In this article, we introduce an estimator for the asymptotic variance of the Greenwood variance estimator, where the latter is crucial for assessing the accuracy of the Kaplan-Meier survival estimator. The result indicates that the asymptotic variance of the Greenwood variance estimator is considerably smaller than that of the Kaplan-Meier variance estimator. This finding emphasizes the robustness of the Greenwood estimator.