Developing and Applying the Propensity Score to Make Causal Inferences: Variable Selection and Stratification.

This Monte Carlo simulation examined the effects of variable selection (combinations of confounders with four patterns of relationships to outcome and assignment to treatment) and number of strata (5, 10, or 20) in propensity score analyses. The focus was on how the variations affected the average effect size compared to quasi-assignment without adjustment for bias. Results indicate that if a propensity score model does not include variables strongly related to both outcome and assignment, not only will bias not decrease, but it may possibly increase.