The Safe Logrank Test: Error Control under Optional Stopping, Continuation and Prior Misspecification
Proceedings of AAAI Spring Symposium on Survival Prediction - Algorithms, Challenges, and Applications 2021, PMLR 146:107-117, 2021.
We introduce the safe logrank test, a version of the logrank test that can retain type-I error guarantees under optional stopping and continuation. It allows for effortless combination of data from different trials on different sub-populations while keeping type-I error guarantees and can be extended to define always-valid confidence intervals. Prior knowledge can be accounted for via prior distributions on the hazard ratio in the alternative, but even under ‘bad’ priors Type I error bounds are guaranteed. The test is an instance of the recently developed martingale tests based on e-values. Initial experiments show that the safe logrank test performs well in terms of the maximal and the expected amount of events needed to obtain a desired power.