Causal Mediation Analysis: Selection with Asymptotically Valid Inference

TL;DR

This paper introduces a new method for causal mediation analysis that accurately identifies mediators and provides valid inference, even when confounding is complex and traditional assumptions do not hold.

Contribution

It develops a data-adaptive regularization approach with asymptotic guarantees and a bootstrap method for valid post-selection inference in mediation analysis.

Findings

Method effectively identifies important mediators.

Provides asymptotically valid inference for mediated effects.

Demonstrates superior performance in simulations.

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.