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Robust inference for mediated effects in partially linear models

Oliver Hines, Stijn Vansteelandt (UGent) and Karla Diaz-Ordaz
(2021) PSYCHOMETRIKA. 86(2). p.595-618
Author
Organization
Abstract
We consider mediated effects of an exposure, X on an outcome, Y, via a mediator, M, under no unmeasured confounding assumptions in the setting where models for the conditional expectation of the mediator and outcome are partially linear. We propose G-estimators for the direct and indirect effects and demonstrate consistent asymptotic normality for indirect effects when models for the conditional means of M, or X and Y are correctly specified, and for direct effects, when models for the conditional means of Y, or X and M are correct. This marks an improvement, in this particular setting, over previous 'triple' robust methods, which do not assume partially linear mean models. Testing of the no-mediation hypothesis is inherently problematic due to the composite nature of the test (either X has no effect on M or M no effect on Y), leading to low power when both effect sizes are small. We use generalized methods of moments (GMM) results to construct a new score testing framework, which includes as special cases the no-mediation and the no-direct-effect hypotheses. The proposed tests rely on an orthogonal estimation strategy for estimating nuisance parameters. Simulations show that the GMM-based tests perform better in terms of power and small sample performance compared with traditional tests in the partially linear setting, with drastic improvement under model misspecification. New methods are illustrated in a mediation analysis of data from the COPERS trial, a randomized trial investigating the effect of a non-pharmacological intervention of patients suffering from chronic pain. An accompanying R package implementing these methods can be found at github.com/ohines/plmed.
Keywords
Applied Mathematics, General Psychology, G-estimation, Mediation, Robust inference, GENERALIZED-METHOD, CAUSAL, TESTS

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MLA
Hines, Oliver, et al. “Robust Inference for Mediated Effects in Partially Linear Models.” PSYCHOMETRIKA, vol. 86, no. 2, 2021, pp. 595–618, doi:10.1007/s11336-021-09768-z.
APA
Hines, O., Vansteelandt, S., & Diaz-Ordaz, K. (2021). Robust inference for mediated effects in partially linear models. PSYCHOMETRIKA, 86(2), 595–618. https://doi.org/10.1007/s11336-021-09768-z
Chicago author-date
Hines, Oliver, Stijn Vansteelandt, and Karla Diaz-Ordaz. 2021. “Robust Inference for Mediated Effects in Partially Linear Models.” PSYCHOMETRIKA 86 (2): 595–618. https://doi.org/10.1007/s11336-021-09768-z.
Chicago author-date (all authors)
Hines, Oliver, Stijn Vansteelandt, and Karla Diaz-Ordaz. 2021. “Robust Inference for Mediated Effects in Partially Linear Models.” PSYCHOMETRIKA 86 (2): 595–618. doi:10.1007/s11336-021-09768-z.
Vancouver
1.
Hines O, Vansteelandt S, Diaz-Ordaz K. Robust inference for mediated effects in partially linear models. PSYCHOMETRIKA. 2021;86(2):595–618.
IEEE
[1]
O. Hines, S. Vansteelandt, and K. Diaz-Ordaz, “Robust inference for mediated effects in partially linear models,” PSYCHOMETRIKA, vol. 86, no. 2, pp. 595–618, 2021.
@article{8710286,
  abstract     = {{We consider mediated effects of an exposure, X on an outcome, Y, via a mediator, M, under no unmeasured confounding assumptions in the setting where models for the conditional expectation of the mediator and outcome are partially linear. We propose G-estimators for the direct and indirect effects and demonstrate consistent asymptotic normality for indirect effects when models for the conditional means of M, or X and Y are correctly specified, and for direct effects, when models for the conditional means of Y, or X and M are correct. This marks an improvement, in this particular setting, over previous 'triple' robust methods, which do not assume partially linear mean models. Testing of the no-mediation hypothesis is inherently problematic due to the composite nature of the test (either X has no effect on M or M no effect on Y), leading to low power when both effect sizes are small. We use generalized methods of moments (GMM) results to construct a new score testing framework, which includes as special cases the no-mediation and the no-direct-effect hypotheses. The proposed tests rely on an orthogonal estimation strategy for estimating nuisance parameters. Simulations show that the GMM-based tests perform better in terms of power and small sample performance compared with traditional tests in the partially linear setting, with drastic improvement under model misspecification. New methods are illustrated in a mediation analysis of data from the COPERS trial, a randomized trial investigating the effect of a non-pharmacological intervention of patients suffering from chronic pain. An accompanying R package implementing these methods can be found at github.com/ohines/plmed.}},
  author       = {{Hines, Oliver and Vansteelandt, Stijn and Diaz-Ordaz, Karla}},
  issn         = {{0033-3123}},
  journal      = {{PSYCHOMETRIKA}},
  keywords     = {{Applied Mathematics,General Psychology,G-estimation,Mediation,Robust inference,GENERALIZED-METHOD,CAUSAL,TESTS}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{595--618}},
  title        = {{Robust inference for mediated effects in partially linear models}},
  url          = {{http://dx.doi.org/10.1007/s11336-021-09768-z}},
  volume       = {{86}},
  year         = {{2021}},
}
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