Causal Mediation Analysis: Selection with Asymptotically Valid Inference

Jeremiah Jones; Ashkan Ertefaie; Robert L. Strawderman

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arXiv · 2110.06127

Causal Mediation Analysis: Selection with Asymptotically Valid Inference

Jeremiah Jones·Ashkan Ertefaie·Robert L. Strawderman

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Abstract

Researchers are often interested in learning not only the effect of treatments on outcomes, but also the pathways through which these effects operate. A mediator is a variable that is affected by treatment and subsequently affects outcome. Existing methods for penalized mediation analyses may lead to ignoring important mediators and either assume that finite-dimensional linear models are sufficient to remove confounding bias, or perform no confounding control at all. In practice, these assumptions may not hold. We propose a method that considers the confounding functions as nuisance parameters to be estimated using data-adaptive methods. We then use a novel regularization method applied to this objective function to identify a set of important mediators. We derive the asymptotic properties of our estimator and establish the oracle property under certain assumptions. Asymptotic results are also presented in a local setting which contrast the proposal with the standard adaptive lasso. We also propose a perturbation bootstrap technique to provide asymptotically valid post-selection inference for the mediated effects of interest. The performance of these methods will be discussed and demonstrated through simulation studies.

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BibTeX RIS

Jeremiah Jones, Ashkan Ertefaie, Robert L. Strawderman. 2021-10-12. Causal Mediation Analysis: Selection with Asymptotically Valid Inference. https://arxiv.org/abs/2110.06127

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