How to achieve model-robust inference in stepped wedge trials with model-based methods?

TL;DR

This paper investigates the robustness of model-based methods like linear mixed models and GEE in stepped wedge trials, showing conditions under which they provide consistent treatment effect estimates even when models are misspecified.

Contribution

It provides theoretical conditions for model robustness in stepped wedge designs and demonstrates how to achieve valid inference despite model misspecification.

Findings

Consistency often requires correct treatment effect structure

Sandwich variance estimator ensures valid inference

G-computation improves robustness for ratio estimands

Abstract

A stepped wedge design is a unidirectional crossover design where clusters are randomized to distinct treatment sequences. While model-based analysis of stepped wedge designs is standard practice to evaluate treatment effects accounting for clustering and adjusting for covariates, their properties under misspecification have not been systematically explored. In this article, we focus on model-based methods, including linear mixed models and generalized estimating equations with an independence, simple exchangeable, or nested exchangeable working correlation structure. We study when a potentially misspecified working model can offer consistent estimation of the marginal treatment effect estimands, which are defined nonparametrically with potential outcomes and may be functions of calendar time and/or exposure time. We prove a central result that consistency for nonparametric estimands usually requires a correctly specified treatment effect structure, but generally not the remaining aspects of the working model (functional form of covariates, random effects, and residual distribution), and valid inference is obtained via the sandwich variance estimator. Furthermore, an additional g-computation step is required to achieve model-robust inference under non-identity link functions or for ratio estimands. The theoretical results are illustrated via several simulation experiments and re-analysis of a completed stepped wedge cluster randomized trial.