Performance of propensity score calibration--a simulation study.

Confounding can be a major source of bias in nonexperimental research. The authors recently introduced propensity score calibration (PSC), which combines propensity scores and regression calibration to address confounding by variables unobserved in the main study by using variables observed in a validation study. Here, the authors assess the performance of PSC using simulations in settings with and without violation of the key assumption of PSC: that the error-prone propensity score estimated in the main study is a surrogate for the gold-standard propensity score (i.e., it contains no additional information on the outcome). The assumption can be assessed if data on the outcome are available in the validation study. If data are simulated allowing for surrogacy to be violated, results depend largely on the extent of violation. If surrogacy holds, PSC leads to bias reduction between 32% and 106% (>100% representing overcorrection). If surrogacy is violated, PSC can lead to an increase in bias. Surrogacy is violated when the direction of confounding of the exposure-disease association caused by the unobserved variable(s) differs from that of the confounding due to observed variables. When surrogacy holds, PSC is a useful approach to adjust for unmeasured confounding using validation data.