Two-sample nonparametric test for proportional reversed hazards

TL;DR

This paper introduces a new nonparametric test for the proportional reversed hazard rate hypothesis using U-statistics, jackknife empirical likelihood, and adjusted methods, validated through simulations and applied to biomedical data.

Contribution

It develops the first specific statistical methodology for testing PRHR hypotheses using three innovative approaches based on U-statistics.

Findings

The proposed tests perform well in simulation studies.

The methods successfully analyze real biomedical datasets.

The approaches provide reliable inference for PRHR hypotheses.

Abstract

Several works have been undertaken in the context of proportional reversed hazard rate (PRHR) since last few decades. But any specific statistical methodology for the PRHR hypothesis is absent in the literature. In this paper, a two-sample nonparametric test based on two independent samples is proposed for verifying 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 procedures. Finally, the test is applied to a data in the context of brain injury-related biomarkers and a data related to Ducheme muscular dystrophy.