  For Huntington disease, identification of brain regions related to motor
impairment can be useful for developing interventions to alleviate the motor
symptom, the major symptom of the disease. However, the effects from the brain
regions to motor impairment may vary for different groups of patients. Hence,
our interest is not only to identify the brain regions but also to understand
how their effects on motor impairment differ by patient groups. This can be
cast as a model selection problem for a varying-coefficient regression.
However, this is challenging when there is a pre-specified group structure
among variables. We propose a novel variable selection method for a
varying-coefficient regression with such structured variables. Our method is
empirically shown to select relevant variables consistently. Also, our method
screens irrelevant variables better than existing methods. Hence, our method
leads to a model with higher sensitivity, lower false discovery rate and higher
prediction accuracy than the existing methods. Finally, we found that the
effects from the brain regions to motor impairment differ by disease severity
of the patients. To the best of our knowledge, our study is the first to
identify such interaction effects between the disease severity and brain
regions, which indicates the need for customized intervention by disease
severity.
