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Robust Inference for Mediated Effects in Partially Linear Models

Published online by Cambridge University Press:  01 January 2025

Oliver Hines Open the ORCID record for Oliver Hines [Opens in a new window] ,
Stijn Vansteelandt Open the ORCID record for Stijn Vansteelandt [Opens in a new window]  and
Karla Diaz-Ordaz Open the ORCID record for Karla Diaz-Ordaz [Opens in a new window]
Oliver Hines*
Affiliation:
London School of Hygiene and Tropical Medicine
Stijn Vansteelandt
Affiliation:
London School of Hygiene and Tropical Medicine Ghent University
Karla Diaz-Ordaz
Affiliation:
London School of Hygiene and Tropical Medicine
*
Correspondence should be made to Oliver Hines, Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK. Email: [email protected] https://www.unibo.it/sitoweb/aldo.gardini2
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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

G-estimationMediationRobust inference
Type
Theory and Methods (T&M)
Information
Psychometrika , Volume 86 , Issue 2 , June 2021 , pp. 595 - 618
Copyright
Copyright © 2021 The Psychometric Society

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