# Propensity score weighting for causal inference with clustered data

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-specific variables that are related to both the treatment assignment and the 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 effects. We then provide a consistent propensity score weighting estimator of the average treatment effect when the propensity score and outcome follow generalized linear mixed effects models. The proposed propensity score weighting estimator is attractive, because it does not require specification of functional forms of the propensity score and outcome models, and therefore is robust to model misspecification. 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.

**Comments:**37 pages, 1 figure and 3 tables. arXiv admin note: text overlap with arXiv:1607.07521

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