On Combined Maximal Precedence–Exceedance Test with Application to HIV Clinical Trials

This paper proposes a combined maximal precedence–exceedance test (MPErs) that integrates maximal precedence and maximal exceedance statistics tests to provide sensitivity to both early and late distributional differences between two samples. The maximal exceedance component was introduced to complement the maximal precedence approach, thereby addressing the limited sensitivity of precedence-based procedures to late failures. The proposed (MPErs) test integrates precedence and exceedance statistics to provide a unified framework for detecting distributional differences occurring at different stages of the failure process. Classical precedence tests often lack a balanced sensitivity to early and late failures, motivating the proposed combined approach for reliable life-testing. Extensive Monte Carlo simulations demonstrated that MPErs achieved a superior statistical power compared to standard precedence (Pr) and maximal precedence (MPr) tests, with stable critical values and a consistent empirical size across distributions. The performance of MPErs was further validated on HIV clinical trial data comparing ZDV-only and ddI-only regimens. Across different early-stopping thresholds (r,s), MPErs outperformed other tests, achieving strong results at the earliest monitoring point (p=0.011). The test performed reliably across all scenarios, demonstrating its usefulness for analyzing early and late failure patterns in clinical trial data.