A stepped wedge design is a unidirectional crossover design where clusters are randomized to distinct treatment sequences defined by calendar time. While model-based analysis of stepped wedge designs -- via linear mixed models or generalized estimating equations -- is standard practice to evaluate treatment effects accounting for clustering and adjusting for baseline covariates, formal results on their model-robustness properties remain unavailable. In this article, we study when a potentially misspecified multilevel model can offer consistent estimators for treatment effect estimands that are functions of calendar time and/or exposure time. We describe a super-population potential outcomes framework to define treatment effect estimands of interest in stepped wedge designs, and adapt linear mixed models and generalized estimating equations to achieve estimand-aligned inference. We prove a central result that, as long as the treatment effect structure is correctly specified in each working model, our treatment effect estimator is robust to arbitrary misspecification of all remaining model components. The theoretical results are illustrated via simulation experiments and re-analysis of a cardiovascular stepped wedge cluster randomized trial.

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