A monotonicity property of weighted log-rank tests

TL;DR

This paper investigates a monotonicity property of the $G^{ ho}$ family of weighted log-rank tests, which are used in survival analysis to compare distributions with censored data, aiding in deriving bounds for imprecise data.

Contribution

It establishes a monotonicity property for the $G^{ ho}$ tests, enhancing understanding of their behavior under data imprecision.

Findings

Proves a monotonicity property for weighted log-rank tests.

Provides bounds for test statistics with imprecise data.

Enhances robustness analysis of survival tests.

Abstract

The logrank test is a well-known nonparametric test which is often used to compare the survival distributions of two samples including right censored observations, it is also known as the Mantel-Haenszel test. The $G^{\rho}$ family of tests, introduced by Harrington and Fleming (1982), generalizes the logrank test by using weights assigned to observations. In this paper, we present a monotonicity property for the $G^{\rho}$ family of tests, which was motivated by the need to derive bounds for the test statistic in case of imprecise data observations.