A Bayesian machine learning approach to direct and spillover effects in cluster-randomized trials with noncompliance

Abstract

We develop a Bayesian machine learning approach for estimating direct and spillover effects in cluster-randomized trials with treatment noncompliance. To flexibly model outcomes and treatment receipt while accounting for within-cluster dependence, we combine Bayesian additive regression trees with cluster-level random effects. We augment the outcome regression with a peer-treatment clever covariate, defined as the predicted mean proportion of treated peers from a preliminary receipt model, to mitigate regularization-induced distortion of the effect decomposition. Within a Bayesian g-computation framework, we estimate cluster-average intent-to-treat effects and cluster-average local average treatment effects and examine sensitivity to the cross-world restrictions underlying their decomposition. Simulation studies show reduced bias under model misspecification, while the correctly specified parametric models show expected frequentist properties. We find that the clever covariate improves the decomposition of the total effect into direct and spillover components under moderate or strong spillover, with similar gains in smaller clusters. Its benefits vary with spillover strength, and the $95\%$ credible intervals remain conservative. An application to the Primary School Deworming Project in Kenya suggests reduced infection risk, with a larger estimated contribution from individual treatment receipt than from peer receipt. Overall, our approach provides a flexible Bayesian estimation of direct and spillover effect decomposition in the presence of treatment noncompliance.