A two-step approach for analyzing time to event data under non-proportional hazards

TL;DR

This paper proposes a two-step testing procedure for time-to-event data that adapts to violations of proportional hazards, using a permutation framework to control error rates and improve analysis robustness in clinical trials.

Contribution

It introduces a novel two-stage test that adjusts based on a pre-test of proportional hazards, ensuring valid inference under non-proportional hazards conditions.

Findings

The two-stage test maintains correct type-I error rates.

It outperforms traditional tests under non-proportional hazards.

Permutation embedding ensures robust error control.

Abstract

The log-rank test and the Cox proportional hazards model are commonly used to compare time-to-event data in clinical trials, as they are most powerful under proportional hazards. But there is a loss of power if this assumption is violated, which is the case for some new oncology drugs like immunotherapies. We consider a two-stage test procedure, in which the weighting of the log-rank test statistic depends on a pre-test of the proportional hazards assumption. I.e., depending on the pre-test either the log-rank or an alternative test is used to compare the survival probabilities. We show that if naively implemented this can lead to a substantial inflation of the type-I error rate. To address this, we embed the two-stage test in a permutation test framework to keep the nominal level alpha. We compare the operating characteristics of the two-stage test with the log-rank test and other tests by clinical trial simulations.