We propose and discuss a Bayesian procedure to estimate the average treatment effect (ATE) for multilevel observations in the presence of confounding. We focus on situations where the confounders may be latent (e.g., spatial latent effects). This work is motivated by an interest in determining the causal impact of directly observed therapy (DOT) on the successful treatment of Tuberculosis (TB); the available data correspond to individual-level information observed across different cities in a state in Brazil. We focus on propensity score regression and covariate adjustment to balance the treatment (DOT) allocation. We discuss the need to include latent local-level random effects in the propensity score model to reduce bias in the estimation of the ATE. A simulation study suggests that accounting for the multilevel nature of the data with latent structures in both the outcome and propensity score models has the potential to reduce bias in the estimation of causal effects.

翻译：我们提出并讨论了一种贝叶斯程序，用于在存在混杂因素的情况下估计多层次观测数据的平均处理效应（ATE）。我们重点关注混杂因素可能是潜在（例如空间潜在效应）的情形。本研究源于确定直接观察治疗（DOT）对结核病（TB）成功治疗的因果影响的实际需求；可用数据对应于巴西某州不同城市观测到的个体层面信息。我们聚焦于倾向得分回归和协变量调整以平衡处理（DOT）分配。讨论认为，在倾向得分模型中纳入潜在的地方层面随机效应以减小ATE估计偏差是必要的。模拟研究表明，在结果模型和倾向得分模型中同时考虑数据的多层次性质及潜在结构，具有减少因果效应估计偏差的潜力。