Title: Design & analysis of cross-sectional stepped wedge cluster randomized trials with time-to-event endpoints
Abstract: Stepped wedge cluster randomized trials (SW-CRTs) are a form of randomized trial where clusters are progressively transitioned from control to intervention, and the timing of transition is randomized for each cluster. An important task at the design stage is to ensure that the planned trial has sufficient power to observe clinically meaningful effects. While methods for determining study power have been developed for SW-CRTs with continuous, binary or count outcomes, limited methods are available for SW-CRTs with censored time-to-event outcomes. To bridge this gap, I propose a stratified marginal Cox model to account for confounding by time in SW-CRTs and develop analytical power calculation methods based on a nested Archimedean copula that differentiates between within- and between-period dependencies for the latent survival time. I also derive the explicit expression of the robust sandwich variance and develop new with- and between-period correlation metrics on the martingale scale. Power formulas based on both the Wald and robust score tests are analytically developed and compared via simulations, demonstrating different finite-sample behaviors. Finally, I illustrate these methods using the context of a recently completed SW-CRT testing the effect of a new pediatric ventilator liberation protocol on time to ventilator liberation.