Advancing Stepped Wedge Cluster Randomized Trials Analysis: Bayesian Hierarchical Penalized Spline Models for Immediate and Time-Varying Intervention Effects

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Abstract
Stepped wedge cluster randomized trials (SWCRTs) often face challenges with potential confounding by time trends. Traditional frequentist methods can fail to provide adequate coverage of the intervention's true effect using confidence intervals, whereas Bayesian approaches show potential for better coverage of intervention effects. However, Bayesian methods have seen limited development in SWCRTs. We propose two novel Bayesian hierarchical penalized spline models for SWCRTs. The first model is for SWCRTs involving many clusters and time periods, focusing on immediate intervention effects. To evaluate its efficacy, we compared this model to traditional frequentist methods. We further developed the model to estimate time-varying intervention effects. We conducted a comparative analysis of this Bayesian spline model against an existing Bayesian monotone effect curve model. The proposed models are applied in the Primary Palliative Care for Emergency Medicine stepped wedge trial to evaluate the effectiveness of primary palliative care intervention. Extensive simulations and a real-world application demonstrate the strengths of the proposed Bayesian models. The Bayesian immediate effect model consistently achieves near the frequentist nominal coverage probability for true intervention effect, providing more reliable interval estimations than traditional frequentist models, while maintaining high estimation accuracy. The proposed Bayesian time-varying effect model exhibits advancements over the existing Bayesian monotone effect curve model in terms of improved accuracy and reliability. To the best of our knowledge, this is the first development of Bayesian hierarchical spline modeling for SWCRTs. The proposed models offer an accurate and robust analysis of intervention effects. Their application could lead to effective adjustments in intervention strategies.

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