Two-sample nonparametric test for proportional reversed hazards

Abstract

In the last few decades, several works have been undertaken in the context of proportional reversed hazard rates (PRHR) but any specific statistical methodology for the PRHR hypothesis is absent in the literature. This paper proposes a two-sample nonparametric test based on two independent samples to verify the PRHR assumption. Based on a consistent U-statistic three statistical methodologies have been developed exploiting U-statistics theory, jackknife empirical likelihood and adjusted jackknife empirical likelihood method. A simulation study has been performed to assess the merit of the proposed test procedure. Finally, the proposed procedure is applied to a data set in the context of brain injury-related biomarkers and a data set related to Duchenne muscular dystrophy.