CauchyCP: a powerful test under non-proportional hazards using Cauchy combination of change-point Cox regressions

Abstract: Non-proportional hazards data are routinely encountered in randomized clinical trials. In such cases, classic Cox proportional hazards model can suffer from severe power loss, with difficulty in interpretation of the estimated hazard ratio since the treatment effect varies over time. We propose CauchyCP, an omnibus test of change-point Cox regression models, to overcome both challenges while detecting signals of non-proportional hazards patterns. Extensive simulation studies demonstrate that, compared to existing treatment comparison tests under non-proportional hazards, the proposed CauchyCP test 1) controls the type I error better at small $\alpha$ levels ($< 0.01$); 2) increases the power of detecting time-varying effects; and 3) is more computationally efficient. The superior performance of CauchyCP is further illustrated using retrospective analyses of two randomized clinical trial datasets and a pharmacogenetic biomarker study dataset. The R package $\textit{CauchyCP}$ is publicly available on CRAN.