A monotonicity property of weighted log-rank tests
2021
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.
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