Propensity scores: When are they needed and methods of implementation

Achieving unbiased estimates of the effect of a treatment on an outcome in observational (non-random) studies is crucial. The propensity score (the probability that a person is treated, conditional on measured covariates) has been widely used over the past two decades to address such problems. I present three topics in propensity score research.; First, I examine when propensity scores correct the bias that can occur when standard regression techniques are applied to observational data. I show, conceptually and via simulation, that this potential exists only in the presence of (1) differing covariate distributions between treatment groups and (2) model misspecification. In comparing crude (unadjusted) estimates, covariate adjustment through standard regression (SR), and propensity scores, only the last produces unbiased estimates of treatment effect.; I then compare SR to propensity score and instrumental variable analyses (IVA). SR can lead to biased estimates of treatment effects in the presence of bias from standard regression. Propensity score techniques reduce bias by comparing treated and untreated observations with similar measured characteristics. Only IVA can effectively address bias due to differences in unmeasured covariates. However, IVA estimates become biased when assumptions are not met.; Propensity score methods use sub-sampling or weighting to choose an analytic sample with similar (measured) characteristics for treated and untreated cases. I review existing methods of sample selection/weighting and propose two new methods---weighting within strata (WWS) and proportional weighting within strata (PWWS). Weights reflect the frequency of observations in treatment groups within strata of the propensity score. PWWS addresses potentially uneven sample sizes among treatment groups in polychotomous exposures. I demonstrate that random selection within strata, WWS, and propensity score regression result in less bias than other methods.; In summary, (1) propensity score methods are needed when treatment groups differ in their covariate distributions and the model is misspecified, (2) instrumental variable analyses can address imbalances in unmeasured covariates, but introduce bias when assumptions are violated, and (3) propensity score methods address bias, with random selection within strata, weighting within strata, and propensity score regression being superior to other methods.