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A monotonicity property of weighted log-rank tests

Coolen-Maturi, T.; Coolen, F.P.A.

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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.

Journal Article Type Article
Acceptance Date Jun 30, 2021
Online Publication Date Jul 14, 2021
Publication Date 2023
Deposit Date Jun 30, 2021
Publicly Available Date May 17, 2023
Journal Communications in Statistics - Theory and Methods
Print ISSN 0361-0926
Electronic ISSN 1532-415X
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 52
Issue 7
Pages 2402-2416
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Copyright Statement
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.

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