Power calculation for cross-sectional stepped wedge cluster randomized trials with a time-to-event endpoint

Abstract

Stepped wedge cluster randomized trials (SW-CRTs) are a form of randomized trial whereby clusters are progressively transitioned from control to intervention, with the timing of transition randomized for each cluster. An important task at the design stage is to ensure that the planned trial has sufficient power. While methods for determining power have been well-developed for SW-CRTs with continuous and binary outcomes, limited methods for power calculation are available for SW-CRTs with censored time-to-event outcomes. In this article, we propose a stratified marginal Cox model to analyze cross-sectional SW-CRTs and then derive an explicit expression of the robust sandwich variance to facilitate power calculations without the need for computationally intensive simulations. Power formulas based on both the Wald and robust score tests are developed, assuming constant within-period and between-period correlation parameters, and are further validated via simulation under different finite-sample scenarios. Finally, we illustrate our methods in the context of a SW-CRT testing the effect of a new electronic reminder system on time to catheter removal in hospital settings. We also offer an R Shiny application to facilitate sample size and power calculations using our proposed methods.

Keywords: Kendall’s tau; generalized intracluster correlation coefficient; marginal Cox proportional hazards model; sample size estimation; small-sample corrections; survival analysis.