Sturmer et al. Respond to "Propensity Score Methods in Epidemiology"

We appreciate the thoughtful commentary of Oakes and Church (1) on our paper (2) and their conclusion that propensity score calibration (PSC) may be helpful when some confounders are unmeasured. We agree that usual applications of propensity score methods control only for confounding by “observable selection,” but we see much closer links between instrumental variables (3–5) and PSC than those described by Oakes and Church. Indeed, the gold-standard propensity score estimated in the validation study hopefully better approaches the true, but unknown, propensity of treatment than the error-prone propensity score and thus performs as an approximate instrument under assumptions similar to surrogacy (6, 7). PSC is no panacea for missing data on confounders—there is no substitute for having good data on important confounders for every subject. PSC was developed in a pharmacoepidemiologic analysis of claims data that lack information on a variety of confounders (8). Using data from a validation study, we obtained an estimate of the association between use of nonsteroidal antiinflammatory drugs and short-term all-cause mortality in older adults (9) that was more plausible than the naïve estimate. Below, we briefly respond to six issues raised by Oakes and Church in their commentary (1).