Abstract：
Propensity score (PS) analyses are increasingly popular in behavioral sciences. Two issues often add complexities to PS analyses, including missing data in observed covariates and clustered data structure. In previous research, methods for conducting PS analyses with considering either issue alone were examined. In practice, the two issues often co-occur; but the performance of methods for PS analyses in the presence of both issues has not been evaluated previously. In this study, we consider PS weighting analysis when data are clustered and observed covariates have missing values. A simulation study is conducted to evaluate the performance of different missing data handling methods (complete-case, single-level imputation, or multilevel imputation) combined with different multilevel PS weighting methods (fixed- or random-effects PS models, inverse-propensity-weighting or the clustered weighting, weighted single-level or multilevel outcome models). The results suggest that the bias in average treatment effect estimation can be reduced, by better accounting for clustering in both the missing data handling stage (such as with the multilevel imputation) and the PS analysis stage (such as with the fixed-effects PS model, clustered weighting, and weighted multilevel outcome model). A real-data example is provided for illustration.
摘要：
倾向得分(PS)分析在行为科学中越来越受欢迎。两个问题经常增加PS分析的复杂性，包括观察到的协变量和聚类数据结构中的缺失数据。在以前的研究中，研究了单独考虑任一问题的进行PS分析的方法。在实践中,这两个问题经常同时发生;但是在存在这两个问题的情况下进行PS分析的方法的性能之前尚未进行评估。在这项研究中,当数据被聚类并且观察到的协变量有缺失值时,我们考虑PS加权分析.进行了一项模拟研究，以评估不同缺失数据处理方法的性能(完整案例，单层插补,或多级插补)结合不同的多级PS加权方法(固定或随机效应PS模型，逆倾向加权或聚类加权，加权单水平或多水平结果模型)。结果表明，平均治疗效果估计的偏差可以减少，通过更好地考虑缺失数据处理阶段(如多级插补)和PS分析阶段(如固定效应PS模型)的聚类，聚类加权，和加权多级结果模型)。提供了一个真实数据示例来进行说明。
