Best precedence tests for censored data

The prevalence of survival analyses based on a fixed duration of time-on-test, together with the need for generally powerful two-sample censored-data rank tests against stochastically ordered but not proportional-hazard alternatives, are used to motivate an extension of ‘precedence tests’ (Nelson (1963), Lin and Sukhatme (1989)) to right-censored survival data. The idea is to compare the r -th Kaplan-Meier quantile from the first sample with the s -th Kaplan-Meier quantile from the second sample, where r and s are nearby values chosen to give size α and best power against local proportional-hazards alternatives.