Data-adaptive estimation of the treatment-specific mean

In this article, we introduce estimators that allow the marginal structural model as well as the parametric model for the relevant nuisance parameter to be selected data-adaptively. Our methodology is based on the unified loss-based estimation approach recently developed by van der Laan and Dudoit [2003. Unified cross-validation methodology for selection among estimators and a general cross-validated adaptive epsilonnet estimator: finite sample oracle inequalities and examples. Technical Report 130, Division of Biostatistics, University of California, Berkeley, November 2003] that in particular extends loss-based estimation to missing data problems. We study the practical performance of our proposed estimators in an extensive simulation study and also apply them to a data set derived from an epidemiologic study to assess the causal effect of forced expiratory volume on mortality in the elderly. All of the estimators presented in this article are made publicly available in the R package cvDSA.