Quantifying treatment differences in confirmatory trials with delayed effects
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Dealing with non-proportional hazards is increasingly common nowadays when designing confirmatory clinical trials in oncology. Under these circumstances, the hazard ratio may not be the best statistical measurement of treatment effect, and nor is log-rank test since it will no longer be the most powerful statistical test. Possible alternatives include the restricted mean survival time (RMST), that does not rely on the proportional hazards assumption and is clinically interpretable, and the weighted log-rank test, which is proven to outperform the log-rank test in delayed effects settings. We conduct simulations to evaluate the performance and operating characteristics of the RMST-based inference and compared to the log-rank test and weighted log-rank test with parameter values (ρ=0, γ=1), as well as their linked hazard ratios. The weighted log-rank test is generally the most powerful test in a delayed effects setting, and RMST-based tests have, under certain conditions, better performance than the log-rank test when the truncation time is reasonably close to the tail of the observed curves. In terms of treatment effect quantification, the hazard ratio linked to the weighted log-rank test is able to capture the maximal treatment difference and provides a valuable summary of the treatment effect in delayed effect settings. Hence, we recommend the inclusion of the hazard ratio linked to the weighted log-rank test among the measurements of treatment effect in settings where there is suspicion of substantial departure from the proportional hazards assumption.
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