Stein-like Estimators for Causal Mediation Analysis in Randomized Trials

TL;DR

This paper introduces a Stein-like estimator for causal mediation analysis in randomized trials, balancing bias and variance when estimating direct and indirect effects, especially with unmeasured confounding.

Contribution

It adapts the Semi-Parametric Stein-Like estimator for causal mediation, providing a data-driven shrinkage approach to improve estimation in randomized trials.

Findings

The Stein-like estimator reduces variance compared to traditional IV methods.

Simulation studies show improved bias-variance trade-off under various confounding and instrument strengths.

Application to mental health trial demonstrates practical utility.

Abstract

Causal mediation analysis aims to estimate the natural direct and indirect effects under clearly specified assumptions. Traditional mediation analysis based on Ordinary Least Squares (OLS) relies on the absence of unmeasured causes of the putative mediator and outcome. When this assumption cannot be justified, Instrumental Variables (IV) estimators can be used in order to produce an asymptotically unbiased estimator of the mediator-outcome link. However, provided that valid instruments exist, bias removal comes at the cost of variance inflation for standard IV procedures such as Two-Stage Least Squares (TSLS). A Semi-Parametric Stein-Like (SPSL) estimator has been proposed in the literature that strikes a natural trade-off between the unbiasedness of the TSLS procedure and the relatively small variance of the OLS estimator. Moreover, the SPSL has the advantage that its shrinkage parameter can be directly estimated from the data. In this paper, we demonstrate how this Stein-like estimator can be implemented in the context of the estimation of natural direct and natural indirect effects of treatments in randomized controlled trials. The performance of the competing methods is studied in a simulation study, in which both the strength of hidden confounding and the strength of the instruments are independently varied. These considerations are motivated by a trial in mental health evaluating the impact of a primary care-based intervention to reduce depression in the elderly.