  This paper is motivated by the joint analysis of genetic, imaging, and
clinical (GIC) data collected in the Alzheimer's Disease Neuroimaging
Initiative (ADNI) study. We propose a regression framework based on partially
functional linear regression models to map high-dimensional GIC-related
pathways for Alzheimer's Disease (AD). We develop a joint model selection and
estimation procedure by embedding imaging data in the reproducing kernel
Hilbert space and imposing the L0 penalty for the coefficients of genetic
variables. We apply the proposed method to the ADNI dataset to identify
important features from tens of thousands of genetic polymorphisms (reduced
from millions using a preprocessing step) and study the effects of a certain
set of informative genetic variants and the baseline hippocampus surface on
thirteen future cognitive scores measuring different aspects of cognitive
function. We explore the shared and different heritability patterns of these
cognitive scores. Analysis results suggest that both the hippocampal and
genetic data have heterogeneous effects on different scores, with the trend
that the value of both hippocampi is negatively associated with the severity of
cognition deficits. Polygenic effects are observed for all thirteen cognitive
scores. The well-known APOE4 genotype only explains a small part of cognitive
function. Shared genetic etiology exists, however, greater genetic
heterogeneity exists within disease classifications after accounting for the
baseline diagnosis status. These analyses are useful in further investigation
of functional mechanisms for AD evolution.
