# The Contribution Plot: Decomposition and Graphical Display of the RV Coefficient, with Application to Genetic and Brain Imaging Biomarkers of Alzheimer's Disease

## TL;DR

This paper introduces a method for decomposing and visually displaying the RV coefficient to analyze associations between genetic variants and brain imaging biomarkers in Alzheimer's disease, aiding interpretation of complex multivariate data.

## Contribution

It develops a contribution plot framework for the RV coefficient, including properties, estimation in sparse signals, and applications to Alzheimer's genetic and imaging data.

## Key findings

- Effective visualization of genetic-brain associations
- Insights into the contribution of individual variants
- Application to real Alzheimer's data

## Abstract

Alzheimer's disease (AD) is a chronic neurodegenerative disease that causes memory loss and decline in cognitive abilities. AD is the sixth leading cause of death in the United States, affecting an estimated 5 million Americans. To assess the association between multiple genetic variants and multiple measurements of structural changes in the brain a recent study of AD used a multivariate measure of linear dependence, the RV coefficient. The authors decomposed the RV coefficient into contributions from individual variants and displayed these contributions graphically. We investigate the properties of such a `contribution plot' in terms of an underlying linear model, and discuss estimation of the components of the plot when the correlation signal may be sparse. The contribution plot is applied to simulated data and to genomic and brain imaging data from the Alzheimer's Disease Neuroimaging Initiative.