  The log-rank test is most powerful under proportional hazards (PH). In
practice, non-PH patterns are often observed in clinical trials, such as in
immuno-oncology; therefore, alternative methods are needed to restore the
efficiency of statistical testing. Three categories of testing methods were
evaluated, including weighted log-rank tests, Kaplan-Meier curve-based tests
(including weighted Kaplan-Meier and Restricted Mean Survival Time, RMST), and
combination tests (including Breslow test, Lee's combo test, and MaxCombo
test). Nine scenarios representing the PH and various non-PH patterns were
simulated. The power, type I error, and effect estimates of each method were
compared. In general, all tests control type I error well. There is not a
single most powerful test across all scenarios. In the absence of prior
knowledge regarding the PH or non-PH patterns, the MaxCombo test is relatively
robust across patterns. Since the treatment effect changes overtime under
non-PH, the overall profile of the treatment effect may not be represented
comprehensively based on a single measure. Thus, multiple measures of the
treatment effect should be pre-specified as sensitivity analyses to evaluate
the totality of the data.
