Can discrete-time analyses be trusted for stepped wedge trials with continuous recruitment?

In stepped wedge cluster randomized trials (SW-CRTs), the intervention is rolled out to clusters sequentially over multiple periods. It is common practice to analyze data from SW-CRTs using linear mixed models that treat time as discrete. However, a recent systematic review found that 95.1% of cross-sectional SW-CRTs recruit individuals continuously over time. Despite the prevalence of continuous recruitment, there has been limited guidance on how to draw model-robust inference for such designs. In this article, we conduct simulation studies to examine the performance of discrete-time linear mixed models in the case of continuous recruitment designs with a continuous outcome. Specifically, we generate outcomes under a continuous-time exponential decay correlation structure with either discrete or continuous fixed period effects. We consider constant and exposure-time-dependent intervention effects, with and without random intervention effects across clusters. We then analyze the simulated data using linear mixed models under three discrete-time working correlation structures: simple exchangeable, nested exchangeable, and discrete-time exponential decay, with robust sandwich variance estimation. Our results demonstrate that discrete-time analysis often yields negligible bias and that the robust variance estimator with the Mancl and DeRouen correction consistently achieves nominal coverage and type I error rate. However, when recruitment patterns vary systematically between control and intervention periods, discrete-time analyses give slightly biased intervention effect estimates. Finally, we illustrate these findings by reanalyzing a completed SW-CRT.