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

$\mathbf{\text{Background:}}$ 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. $\mathbf{\text{Methods:}}$ 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. $\mathbf{\text{Results:}}$ 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 $\mathit{\text{uis}}$ drug-treatment data, it yielded sharper treatment-specific effect estimates under clear treatment–mediator interaction. In the $\mathit{\text{jobs}}$ social-program data, the semiparametric analysis produced shorter confidence intervals for mediated effects and detected nonzero mediation where OLS did not. $\mathbf{\text{Conclusions:}}$ 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.