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

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 <i>in utero</i> 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 <i>in utero</i> metal exposures on the children’s neurodevelopment. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

基因-环境与营养-环境相关研究往往需要检验两组变量间的高维交互效应，且每组变量对结局变量均可能存在复杂的非线性主效应。针对此类交互效应构建有效且效能优异的假设检验颇具挑战，其难点在于难以针对复杂的非线性主效应构造高效无偏的估计量。本研究针对该问题提出了交叉验证核集成方法（cross-validated ensemble of kernels, CVEK），该方法通过交叉验证集成策略学习适配主效应的函数空间。依托精心选取的基础核函数库，CVEK可从数据中灵活拟合主效应函数的形式，并通过规避备择假设下的过拟合风险提升检验效能。本方法的提出源于一项孟加拉国农村地区的研究，该研究探究了宫内金属暴露与母体营养对儿童神经发育的交互效应。所提检验方法发现了矿物质与维生素摄入，以及砷和锰暴露之间存在交互效应的证据。研究结果显示，此类金属的有害效应在营养素摄入水平较低时最为显著，这提示对孕妇开展营养干预或可减轻宫内金属暴露对儿童神经发育造成的不良影响。本文的补充材料（包含可用于复现研究的标准化材料说明）可作为在线补充材料获取。