  We present a new method for the detection of gene pathways associated with a
multivariate quantitative trait, and use it to identify causal pathways
associated with an imaging endophenotype characteristic of longitudinal
structural change in the brains of patients with Alzheimer's disease (AD). Our
method, known as pathways sparse reduced-rank regression (PsRRR), uses group
lasso penalised regression to jointly model the effects of genome-wide single
nucleotide polymorphisms (SNPs), grouped into functional pathways using prior
knowledge of gene-gene interactions. Pathways are ranked in order of importance
using a resampling strategy that exploits finite sample variability. Our
application study uses whole genome scans and MR images from 464 subjects in
the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. 66,182 SNPs
are mapped to 185 gene pathways from the KEGG pathways database. Voxel-wise
imaging signatures characteristic of AD are obtained by analysing 3D patterns
of structural change at 6, 12 and 24 months relative to baseline. High-ranking,
AD endophenotype-associated pathways in our study include those describing
chemokine, Jak-stat and insulin signalling pathways, and tight junction
interactions. All of these have been previously implicated in AD biology. In a
secondary analysis, we investigate SNPs and genes that may be driving pathway
selection, and identify a number of previously validated AD genes including
CR1, APOE and TOMM40.
