The Safe Log Rank Test: Error Control under Optional Stopping, Continuation and Prior Misspecification

We introduce the safe log rank test, a version of the log rank test that can retain type-I error guarantees under optional stopping and continuation. It allows for effortless combination of data from different trials while keeping type-I error guarantees, and can be extended to define always-valid confidence intervals. The test is an instance of the recently developed martingale tests based on e-values. We demonstrate the validity of the underlying nonnegative martingale and show how to extend it to sequences of events with ties and to Cox proportional hazards regression. Initial experiments show that the safe log rank test performs well in terms of the maximal and the expected amount of events needed to obtain a desired power.