Propensity Scores - Confounding in Observational Studies Sample Clauses

Propensity Scores - Confounding in Observational Studies. As mentioned in the previous section, conditional independence assumptions (1.6) are re- quired to draw causal conclusions from observational data. One popular causal inference method is the use of propensity scores to adjust for covariates X in 1.6. In essence, it sum- marizes each patient’s covariates compared to the rest of the sample, and then evaluates how similar or dissimilar that observation is to others who received treatment or control. The goal behind propensity score analyses is that within subclassifications of the propen- sity score, the distributions of covariates X are as similar as possible between treatment and control groups. Another way to think about the propensity score is as teasing out the analogous case-control study hidden in each observational study [Xxxxxx, 2006]. One of the features of propensity scores that also makes them similar to randomization (rather than traditional adjustment for confounding) is a focus on the relationship between covariates and treatment assignment regardless of the relationship between covariates and the outcome of interest [Xxxxx and Xxxxxx, 2000]. Put another way, propensity score methods differ from traditional methods in that they “. . . adjust for confounding by modeling aspects of the marginal association of the exposures of interest with the confounders rather than by modeling the independent association of the confounders with the outcome [Robins et al., 1992a].” The propensity score is the coarsest function of X that fulfills the definition of a balancing score, b(x), namely that for some dichotomous treatment indicator z the “. . . distribution of x given b(x) is the same for treated (z = 1) and control (z = 0) units; that is, in Dawid’s (1979) notation, x ⊥ z|b(x) [Xxxxxxxxx and Xxxxx, 1983a].” The propensity score is then formally defined as