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

svReg: Structural Varying-coefficient regression to differentiate how  regional brain atrophy affects motor impairment for Huntington disease  severity groups