Using propensity score weighting with clustered data when the treatment is applied at the level of the cluster and outcomes are assessed at the level of the individual: the observational analog of cluster randomization trials

Propensity score methods allow researchers to mimic some (but not all) of the characteristics of a randomized controlled trial (RCT). Propensity score methods are usually applied to unstructured data, which allows one to mimic an RCT in which the individual is the unit of randomization. There is a small literature on how to use the propensity score with clustered data. However, these studies focused on settings in which the treatment is applied at the level of the individual, not to the cluster (thus there is within-cluster variation in treatment received). Cluster randomization trials are RCTs in which intact clusters of individuals (i.e., primary care practices) are randomized to either treatment or control. There is a paucity of information on how to apply propensity score methods in observational studies in which individuals are nested in clusters, treatment is applied at the level of the cluster, and outcomes are assessed at the level of the individual. We described four strategies for using inverse probability of treatment weighting in such settings and evaluated their performance using simulations. While the propensity score is estimated as the level of the cluster (since treatment status does not vary within clusters), incorporating baseline individual-level variables in the propensity score model (via computing cluster-level means of these variables) or in the outcome linear regression model resulted in estimates with the lowest bias. Including the individual-level baseline variable in the outcome linear model resulted in estimated treatment effects with the greatest precision and lowest mean squared error.