Both genetic variants and brain region abnormalities are recognized to play a role in cognitive decline. In this project, we explore the relationship between genome-wide variation and region-specific rates of decline in brain structure, as measured by magnetic resonanceimaging. The correspondence between rates of decline in brain regions and single nucleotide polymorphisms (SNPs) is investigated using data from the Alzheimer’s Disease Neuroimaging Initiative 1 (ADNI-1), a study of Alzheimer’s disease and mild cognitive impairment. In these data, the number of SNP and imaging biomarkers greatly exceeds the number of study subjects. To explore these data, we therefore look to modern multivariate statistical techniques that find sparse linear combinations of the two datasets having maximum correlation. These methods are particularly appealing because they greatly reduce the dimensions of the data, providing a low-dimensional representation of the data to explore. Regularization of the correlation structure through a “sparse” singular value decomposition makes multivariate analysis on a large set of biomarkers possible. Using sparse linear combinations of the two datasets also incorporates variable selection into the analysis, providing insight into which genetic variants are associated with cognitive decline. Resampling techniques are used to examine the validity of the results by exploring their reproducibility in independent test sets, and by assessing the stability of the variable selection.
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