# A Cross-validated Ensemble Approach to Robust Hypothesis Testing of Continuous Nonlinear Interactions: Application to Nutrition-Environment Studies

## TL;DR

This paper introduces a cross-validated ensemble kernel method for robust hypothesis testing of complex nonlinear interactions in high-dimensional gene-environment and nutrition studies, demonstrated through a study on maternal nutrition and metal exposure effects.

## Contribution

The authors propose CVEK, a novel ensemble kernel approach that flexibly estimates nonlinear main effects and improves interaction testing power in high-dimensional settings.

## Key findings

- Identified significant interactions between nutrient intake and metal exposures affecting neurodevelopment.
- Demonstrated CVEK's effectiveness in controlling false positives and capturing true interactions.
- Applied method revealed potential nutritional interventions to mitigate metal toxicity effects.

## Abstract

Gene-environment and nutrition-environment studies often involve testing of high-dimensional interactions between two sets of variables, each having potentially complex nonlinear main effects on an outcome. Construction of a valid and powerful hypothesis test for such an interaction is challenging, due to the difficulty in constructing an efficient and unbiased estimator for the complex, nonlinear main effects. In this work we address this problem by proposing a Cross-validated Ensemble of Kernels (CVEK) that learns the space of appropriate functions for the main effects using a cross-validated ensemble approach. With a carefully chosen library of base kernels, CVEK flexibly estimates the form of the main-effect functions from the data, and encourages test power by guarding against over-fitting under the alternative. The method is motivated by a study on the interaction between metal exposures in utero and maternal nutrition on children's neurodevelopment in rural Bangladesh. The proposed tests identified evidence of an interaction between minerals and vitamins intake and arsenic and manganese exposures. Results suggest that the detrimental effects of these metals are most pronounced at low intake levels of the nutrients, suggesting nutritional interventions in pregnant women could mitigate the adverse impacts of in utero metal exposures on children's neurodevelopment.