Nonparametric likelihood and doubly robust estimating equations for marginal and nested structural models

This article considers Robins s marginal and nested structural models in the cross sectional setting and develops likelihood and regression estimators First a nonparametric likelihood method is proposed by retaining a finite subset of all inherent and modelling constraints on the joint distributions of potential outcomes and covariates under a correctly specified propensity score model A profile likelihood is derived by maximizing the nonparametric likelihood over these joint distributions subject to the retained constraints The maximum likelihood estimator is intrinsically efficient based on the retained constraints and weakly locally efficient Second two regression estimators named hat and tilde are derived as first order approximations to the likelihood estimator under the propensity score model The tilde regression estimator is intrinsically and weakly locally efficient and doubly robust The methods are Illustrated by data analysis for an observational study on right heart catheterization The Canadian Journal of Statistics 38 609-632 2010 (C) 2010 Statistical Society of Canada