Abstract Title Page Title: Evaluation of Model Specification, Variable Selection, and Adjustment Methods in Relation to Propensity Scores and Prognostic Scores in Multilevel Data Authors and Affiliations:

multilevel data has received increasing attention in the literature. The issues include how to select covariates for the propensity score model, how to make additional adjustment for covariates in the outcome model, and how to specify a multilevel propensity score model. The choice of an optimal analytic procedure may depend on how the multilevel data are generated. We consider three distinct multilevel settings representing different data generation processes. In a random intercept and slopes (RIS) setting, whether an individual will receive a treatment depends on individual characteristics, measured and unmeasured characteristics of the cluster to which this individual belongs, and certain interaction effects between the individual characteristics and the cluster characteristics. In a random intercept (RI) setting, unmeasured characteristics of clusters only affect the cluster average probability of treatment assignment. Individual treatment assignment may depend on individual characteristics, measured cluster characteristics, and their interactions. In a third setting, the treatment assignment occurs at the cluster level and hence does not depend on individual characteristics. Because the data generation process is often unknown to the researchers, a user-specified multilevel propensity score model may or may not correspond to the data generation process