Understanding Causal Distributional and Subgroup Effects With the Instrumental Propensity Score.

To address issues with measured and unmeasured confounding in observational studies, we developed a unified approach to using an instrumental variable in more flexible ways to evaluate treatment effects. The approach is based on an instrumental propensity score conditional on baseline variables, which can then be incorporated in matching, regression, subclassification, or weighting along with various parametric, semiparametric, or nonparametric methods for the assessment of treatment effects. Therefore, the application of the instrumental propensity score allows different methods for outcome effect evaluations in addition to standard 2-stage least square models while controlling for unmeasured confounders. Several properties of the instrumental propensity score are discussed. The approach is then illustrated using subclassification along with a semiparametric density ratio model and empirical likelihood. This method allows us to evaluate distributional and subgroup treatment effects in addition to the overall average treatment effect. Simulation studies showed that the method works well. We applied our method to a study of the effects of attending a Catholic school versus a public school and found that attending a Catholic school had significant beneficial effects on subsequent wages among a subgroup of subjects.