Model-assisted analysis of covariance estimators for stepped wedge cluster randomized experiments
Stepped wedge cluster randomized experiments represent a class of unidirectional crossover designs that are increasingly adopted for comparative effectiveness and implementation science research. Although stepped wedge cluster randomized experiments have become popular, definitions of estimands and robust methods to target clearly-defined estimands remain insufficient. To address this gap, we describe a class of estimands that explicitly acknowledge the multilevel data structure in stepped wedge cluster randomized experiments, and highlight three typical members of the estimand class that are interpretable and are of practical interest. We then discuss four formulations of analysis of covariance (ANCOVA) working models to achieve estimand-aligned analyses. By exploiting baseline covariates, each ANCOVA model can potentially improve the estimation efficiency over the unadjusted estimators. In addition, each ANCOVA estimator is model-assisted in a sense that its point estimator is consistent to the target estimand even when the working model is misspecified. Under the stepped wedge randomization scheme, we establish the finite population Central Limit Theorem for each estimator, which motivates design-based variance estimators. Through simulations, we study the finite-sample operating characteristics of the ANCOVA estimators under different data generating processes. We illustrate their applications via the analysis of the Washington State Expedited Partner Therapy study.