Bayesian Spatial Point Process Modeling for Cluster Randomized Trials

Cluster randomized trials (CRTs) offer a practical alternative for addressing logistical challenges and ensuring feasibility in community health, education, and prevention studies, even though randomized controlled trials are considered the gold standard in evaluating therapeutic interventions. Despite their utility, CRTs are often criticized for limited precision and complex modeling requirements. Advances in robust Bayesian methods and the incorporation of spatial correlation into CRT design and analysis remain relatively underdeveloped. This paper introduces a Bayesian spatial point process framework that models individuals nested within geographic clusters while explicitly accounting for spatial dependence. We demonstrate that conventional non-spatial models consistently underestimate uncertainty and lead to misleading inferences, whereas our spatial approach improves estimation stability, controls type I error, and enhances statistical power. Our results underscore the value and need for wider adoption of spatial methods in CRT.