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, generalizes the logrank test by using weights assigned to observations. In this paper, we present a switch 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. 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.

摘要

对数秩检验是一种著名的非参数检验，常用于比较包括右删失观察在内的两个样本的生存分布，也称为 Mantel-Haenszel 检验。这$G^{\rho }$系列测试，通过使用分配给观察值的权重来推广对数秩检验。在本文中，我们提出了开关单调性属性$G^{\rho }$测试族，其动机是在不精确的数据观察的情况下需要推导测试统计量的界限。此属性指出，当来自两个独立组的所有观察值一起排名时， z检验统计量的值在切换两个组中的一对相邻值后单调增加。提供了两个例子来激发和说明本文中提出的结果。