Causal Inference with Multilevel Data: A Comparison of Different Propensity Score Weighting Approaches

Propensity score methods are a widely recommended approach to adjust for confounding and to recover treatment effects with non-experimental, single-level data. This article reviews propensity score weighting estimators for multilevel data in which individuals (level 1) are nested in clusters (level 2) and nonrandomly assigned to either a treatment or control condition at level 1. We address the choice of a weighting strategy (inverse probability weights, trimming, overlap weights, calibration weights) and discuss key issues related to the specification of the propensity score model (fixed-effects model, multilevel random-effects model) in the context of multilevel data. In three simulation studies, we show that estimates based on calibration weights, which prioritize balancing the sample distribution of level-1 and (unmeasured) level-2 covariates, should be preferred under many scenarios (i.e., treatment effect heterogeneity, presence of strong level-2 confounding) and can accommodate covariate-by-cluster interactions. However, when level-1 covariate effects vary strongly across clusters (i.e., under random slopes), and this variation is present in both the treatment and outcome data-generating mechanisms, large cluster sizes are needed to obtain accurate estimates of the treatment effect. We also discuss the implementation of survey weights and present a real-data example that illustrates the different methods.倾向得分（propensity score）方法是被广泛推荐的用于控制混杂偏倚、从非实验性单水平数据中还原处理效应的分析手段。本文针对多水平数据（其中个体（水平1）嵌套于集群（水平2）中，且在水平1层面被非随机分配至处理组或对照组），综述了倾向得分加权估计量的相关研究。我们探讨了加权策略的选择问题，包括逆概率权重（inverse probability weights）、截断法、重叠权重（overlap weights）、校准权重（calibration weights），并围绕多水平数据场景下倾向得分模型的设定（固定效应模型（fixed-effects model）、多水平随机效应模型（multilevel random-effects model））讨论了核心议题。三项模拟研究结果表明，在多数场景下（如处理效应异质性、存在较强水平2混杂偏倚时），优先平衡水平1与（未观测的）水平2协变量样本分布的校准权重估计量更具优势，且该方法可适配协变量-集群交互项。不过，当水平1协变量效应在集群间存在显著差异（即随机斜率（random slopes）场景），且该差异同时存在于处理分配与结果变量的生成机制中时，则需要较大的集群样本量才能获得准确的处理效应估计值。本文还讨论了调查权重（survey weights）的实现方式，并提供了一个真实数据集案例以展示不同方法的应用效果。