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A monotonicity property of weighted log-rank tests

Coolen-Maturi, T. and Coolen, F.P.A. (2022) 'A monotonicity property of weighted log-rank tests.', Communications in statistics - theory and methods. .

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, introduced by Harrington and Fleming (1982), 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.

Item Type:Article
Full text:Publisher-imposed embargo
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1080/03610926.2021.1952270
Publisher statement:© 2021 The Author(s). Published with license by Taylor & Francis Group, LLC This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), 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.
Date accepted:30 June 2021
Date deposited:30 June 2021
Date of first online publication:14 July 2021
Date first made open access:20 December 2021

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