Sample size calculations in two-arm clinical trials with survival endpoint often utilize the proportional hazards (PH) assumption. In case of nonproportional hazards (NPH), much research is ongoing with some newer methods developed that work well in specific scenarios. Recent developments have considered the nonparametric Max-Combo logrank test for both design and analysis of survival data with NPH. Although many approaches have been proposed for analyzing time-to-event data with NPH such as Restricted Mean Survival Time, Average Hazard Ratios, and piecewise exponential model with hazard ratios changing over time, translation into sample size calculation is not obvious and relies on simulations for very specific scenarios of NPH. In the parametric setting, accelerated failure time models that allow NPH but require a constant time ratio assumption (PT assumption) have been proposed. Recently, a parametric approach that simultaneously allows both nonproportional hazards (NPH) and nonproportional time (NPT) has been proposed. It utilizes the concept of Relative Time (RT) with two different Weibull distributions for the two trial arms in the case of monotonically increasing/decreasing time ratios. A key limitation is that the hypotheses leading to the sample size calculation rely on a single effect size defined at a specific survival percentile. In our current work, we extend the parent RT method by utilizing the concept of Weighted Relative Time (WRT) that allows us comparison of the full survival curves. Performance of the proposed method is compared to the Max-Combo method under different weighting schemes, and its operation characteristics are studied via simulations.

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