Randomization inference for treatment effects on survival outcomes

Abstract

The log-rank test and Kaplan--Meier plot are standard tools for analyzing time-to-event data in randomized clinical trials, yet neither provides a summary of the magnitude of the treatment effect. Practitioners typically fill this gap by reporting a hazard ratio from a Cox proportional-hazards model or an acceleration factor from an accelerated failure time (AFT) model, but both require assumptions beyond those needed for the log-rank test or Kaplan--Meier estimator. We propose two nonparametric confidence intervals for scalar effect-size summaries, an additive shift c and a multiplicative factor $ρ$, obtained by inverting the log-rank test under sharp null hypotheses of constant treatment effects. Building on the randomization-inference framework of Li and Small (2023), both intervals are valid under the randomization distribution alone, requiring no assumptions for the event-time distribution. We evaluate the proposed multiplicative interval via simulation, finding that it maintains nominal coverage across a range of censoring rates and sample sizes, including under data-generating processes that misspecify a parametric AFT model, while incurring only a modest efficiency loss compared to parametric AFT inference under correct specification. We illustrate the approach using data from a randomized trial of rhDNase for cystic fibrosis and provide R code and a Shiny application for ease of implementation.