A monotonicity property of weighted log-rank tests

Tahani Coolen-Maturi and Frank P. A. Coolen

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 7, 2402-2416

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 Gρ family of tests, generalizes the logrank test by using weights assigned to observations. In this paper, we present a switch monotonicity property for the Gρ family of tests, which was motivated by the need to derive bounds for the test statistic in case of imprecise data observations. This property states that, when all observations from two independent groups are ranked together, the value of the z-test statistic is monotonically increasing after switching a pair of adjacent values from the two groups. Two examples are provided to motivate and illustrate the result presented in this paper.

Date: 2023
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DOI: 10.1080/03610926.2021.1952270

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