Cluster-randomized trials often struggle with treatment noncompliance, making it hard to separate the effect of receiving treatment from the effect of having treated peers. The authors propose a Bayesian machine learning approach that combines Bayesian additive regression trees with cluster-level random effects. This setup flexibly models outcomes and treatment receipt while accounting for within-cluster dependence.
To avoid distortion from regularization, they augment the outcome regression with a clever covariate: the predicted mean proportion of treated peers from a preliminary receipt model. Using Bayesian g-computation, they estimate cluster-average intent-to-treat effects and cluster-average local average treatment effects, and they examine sensitivity to the cross-world restrictions underlying the decomposition.
Simulation studies show that the method reduces bias under model misspecification, while correctly specified parametric models retain expected frequentist properties. The clever covariate improves the direct–spillover decomposition under moderate or strong spillover, with similar gains in smaller clusters, though the benefits vary with spillover strength and the 95% credible intervals remain conservative.
Applied to the Primary School Deworming Project in Kenya, the approach suggests reduced infection risk, with a larger estimated contribution from individual treatment receipt than from peer receipt. Overall, the method offers a flexible Bayesian route to estimating direct and spillover effects in the presence of noncompliance.