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A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear randomized. The propensity score is a natural quantity that arises in this setting. Propensity score weights have desirable asymptotic properties, but they often fail to adequately balance covariate data in finite samples. Empirical covariate balancing methods pose as an appealing alternative by exactly balancing the sample moments of the covariate distribution. With this objective in mind, we propose a framework for estimating balancing weights by solving a constrained convex program, where the criterion function to be optimized is a Bregman distance. We then show that the different distances in this class render identical weights to those of other covariate balancing methods. A series of numerical studies are presented to demonstrate these similarities. 

We show how entropy balancing can be used for transporting experimental treatment effects from a trial population onto a target population. This method is doubly robust in the sense that if either the outcome model or the probability of trial participation is correctly specified, then the estimate of the target population average treatment effect is consistent. Furthermore, we only require the sample moments of the effect modifiers drawn from the target population to consistently estimate the target population average treatment effect. We compared the finite‐sample performance of entropy balancing with several alternative methods for transporting treatment effects between populations. Entropy balancing techniques are efficient and robust to violations of model misspecification. We also examine the results of our proposed method in an applied analysis of the Action to Control Cardiovascular Risk in Diabetes Blood Pressure trial transported to a sample of US adults with diabetes taken from the National Health and Nutrition Examination Survey cohort.