No-harm calibration for generalized Oaxaca-Blinder estimators

In randomized experiments, linear regression with baseline features can be used to form an estimate of the sample average treatment effect that is asymptotically no less efficient than the treated-minus-control difference in means. Randomization alone provides this "do-no-harm" property, with neither truth of a linear model nor a generative model for the outcomes being required. We present a general calibration step which confers the same no-harm property onto estimators leveraging a broad class of nonlinear models. The process recovers the usual regression-adjusted estimator when ordinary least squares is used, and further provides non-inferior treatment effect estimators using methods such as logistic and Poisson regression. The resulting estimators are non-inferior with respect to both the difference in means estimator and with respect to treatment effect estimators that have not undergone calibration.