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

In stepped wedge cluster randomized trials (SW-CRTs), interventions are sequentially rolled out to clusters over multiple periods. It is common practice to analyze SW-CRTs using discrete-time linear mixed models, in which measurements are considered to be taken at discrete time points. However, a recent systematic review found that 95.1\% of cross-sectional SW-CRTs recruit individuals continuously over time. Despite the high prevalence of designs with continuous recruitment, there has been limited guidance on how to draw model-robust inference when analyzing such SW-CRTs. In this article, we investigate through simulations the implications of using discrete-time linear mixed models in the case of continuous recruitment designs with a continuous outcome. First, in the data-generating process, we characterize continuous recruitment with a continuous-time exponential decay correlation structure in the presence or absence of a continuous period effect, addressing scenarios both with and without a random or exposure-time-dependent intervention effect. Then, we analyze the simulated data under three popular discrete-time working correlation structures: simple exchangeable, nested exchangeable, and discrete-time exponential decay, with a robust sandwich variance estimator. Our results demonstrate that discrete-time analysis often yields minimum bias, and the robust variance estimator with the Mancl and DeRouen correction consistently achieves nominal coverage and type I error rate. One important exception occurs when recruitment patterns vary systematically between control and intervention periods, where discrete-time analysis leads to slightly biased estimates. Finally, we illustrate these findings by reanalyzing a concluded SW-CRT.