Detecting Early and Late Divergences in Survival Curves Using Nonparametric Effect Measures

Abstract

Clinical trials often show treatment curves that diverge early and converge later, or vice versa patterns that are poorly captured by the proportional-hazards assumption. We develop a joint inferential framework for two nonparametric functionals of censored survival data: the Kaplan--Meier-based Mann--Whitney effect and a novel temporal contrast separating early and late differences. The approach provides interpretable, probability-scale effect measures and enables joint inference for global and temporal contrasts under right censoring. In simulation studies, the method outperforms the log-rank test under non-proportional hazards while maintaining nominal type-I error. A real-world application illustrates how the temporal contrast reveals clinically meaningful early treatment advantages that remain hidden in standard analyses