Conformal causal inference for cluster randomized trials: model-robust inference without asymptotic approximations

Abstract: Traditional statistical inference in cluster randomized trials typically invokes the asymptotic theory that requires the number of clusters to approach infinity. In this article, we propose an alternative conformal causal inference framework for analyzing cluster randomized trials that achieves the target inferential goal in finite samples without the need for asymptotic approximations. Different from traditional inference focusing on estimating the average treatment effect, our conformal causal inference aims to provide prediction intervals for the difference of counterfactual outcomes, thereby providing a new decision-making tool for clusters and individuals in the same target population. We prove that this framework is compatible with arbitrary working outcome models -- including data-adaptive machine learning methods that maximally leverage information from baseline covariates, and enjoys robustness against misspecification of working outcome models. Under our conformal causal inference framework, we develop efficient computation algorithms to construct prediction intervals for treatment effects at both the cluster and individual levels, and further extend to address inferential targets defined based on pre-specified covariate subgroups. Finally, we demonstrate the properties of our methods via simulations and a real data application based on a completed cluster randomized trial for treating chronic pain.