In order to estimate the causal effect of treatments on an outcome of interest, one has to account for the effect of confounding factors which covary with the treatments and also contribute to the outcome of interest. In this paper, we use the semiparametric regression model to estimate the causal parameters. We assume the causal effect of the treatments can be described by the parametric component of the semiparametric regression model. Following the general methodology which was developed in van der Laan and Robins (2002) we give the orthogonal complement of the nuisance tangent space which identifies all the estimating functions. The estimating function which leads to an estimator given in Newey (1990) is an element of our class of estimating functions. We also give the methods to estimate the influence curve and variance of the resulting estimate. Double protection property is discussed when the nuisance parameters are misspecified. The optimal estimating function or the efficient influence curve is obtained in closed form. A one-step estimator is suggested. If the nuisance parameters in the estimating function are correctly specified, then our estimate is efficient.
Clinical Trials | Statistical Methodology | Statistical Models | Statistical Theory
Yu, Zhuo and van der Laan, Mark J., "Measuring Treatment Effects Using Semiparametric Models" (September 2003). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 136.