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Using simulated data, this study evaluates the relative performance of different variable selection approaches and adjustment methods in relation to propensity scores and prognostic scores. Three dimensions will be under investigation: variable selection for propensity score models (treatment-covariate PS models, outcome-covariate PS models, and confounder-covariate PS models); adjustment methods in the outcome models (adjusting for the propensity scores, adjusting for the propensity scores in combination with the prognostic scores, and adjusting for the propensity score in combination with strong outcome predictors); and two types of outcome distributions (normal distributions, and Bernoulli distributions). Evaluation criteria include bias, precision, MSE, remaining sample size after stratification, and confidence interval coverage percentage.