Bayesian Hierarchical Penalized Spline Models for Immediate and Time-Varying Intervention Effects in Stepped Wedge...

Stepped wedge cluster randomized trials (SWCRTs) often face challenges related to potential confounding by time. Traditional frequentist methods may not provide adequate coverage of an intervention's true effect using confidence intervals, whereas Bayesian approaches show potential for better coverage of intervention effects. However, Bayesian methods remain underexplored in the context of SWCRTs. To bridge this gap, we propose two innovative Bayesian hierarchical penalized spline models. Our first model accommodates large numbers of clusters and time periods, focusing on immediate intervention effects. To evaluate this approach, we compared this model to traditional frequentist methods. We then extend our approach to account for time-varying intervention effects, conducting a comprehensive comparison with an existing Bayesian monotone effect curve model and alternative frequentist methods. The proposed models were applied in the Primary Palliative Care for Emergency Medicine stepped wedge trial to evaluate the effectiveness of the intervention. Through extensive simulations and real-world application, we demonstrate the robustness of our proposed Bayesian models. Notably, the Bayesian immediate effect model consistently achieves the nominal coverage probability, providing more reliable interval estimations while maintaining high estimation accuracy. Furthermore, our proposed Bayesian time-varying effect model represents a significant advancement over the existing Bayesian monotone effect curve model, offering improved accuracy and reliability in estimation while also achieving higher coverage probability than alternative frequentist methods. To the best of our knowledge, this marks the first development of Bayesian hierarchical spline modeling for SWCRTs. Our proposed models offer promising tools for researchers and practitioners, enabling more precise evaluation of intervention impacts.