In the analysis of cluster randomized trials, two typical features are that individuals within a cluster are correlated and that the total number of clusters can sometimes be limited. While model-robust treatment effect estimators have been recently developed, their asymptotic theory requires the number of clusters to approach infinity, and one often has to empirically assess the applicability of those methods in finite samples. To address this challenge, we propose a conformal causal inference framework that achieves the target coverage probability of treatment effects in finite samples without the need for asymptotic approximations. Meanwhile, we prove that this framework is compatible with arbitrary working models, including machine learning algorithms leveraging baseline covariates, possesses robustness against arbitrary misspecification of working models, and accommodates a variety of within-cluster correlations. Under this framework, we offer efficient algorithms to make inferences on treatment effects at both the cluster and individual levels, applicable to user-specified covariate subgroups and two types of test data. Finally, we demonstrate our methods via simulations and a real data application based on a cluster randomized trial for treating chronic pain.

翻译：在分析群随机试验时，两个典型特征是群内个体之间存在相关性，且群的总数有时可能有限。尽管近期已开发出模型鲁棒的治疗效应估计量，但其渐近理论要求群数量趋近无穷，且通常需通过经验评估这些方法在有限样本中的适用性。为解决这一挑战，我们提出了一种共形因果推断框架，该框架无需渐近近似即可在有限样本中实现治疗效应的目标覆盖概率。同时，我们证明该框架兼容任意工作模型（包括利用基线协变量的机器学习算法），对工作模型的任意错误设定具有鲁棒性，并能适应多种群内相关性结构。在此框架下，我们提供高效算法，可在群和个体两个层面对治疗效应进行推断，适用于用户指定的协变量亚组及两类测试数据。最后，我们通过模拟实验和一项基于慢性疼痛治疗的群随机试验真实数据应用展示了所提方法的效果。