Understanding how genetic and epigenetic factors jointly influence binary health outcomes remains a major challenge in biomedical research. We propose a global test for the overall effect of interactions between DNA methylation and a set of single nucleotide polymorphisms (SNPs) on a binary phenotype. We propose a logistic functional regression model in which methylation measurements at CpG sites are transformed into smooth functional predictors interacting with discrete SNP genotypes through a localized kernel. This framework enables stable inference on region-level interactions while accounting for the spatial structure of methylation around SNPs. Extensive simulations show that the proposed test provides well-calibrated type I error and improved power over classical SNP-CpG pairwise analyses. The practical relevance of the method is illustrated using publicly available methylation and genotyping data from an obesity case-control study.

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