Nonlinear kernel-based high-dimensional inference for set-based genetic association studies.

Nonlinear genetic architectures, including epistasis and threshold effects, are increasingly recognized as contributors to complex disease risk, yet most existing SNP-set association tests rely on linear modeling assumptions, resulting in reduced power and unstable inference when genetic effects are nonlinear or heterogeneously distributed across variants. To address this limitation, we propose a nonlinear high-dimensional inference framework for set-based genetic association analysis that integrates scalable kernel representations with valid statistical inference. The framework combines distance correlation-based sure independence screening to reduce ultra-high dimensional predictors, kernel principal component analysis with Nyström approximation for nonlinear feature extraction, and de-sparsified LASSO to enable asymptotically valid hypothesis testing in high dimensions, together with a two-stage omnibus testing strategy that adaptively aggregates evidence across complementary signal models. Extensive simulation studies demonstrate that the proposed method maintains well-calibrated Type I error and consistently achieves higher power than established set-based approaches, including Sequence Kernel Association Test and adaptive Sum of Powered Score test, particularly under nonlinear and heterogeneous genetic effect scenarios, while remaining competitive in linear settings. Application to Alzheimer's Disease Neuroimaging Initiative data identifies gene-level associations with brain regional volumes that converge on neuronal excitability, calcium signaling, and cytoskeletal regulation, biological processes centrally implicated in neurodegeneration. Together, this work provides a robust and scalable framework for nonlinear set-based inference in genome-wide studies, expanding the analytical toolbox for dissecting complex genetic contributions to disease.