Semiparametric Causal Mediation Analysis for Linear Models with Non-Gaussian Errors: Applications to Drug Treatment and Social Program Evaluation

TL;DR

This paper introduces a semiparametric causal mediation analysis method for linear models with non-Gaussian errors, improving effect estimation accuracy in medical and social science studies.

Contribution

It develops a robust, efficient framework combining semiparametric estimation and confidence interval construction that outperforms traditional OLS in non-Gaussian error settings.

Findings

Semiparametric estimator reduces root mean squared error compared to OLS.

Confidence intervals are shorter and more accurate with non-Gaussian errors.

Method detects significant effects where OLS fails, especially under non-Gaussian error distributions.

Abstract

\textbf{Background:} Mediation analysis is widely used to investigate how treatments and programs exert their effects, but standard ordinary least squares (OLS) inference can be unreliable when regression errors are non-Gaussian. In medical and public-health studies, this can affect whether indirect and direct effects are judged clinically or scientifically meaningful. \textbf{Methods:} We developed a semiparametric causal mediation framework for linear models allowing possibly non-Gaussian errors, covering both standard models and models with treatment--mediator interaction. The method combines semiparametric efficient regression estimation, a reproducible multi-start fitting algorithm for numerical stability, and stacked estimating equations for confidence-interval construction without requiring Gaussian error assumptions. \textbf{Results:} Across Gaussian, skewed, and mixture-error simulations, the semiparametric estimator reduced root mean squared error and confidence-interval length relative to OLS, with the largest gains under non-Gaussian errors. In a near-boundary power design, the OLS confidence interval achieved 18.3\% empirical power, whereas the semiparametric confidence interval identified significant effects in all replications. In the \textit{uis} drug-treatment data, it yielded sharper treatment-specific effect estimates under clear treatment--mediator interaction. In the \textit{jobs} social-program data, the semiparametric analysis produced shorter confidence intervals for mediated effects and detected nonzero mediation where OLS did not. \textbf{Conclusions:} Semiparametric mediation analysis can improve the precision and reliability of effect decomposition in studies with non-Gaussian outcomes, offering a practical alternative to OLS when indirect and direct effects may inform clinical or policy decision-making.