Abstract
Mediation analysis is a fundamental tool for understanding biological mechanisms through which an exposure exerts its effect on an outcome via intermediate variables, or mediators. However, modern biomedical studies often involve multiple exposures and mediators with complex correlation structures, and may also involve multiple outcomes, as in multi-omics or imaging studies, where existing mediation analyses can suffer from instability and limited interpretability. In this work, we propose Envelope-Based Sparse Partial Least Squares for Mediation Analysis (ESPLSM), which integrates dimension reduction and sparsity enforcement via the sparse envelope model to improve estimation and interpretation of causal effects. We embed the envelope model within the causal mediation framework based on potential outcomes, which allows us to formally define and identify direct and indirect effects and to establish theoretical guarantees, including asymptotic efficiency and selection consistency. Through simulation studies, we show that ESPLSM outperforms existing methods in terms of estimation accuracy, statistical power, and variable selection. Finally, we apply ESPLSM to a cancer cell line dataset to investigate the role of RNA expression in mediating the effect of EGFR mutations on drug responses. Our results provide new insights into the molecular mechanisms underlying targeted cancer therapies. Overall, ESPLSM provides a statistically principled yet practical solution for interpretable and efficient mediation analysis in modern high-dimensional biomedical applications.