Mediator Selection in Linear and Nonlinear Mediation Analysis via Adaptive Measurement Errors Infusion

Background: Mediation analysis investigates intermediate mechanisms through which an exposure influences an outcome. When there are multiple candidate mediators, mediator selection should precede the estimation of mediation effects but remains challenging when pathway signals are weak or imbalanced, when mediator-outcome relationships are nonlinear, and when there are mediator-exposure and/or mediator-mediator interactions. Most existing methods rely on coefficient-based regularization under linear outcome models. We propose a multiple-mediator selection framework based on the measurement error model-ing (MEM) principle, which quantifies a mediator's importance by how much the fit of the exposure-mediator and mediator-outcome pathways degrades when the mediator is deliberately perturbed by a controlled infusion of artificial measurement error. Results: For linear mediation systems, the proposed adaptive MEM procedure distributes a constrained measurement-error precision budget across mediators under a joint Gaussian working criterion, then selects exposure-mediator and mediator-outcome pathways separately, and lastly retains a mediator only if it is selected in both pathways. For nonlinear mediator-outcome relationships, an adaptive kernel MEM extension retains linear exposure-mediator models and replaces the error precisions for the mediators in the outcome model with coordinate-specific inverse bandwidths. In simulations, linear MEM was competitive with established methods designed for linear mediation systems, with a modest advantage when mediator residuals were correlated. Kernel MEM substantially improved the selection of mediators entering the outcome model through quadratic or interaction terms relative to the linear methods and outper-formed a generic kernel-ridge importance benchmark in most simulation settings. Applied to a DNA methylation study of childhood trauma and adult cortisol stress reactivity, the linear and kernel MEM methods selected eight and three loci, respectively, several of which had been reported in previous analyses of the same data. Conclusions: The proposed MEM framework provides a practical approach to multiple mediator selection under linear and nonlinear mediator-outcome relationships, yielding candidate mediators supported by evidence from both pathways.