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Multiply Robust Inference for Statistical Interactions

Author
Organization
Abstract
A primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest. Interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures. When the man interest lies in the interaction, this approach is not entirely satisfactory, because it is prone to (possibly severe) bias when the main exposure effects or the associations between outcome and extraneous factors are misspecified. In this article we consider conditional mean models with identity or log link that postulate the statistical interaction in terms of a finite-dimensional parameter but are otherwise unspecified. We show that estimation of the interaction parameter often is not feasible in this model, because it requires nonparametric estimation of auxiliary conditional expectations given high-dimensional variables. We thus consider multiply robust estimation under a union model that assumes that at least one of several working submodels holds. Our approach is novel in that it makes use of information on the joint distribution of the exposures conditional on the extraneous factors in making inferences about the interaction parameter of interest. In the special case of a randomized trial or a family-based genetic study in which the joint exposure distribution is known by design or by Mendelian inheritance, the resulting multiply robust procedure leads to asymptotically distribution-free tests of the null hypothesis of no interaction on an additive scale. We illustrate the methods through simulation and analysis of a randomized follow-up study.
Keywords
CAUSAL, EXPOSURE, REGRESSION, LONGITUDINAL DATA, SEMIPARAMETRIC MODELS, SUFFICIENT CAUSE INTERACTIONS, Semiparametric inference, Longitudinal data, Gene-gene interaction, Double robustness, Gene-environment interaction

Citation

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MLA
Vansteelandt, Stijn et al. “Multiply Robust Inference for Statistical Interactions.” JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 130.484 (2008): 1693–1704. Print.
APA
Vansteelandt, S., Vanderweele, T., Tchetgen, E., & Robins, J. (2008). Multiply Robust Inference for Statistical Interactions. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 130(484), 1693–1704.
Chicago author-date
Vansteelandt, Stijn, Tyler Vanderweele, Eric Tchetgen, and James Robins. 2008. “Multiply Robust Inference for Statistical Interactions.” Journal of the American Statistical Association 130 (484): 1693–1704.
Chicago author-date (all authors)
Vansteelandt, Stijn, Tyler Vanderweele, Eric Tchetgen, and James Robins. 2008. “Multiply Robust Inference for Statistical Interactions.” Journal of the American Statistical Association 130 (484): 1693–1704.
Vancouver
1.
Vansteelandt S, Vanderweele T, Tchetgen E, Robins J. Multiply Robust Inference for Statistical Interactions. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION. ALEXANDRIA . UNITED STATES: AMER STATISTICAL ASSOC; 2008;130(484):1693–704.
IEEE
[1]
S. Vansteelandt, T. Vanderweele, E. Tchetgen, and J. Robins, “Multiply Robust Inference for Statistical Interactions,” JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, vol. 130, no. 484, pp. 1693–1704, 2008.
@article{594189,
  abstract     = {{A primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest. Interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures. When the man interest lies in the interaction, this approach is not entirely satisfactory, because it is prone to (possibly severe) bias when the main exposure effects or the associations between outcome and extraneous factors are misspecified. In this article we consider conditional mean models with identity or log link that postulate the statistical interaction in terms of a finite-dimensional parameter but are otherwise unspecified. We show that estimation of the interaction parameter often is not feasible in this model, because it requires nonparametric estimation of auxiliary conditional expectations given high-dimensional variables. We thus consider multiply robust estimation under a union model that assumes that at least one of several working submodels holds. Our approach is novel in that it makes use of information on the joint distribution of the exposures conditional on the extraneous factors in making inferences about the interaction parameter of interest. In the special case of a randomized trial or a family-based genetic study in which the joint exposure distribution is known by design or by Mendelian inheritance, the resulting multiply robust procedure leads to asymptotically distribution-free tests of the null hypothesis of no interaction on an additive scale. We illustrate the methods through simulation and analysis of a randomized follow-up study.}},
  author       = {{Vansteelandt, Stijn and Vanderweele, Tyler and Tchetgen, Eric and Robins, James}},
  issn         = {{0162-1459}},
  journal      = {{JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION}},
  keywords     = {{CAUSAL,EXPOSURE,REGRESSION,LONGITUDINAL DATA,SEMIPARAMETRIC MODELS,SUFFICIENT CAUSE INTERACTIONS,Semiparametric inference,Longitudinal data,Gene-gene interaction,Double robustness,Gene-environment interaction}},
  language     = {{eng}},
  number       = {{484}},
  pages        = {{1693--1704}},
  publisher    = {{AMER STATISTICAL ASSOC}},
  title        = {{Multiply Robust Inference for Statistical Interactions}},
  url          = {{http://dx.doi.org/10.1198/016214508000001084}},
  volume       = {{130}},
  year         = {{2008}},
}

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