Bayesian variable selection in logistic regression with application to whole-brain functional connectivity analysis for Parkinson's disease

Parkinson's disease is a progressive, chronic, and neurodegenerative disorder that is primarily diagnosed by clinical examinations and magnetic resonance imaging (MRI). In this paper, we propose a Bayesian model to predict Parkinson's disease employing a functional MRI (fMRI) based radiomics approach. We consider a spike and slab prior for variable selection in high-dimensional logistic regression models, and present an approximate Gibbs sampler by replacing a logistic distribution with a t-distribution. Under mild conditions, we establish model selection consistency of the induced posterior and illustrate the performance of the proposed method outperforms existing state-of-the-art methods through simulation studies. In fMRI analysis, 6216 whole-brain functional connectivity features are extracted for 50 healthy controls along with 70 Parkinson's disease patients. We apply our method to the resulting dataset and further show its benefits with a higher average prediction accuracy of 0.83 compared to other contenders based on 10 random splits. The model fitting procedure also reveals the most discriminative brain regions for Parkinson's disease. These findings demonstrate that the proposed Bayesian variable selection method has the potential to support radiological diagnosis for patients with Parkinson's disease.