Robust and efficient semiparametric modeling and inference for the stepped wedge design

Abstract

Stepped wedge designs (SWDs) are increasingly used to evaluate longitudinal cluster-level interventions but pose substantial challenges for valid inference. Because crossover times are randomized, intervention effects are intrinsically confounded with secular time trends, while heterogeneous
cluster effects, complex correlation structures, baseline covariate imbalances, and unreliable standard errors from few clusters further complicate statistical inference. We propose a unified semiparametric framework for estimating
possibly time-varying intervention effects in SWDs that directly addresses these issues.  A nonstandard development of semiparametric efficiency theory
is required to accommodate correlated observations within clusters, non-identically distributed outcomes across clusters due to varying cluster-period sizes, and weakly dependent treatment assignments that are hallmarks of
SWDs. The resulting estimator of treatment contrast is consistent and asymptotically normal even under misspecification of the covariance structure and control cluster-period means, and achieves the semiparametric efficiency bound when both are correctly specified. To facilitate inference for trials with few clusters, we introduce a permutation-based procedure to better capture finite-sample variability and a leave-one-out correction to mitigate plug-in bias.

We further discuss how effect modification can be naturally incorporated, and imbalanced precision variables can be accommodated via a simple adjustment closely related to post-stratification, a novel connection of independent interest. Simulations and application to a public health trial
demonstrate the robustness and efficiency of the proposed method relative to standard approaches.