A monotonicity property of weighted log-rank tests

The logrank test is a well-known nonparametric which often used to compare the survival distributions of two samples including right-censored observations, it also known as Mantel-Haenszel test. Gρ family tests, generalizes by using weights assigned observations. In this paper, we present switch monotonicity property for was motivated need derive bounds statistic in case imprecise data This states that, when all observations from independent groups are ranked together, value z-test monotonically increasing after switching pair adjacent values groups. Two examples provided motivate and illustrate result presented paper.