Augmenting Propensity Score Matching with Outcome Information
*Mike Baiocchi, Stanford 

Keywords: propensity score, matching, causal inference, prognostic score, sensitivity analysis

Propensity score matching is a staple in the health policy world. But, using the way propensity score matching is currently performed in the literature, researchers are wasting information which could be used to reduce bias and get tighter confidence intervals. We propose a method for augmenting propensity score matching with information taken from the prognostic score (see Hansen 2008 in Biometrika). We will examine several applications, including the right heart catheterization study (Connors et al 1996 in JAMA).

Propensity scores can be thought of as a projection of the high dimensional covariate space into a one dimensional ordering of the probability of treatment selection. Prognostic scores are also a dimensional reduction technique but, rather than focusing on treatment selection like the propensity score, the prognostic score orders the units in terms of their predicted outcome under the control. We show how studies with a large pool of control units may use the prognostic score information to reduce bias, decrease the size of the confidence interval, and improve rates of coverage.