Finite-Sample Valid Survival Tests under Continuous Monitoring via Doléans–Dade Exponentials

We present a general framework for constructing e-processes to test equality of hazards in right-censored time-to-event data. We weight a counting-process martingale and take its Doléans–Dade exponential. We propose a weight function tailored to non-proportional-hazards alternatives and evaluate its performance through simulations. Specifically, we compare the resulting e-process with the classical log-rank test and the anytime-valid log-rank test under both proportional-hazards and crossing-hazards alternatives.