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

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume38
Issue number4
DOIs
StatePublished - Dec 1 2010

Fingerprint

Nonparametric Likelihood
Nested Models
Regression Estimator
Estimating Equation
Structural Model
Propensity Score
Joint Distribution
Likelihood
Potential Outcomes
Profile Likelihood
Observational Study
Likelihood Methods
Nonparametric Methods
Maximum Likelihood Estimator
Covariates
Data analysis
First-order
Estimator
Subset
Approximation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

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

Cite this

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Nonparametric likelihood and doubly robust estimating equations for marginal and nested structural models. / Tan, Zhiqiang.

In: Canadian Journal of Statistics, Vol. 38, No. 4, 01.12.2010, p. 609-632.

Research output: Contribution to journalArticle

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