Covariance-adjusted, sparse, reduced-rank regression with adjustment for confounders

There is evidence that common genetic variation in the gene NEDD9 is associated with developing Alzheimer's Disease (AD). In this project, we study the relationship between brain-imaging biomarkers of AD and the gene NEDD9 while adjusting for the effects of genetic population structure. The data used in this project, collected by the Alzheimer's Disease Neuroimaging Initiative (ADNI), consists of magnetic resonance imaging (MRI) measures of 56 brain regions of interest for 200 cognitively normal people and genetic data on Single Nucleotide Polymorphisms (SNPs) obtained from 33 candidate genes for AD. The standard solution to such a multiple response problem is separate simple linear regression models. Such an approach neglects correlations between 56 brain areas and possible sparsity in the SNP effects. In this project, we review a sparse and covariance adjusted reduced-rank regression approach that can select significant predictors and estimate covariance simultaneously, and extend the approach to adjust for confounding variables. We apply the proposed algorithm to the ADNI data, and also simulated data.