发表机构
Department of Biostatistics, University of North Carolina at Chapel Hill; Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校生物统计系; 北卡罗来纳大学教堂山分校环境科学与工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对真实数据的非线性与交互关联问题，提出基于成对交互加性高斯过程的假设检验框架，兼具I类错误控制与复杂关联捕捉能力，在模拟和环境健康研究中验证了其检验功效优势。
AI 中文摘要
真实世界数据常呈现预测变量与结局之间的非线性、交互关联。例如，在公共卫生研究中，环境暴露和人口统计学变量可与健康结局存在非线性关联，并会改变其他预测变量的关联。参数回归模型便于进行可解释的推断和具有I类错误率控制的假设检验，但当关联为非线性时可能存在模型误设。相比之下，灵活的非参数回归模型（如高斯过程（GPs））可捕捉复杂的非线性，但通常更难解释，且不易提供具有I类错误率控制的假设检验。为弥合这一差距，我们提出一种基于受限为成对交互作用的加性高斯过程的假设检验框架，允许对变量关联和交互效应进行具有I类错误率控制的检验。我们进一步建立了加性高斯过程的收缩率，为当不存在高阶交互作用时其对预测变量维度的依赖性降低提供理论支持。通过模拟，我们表明将模型限制为成对交互作用可相对于基于标准高斯过程的方法显著提高检验功效。将其应用于环境健康研究，可识别出金属暴露与健康结局之间的非线性关联，以及人口统计学因素的效应修饰作用。
英文摘要
Real-world data often exhibit nonlinear, interactive associations between predictors and an outcome. For example, in public health studies, environmental exposures and demographic variables can have nonlinear associations with health outcomes and modify the associations of other predictors. Parametric regression models facilitate interpretable inference and hypothesis testing with Type I error rate control, but may be misspecified when associations are nonlinear. In contrast, flexible nonparametric regression models such as Gaussian processes (GPs) can capture complex nonlinearity, but are often more difficult to interpret and do not readily provide hypothesis tests with Type I error rate control. To bridge this gap, we propose a hypothesis testing framework based on additive GPs restricted to pairwise interactions, allowing tests of variable associations and interaction effects with Type I error rate control. We further establish contraction rates for additive GPs, providing theoretical support for their reduced dependence on predictor dimension when higher-order interactions are absent. Through simulations, we show that restricting the model to pairwise interactions can substantially improve testing power relative to methods based on standard GPs. Applications to environmental health studies identify nonlinear associations between metal exposures and health outcomes as well as effect modification by demographic factors.
