Abstract
In order to estimate the average treatment effect E0[E0(Y | A = 1,W) - E0(Y | A = 0,W)] of a single time-point treatment A based on observing n i.i.d. copies of O = (W, A, Y), one might use inverse probability of treatment (i.e., propensity score) weighting of an estimator of the conditional mean of the outcome (i.e., response surface) as a function of the pretreatment covariates. Alternatively, one might use a TMLE defined by a choice of initial estimator, a parametric submodel that codes fluctuations of the initial estimator, and a loss function used to determine the amount of fluctuation, where either the choice of submodel or the loss function will involve inverse probability of treatment weighting. Asymptotically, such double robust estimators may have appealing properties. They can be constructed such that if either the model of the response surface or the model of the probability of treatment assignment is correct, the estimatosr will provide a consistent estimator of the average treatment effect. And if both models are correct, the weighted estimator will be asymptotically efficient. Such estimators are called double robust and locally efficient (Robins et al. 1994, 1995; Robins and Rotnitzky 1995; van der Laan and Robins 2003).
Published Version
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