We consider Bayesian logistic regression models with group‐structured covariates. In high‐dimensional settings, it is often assumed that only a small portion of groups are significant, and thus, consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high‐dimensional settings. Under mild conditions, we establish strong group selection consistency of the induced posterior, which is the first theoretical result in the Bayesian literature. Through simulation studies, we demonstrate that the proposed method outperforms existing state‐of‐the‐art methods in various settings. We further apply our method to a magnetic resonance imaging data set for predicting Parkinson's disease and show its benefits over other contenders.

Background: Depression is a prominent and highly prevalent nonmotor feature in patients with Parkinson’s disease (PD). The neural and pathophysiologic mechanisms of PD with depression (DPD) remain unclear. The current diagnosis of DPD largely depends on clinical evaluation. Methods: We proposed a new family of multinomial tensor regressions that leveraged whole-brain structural magnetic resonance imaging (MRI) data to discriminate among 196 non-depressed PD (NDPD) patients, 84 DPD patients, 200 healthy controls (HC), and to assess the special brain microstructures in NDPD and DPD. The method of maximum likelihood estimation coupled with state-of-art gradient descent algorithms was used to predict the individual diagnosis of PD and the development of DPD in PD patients. Results: The results reveal that the proposed efficient approach not only achieved a high prediction accuracy (0.94) with a multi-class AUC (0.98) for distinguishing between NDPD, DPD, and HC on the testing set but also located the most discriminative regions for NDPD and DPD, including cortical regions, the cerebellum, the brainstem, the bilateral basal ganglia, and the thalamus and limbic regions. Conclusions: The proposed imaging technique based on tensor regression performs well without any prior feature information, facilitates a deeper understanding into the abnormalities in DPD and PD, and plays an essential role in the statistical analysis of high-dimensional complex MRI imaging data to support the radiological diagnosis of comorbidity of depression with PD.

Background: This study aimed to evaluate the value of 3-dimensional pseudocontinuous arterial spin labeling (3D-pcASL) and susceptibility-weighted imaging (SWI) for the early disease-sensitive markers of conversion from amnestic MCI (aMCI) to Alzheimer disease (AD) in this process. Methods: Forty patients with aMCI and AD respectively were recruited in the study, and 40 healthy subjects were taken as controls. Data were recorded using 3T MR scanner. We assessed the cerebral blood flow (CBF) in 11 different regions of interest, and counted number of microhemorrhages (MB) in 3 regions of brain lobes, bilateral basal ganglia/thalamus, and brain stem/cerebellum, and then investigated correlations between Montreal Cognitive Assessment (MoCA) scores, CBF, and susceptibility-weighted imaging (SWI) features in these 3 groups. Results: The results revealed that for AD patients, the MoCA scores and CBF values in frontal gray matter (FGM), occipital gray matter (OGM), temporal gray matter (TGM), parietal gray matter (PGM), hippocampus, anterior cingulate cortex (ACC), precuneus, posterior cingulate cortex (PCC), precuneus, basal ganglia and thalamus decreased compared with aMCI patients and control group, and significant difference was revealed among the 3 groups. While in cerebellum, statistical significance was only found between AD patients and control group. On SWI, the average numbers of hemorrhage in regions of lobes for AD patients were significantly higher than aMCI patients and control group. The same results occurred in the bilateral basal ganglia/thalamus. We further found the MoCA score was positively correlated with CBF, but negatively correlated with hypointense signal on SWI. Conclusion: 3D-pCASL and SWI have promising potential to be biomarkers for conversion from aMCI to AD in this process.

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.