Alzheimer's disease (AD) is a progressive neurodegenerative disorder characterized by cognitive decline, structural brain changes, and genetic predispositions. This study leverages machine-learning and statistical techniques to investigate the mechanistic relationships between cognitive function, genetic markers, and neuroimaging biomarkers in AD progression. Using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), we perform both low-dimensional and high-dimensional analyses to identify key predictors of disease states, including cognitively normal (CN), mild cognitive impairment (MCI), and AD. Our low-dimensional approach utilizes multiple linear and ordinal logistic regression to examine the influence of cognitive scores, cerebrospinal fluid (CSF) biomarkers, and demographic factors on disease classification. The results highlight significant associations between Mini-Mental State Examination (MMSE), Clinical Dementia Rating Sum of Boxes (CDRSB), and phosphorylated tau levels in predicting cognitive decline. The high-dimensional analysis employs Sure Independence Screening (SIS) and LASSO regression to reduce dimensionality and identify genetic markers correlated with cognitive impairment and white matter integrity. Genes such as CLIC1, NAB2, and TGFBR1 emerge as significant predictors across multiple analyses, linking genetic expression to neurodegeneration. Additionally, imaging genetic analysis reveals shared genetic influences across brain hemispheres and the corpus callosum, suggesting distinct genetic contributions to white matter degradation. These findings enhance our understanding of AD pathology by integrating cognitive, genetic, and imaging data. Future research should explore longitudinal analyses and potential gene-environment interactions to further elucidate the biological mechanisms underlying AD progression.

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