In comparing two treatments with the event time observations, the hazard ratio (HR) estimate is routinely used to quantify the treatment difference. However, this model dependent estimate may be difficult to interpret clinically especially when the proportional hazards (PH) assumption is violated. An alternative estimation procedure for treatment efficacy based on the restricted means survival time or t-year mean survival time (t-MST) has been discussed extensively in the statistical and clinical literature. On the other hand, a statistical test 1 via the HR or its asymptotically equivalent counterpart, the logrank test, is asymptotically distribution-free. In this paper, we assess the relative efficiency of the hazard ratio and t-MST tests with respect to the statistical power using various PH and non-PH models under theoretical and practical settings. When the PH assumption is valid, the t-MST test performs almost as well as the HR test. For non-PH models, the t-MST test can substantially outperform its HR counter- part. On the other hand, the HR test can be powerful when the true difference of two survival functions is quite large at end of the study. Unfortunately, for this case, the HR estimate may not have a simple clinical interpretation for the treatment effect due to the violation of the PH assumption.
Tian, Lu; Fu, Haoda; Ruberg, Stephen J.; Uno, Hajime; and Wei, LJ, "Efficiency of Two Sample Tests via the t-Mean Survival Time for Analyzing Event Time Observations" (November 2016). Harvard University Biostatistics Working Paper Series. Working Paper 210.