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Propensity Score Weighting Methods for a Continuous Treatment in a Multilevel Data Setting

*Megan S Schuler, Harvard Medical School 
Wanghuan Chu, Pennsylvania State University 
Donna L Coffman, Pennsylvania State University 

Keywords: causal inference, propensity score

Propensity scores are an effective method for balancing dissimilar treatment groups on baseline covariates. Propensity score methods were developed in the context of independent individuals. Yet, in many applications, the data have a clustered structure that is of substantive importance, such as when individuals are clustered within health care providers. Recent work has extended propensity score methods to a multilevel setting, primarily focusing on the case of a binary treatment. In this paper, we extend previous methodological work to the case of a continuous treatment in a multilevel setting, with a focus on propensity score weighting. We discuss the optimal form of the propensity score model and weights based on results from a simulation study comparing modeling the propensity score with a random effects model, a fixed effect model, and a single-level model. We also describe how to assess covariate balance in the context of a continuous treatment and clustering. Finally, we apply these methods to an observational study evaluating effectiveness of adolescent drug treatment services (measured on a continuous scale) in which youth are clustered by treatment site.