Abstract Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania.

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使用聚类数据进行因果推断的倾向得分加权

摘要 倾向得分加权是一种因果推断工具，用于调整观察性研究中测量的混杂因素。在实践中，数据通常呈现复杂的结构，例如聚类，这使得倾向评分建模和估计具有挑战性。此外，对于聚类数据，可能存在与治疗分配和结果相关的未测量的聚类级协变量。当这种未测量的特定于集群的混杂因素存在并且在倾向评分模型中被忽略时，随后的倾向评分调整可能会有偏差。在本文中，我们提出了一种在潜在可忽略处理分配机制下的倾向评分估计校准技术，即。即，考虑到观察到的协变量和潜在的集群特定混杂因素，治疗-结果关系是无混杂的。我们施加了新的平衡约束，这意味着在治疗组之间观察到的混杂因素和未观察到的集群级混杂因素的精确平衡。我们表明，如果正确指定了倾向评分模型或结果遵循线性混合效应模型，则所提出的校准倾向评分加权估计器具有双重稳健性，因为它与平均治疗效果一致。此外，所提出的加权方法可以与抽样权重相结合，形成一个综合解决方案，以处理聚类调查数据的因果推断的混杂和抽样设计。在模拟研究中，我们表明所提出的估计器优于其他竞争对手。我们估计了学校体重指数筛查对宾夕法尼亚州小学超重和肥胖流行率的影响。