Sample size calculation under nonproportional hazards using average hazard ratios

Abstract

Many clinical trials assess time-to-event endpoints. To describe the difference between groups in terms of time to event, we often employ hazard ratios. However, the hazard ratio is only informative in the case of proportional hazards (PHs) over time. There exist many other effect measures that do not require PHs. One of them is the average hazard ratio (AHR). Its core idea is to utilize a time-dependent weighting function that accounts for time variation. Though propagated in methodological research papers, the AHR is rarely used in practice. To facilitate its application, we unfold approaches for sample size calculation of an AHR test. We assess the reliability of the sample size calculation by extensive simulation studies covering various survival and censoring distributions with proportional as well as nonproportional hazards (N-PHs). The findings suggest that a simulation-based sample size calculation approach can be useful for designing clinical trials with N-PHs. Using the AHR can result in increased statistical power to detect differences between groups with more efficient sample sizes.