Propensity score methods and unobserved covariate imbalance: comments on "squeezing the balloon"

In their recent Health Services Research article titled "Squeezing the Balloon: Propensity Scores and Unmeasured Covariate Balance," Brooks and Ohsfeldt (2013) addressed an important topic on the balancing property of the propensity score (PS) with respect to unmeasured covariates. They concluded that PS methods that balance measured covariates between treated and untreated subjects exacerbate imbalance in unmeasured covariates that are unrelated to measured covariates. Furthermore, they emphasized that for PS algorithms, an imbalance on unmeasured covariates between treatment and untreated subjects is a necessary condition to achieve balance on measured covariates between the groups. We argue that these conclusions are the results of their assumptions on the mechanism of treatment allocation. In addition, we discuss the underlying assumptions of PS methods, their advantages compared with multivariate regression methods, as well as the interpretation of the effect estimates from PS methods.