Model-robust standardization in stepped wedge designs

Abstract

Stepped-wedge cluster-randomized trials (SW-CRTs) are widely used in healthcare and implementation science, providing an ethical advantage by ensuring all clusters eventually receive the intervention. The staggered rollout of treatment introduces complexities in defining and estimating treatment effect estimands, particularly under informative sizes. Traditional model-based methods, including generalized estimating equations (GEE) and linear mixed models (LMM), produce estimates that depend on implicit weighting schemes and parametric assumptions, leading to bias for different types of estimands in the presence of informative sizes. While recent methods have attempted to provide robust estimation in SW-CRTs, they are restrictive on modeling assumptions or lack of general framework for consistent estimating multiple estimands under informative size. In this article, we propose a model-robust standardization framework for SW-CRTs that generalizes existing methods from parallel-arm CRTs. We define causal estimands including horizontal-individual, horizontal-cluster, vertical-individual, and vertical-cluster average treatment effects under a super population framework and introduce an augmented standardization estimator that standardizes parametric and semiparametric working models while maintaining robustness to informative cluster size under arbitrary misspecification. We evaluate the finite-sample properties of our proposed estimators through extensive simulation studies, assessing their performance under various SW-CRT designs. Finally, we illustrate the practical application of model-robust estimation through a reanalysis of two real-world SW-CRTs.

Figures (7)

• Figure 2: Panel (a): Estimated treatment effects in difference on PTSD symptom severity from the TSOS data using both MRS and Coef estimators under working models (W1) through (W6), as well as an unadjusted estimator. Each panel corresponds to one of the four estimands: h-iATE, h-cATE, v-iATE, and v-cATE. Panel (b): Estimated odds ratios of 30-day mortality from the ACS-QUIK trial under MRS and Coef estimators using working models (W7) through (W12), as well as an unadjusted estimator. Each panel corresponds to one of the four estimands: h-iATE, h-cATE, v-iATE, and v-cATE. For each model, point estimates and 95% confidence intervals are displayed for both the MRS and Coef estimators.
• Figure 3: Empirical rejection rates for the pairwise comparison tests for h-iATE versus h-cATE, v-iATE versus v-cATE and omnibus test of informative cluster size under different values of $\delta$, based on continuous outcomes and working models (W1) through (W6), as well as the unadjusted estimator (UNADJ).
• Figure 4: Empirical rejection rates for the pairwise comparison tests for h-iATE versus h-cATE, v-iATE versus v-cATE and omnibus test of informative cluster size under different values of $\delta$, based on binary outcomes and working models (W7) through (W12), as well as the unadjusted estimator (UNADJ).
• Figure 7: Illustration of a stepped-wedge cluster-randomized trial with an implementation period. The dashed columns indicate the baseline and final rollout periods, which are excluded from the estimand definition. Colored cells indicate intervention exposure after a cluster adopts the intervention; the dotted cells represent the implementation period immediately following adoption and are excluded from the estimand definition. Only non-dotted, non-dashed cluster-periods during the rollout contribute to the treatment effect estimands.
• Figure :

Theorems & Definitions (6)

• Remark : General consideration for fitting an outcome model
• Remark : Condition under which the augmented estimator and nonparametric estimator coincide
• proof
• Remark
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