# Discovery of critical thresholds in mixed exposures and estimation of policy intervention effects

## TL;DR

This paper introduces a new method to identify critical exposure thresholds and estimate policy effects for multiple chemical exposures, using advanced statistical techniques and real-world data.

## Contribution

A novel methodology combining recursive partitioning and cross-validated targeted maximum likelihood estimation for multivariate exposure analysis.

## Key findings

- Simulation studies confirm convergence to optimal exposure regions and accurate intervention effect estimation.
- The method successfully identifies true interactions in synthetic mixture data.
- Harmful metal exposures affecting telomere length are discovered in NHANES data.

## Abstract

Regulations of chemical exposures often focus on individual substances, neglecting the amplified toxicity that can arise from multiple concurrent exposures. We propose a novel methodology to identify critical thresholds in multivariate exposure spaces and estimate the effects of policy interventions that limit exposures within these thresholds. Our approach employs a recursive partitioning algorithm integrated with targeted maximum likelihood estimation (TMLE) to discover regions in the exposure space where the expected outcome is minimized or maximized. To address potential overfitting bias from using the same data for threshold discovery and effect estimation, we utilize cross-validated TMLE (CV-TMLE), which ensures asymptotic unbiasedness and efficiency. Simulation studies demonstrate convergence to the optimal exposure region and accurate estimation of intervention effects. We apply our method to synthetic mixture data, successfully identifying true interactions, and to NHANES data, discovering harmful metal exposures affecting telomere length. Our approach provides a flexible and interpretable framework for policy-makers to assess the impact of exposure regulations, and we offer an open-source implementation in the CVtreeMLE R package.