Variable Selection and Adjustment in Relation to Propensity Scores and Prognostic Scores: From Single-level to Multilevel Data

Through three sets of simulations, this dissertation evaluates the effectiveness of alternative approaches to causal inference that make use of propensity scores. In the setting of single-level data, the first study examines the relative performance of (a) three variable selection methods for propensity score models (i.e., including all the treatment predictors, including all the outcome predictors, or including confounders), and (b) three adjustment methods in outcome models (i.e., adjusting for the propensity score only, adjusting for the propensity score in combination with the prognostic score, and adjusting for the propensity score in combination with strong outcome-predictive covariates). The second study tests the robustness of the alternative approaches under a range of model misspecifications, including omitted covariates, omitted nonlinear terms, and omitted interaction terms in a propensity score model, a prognostic score model, or an outcome model. The third study extends the evaluation to multilevel data by additionally examining another dimension unique to multilevel data. The study compares random intercept and slopes models, random intercept models, and single-level models for the propensity score and prognostic score estimations. The impact of omitting cluster-level covariates is also examined under each type of model specification. Evaluation criteria include bias, precision, mean squared error, remaining sample size after stratification, and confidence interval coverage percentage. The main findings are: (1) in general, adjustment methods in outcome models have more important consequences than variable selection for propensity score models for bias reduction, precision, and MSE; (2) the robustness against model misspecifications under alternative approaches depends on the type of misspecifications; (3) multilevel propensity score models show advantages over their single-level counterparts especially when combined with prognostic score adjustment; (4) omitting cluster-level information is not highly consequential once the multilevel structure has been accounted for by using multilevel outcome models.Ph