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

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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.

Original languageEnglish (US)
Pages (from-to)609-632
Number of pages24
JournalCanadian Journal of Statistics
Issue number4
StatePublished - Dec 1 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Causal inference
  • Double robustness
  • Estimating equations
  • Marginal structural model
  • Nested structural model
  • Nonparametric likelihood
  • Profile likelihood
  • Propensity score

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