  In randomized experiments, adjusting for observed features when estimating
treatment effects has been proposed as a way to improve asymptotic efficiency.
However, only linear regression has been proven to form an estimate of the
average treatment effect that is asymptotically no less efficient than the
treated-minus-control difference in means regardless of the true data
generating process. Randomized treatment assignment 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 method which confers
the same no-harm property onto estimators leveraging a broad class of nonlinear
models. This 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 to both the difference in means estimator and to
treatment effect estimators that have not undergone calibration. We show that
our estimator is asymptotically equivalent to an inverse probability weighted
estimator using a logit link with predicted potential outcomes as covariates.
In a simulation study, we demonstrate that common nonlinear estimators without
our calibration procedure may perform markedly worse than both the calibrated
estimator and the unadjusted difference in means.

Methodology