Propensity score weighting for a continuous exposure with multilevel data

Propensity score methods (e.g., matching, weighting, subclassification) provide a statistical approach for balancing dissimilar exposure groups on baseline covariates. These methods were developed in the context of data with no hierarchical structure or clustering. Yet in many applications the data have a clustered structure that is of substantive importance, such as when individuals are nested within healthcare providers or within schools. Recent work has extended propensity score methods to a multilevel setting, primarily focusing on binary exposures. In this paper, we focus on propensity score weighting for a continuous, rather than binary, exposure in a multilevel setting. Using simulations, we compare several specifications of the propensity score: a random effects model, a fixed effects model, and a single-level model. Additionally, our simulations compare the performance of marginal versus cluster-mean stabilized propensity score weights. In our results, regression specifications that accounted for the multilevel structure reduced bias, particularly when cluster-level confounders were omitted. Furthermore, cluster mean weights outperformed marginal weights.