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

Abstract

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.

Sparse Bayesian variable selection in high‐dimensional logistic regression models with correlated priors

“…Following simulation settings in Cao et al [11], we investigate the behavior of proposed methods under small and large signals for the true coefficient vector $$$ \boldsymbol{\beta} $$$Setting 1: all the active covariates of $$$ \boldsymbol{\beta} $$$ are set to be $$$ 1.5 $$$. Setting 2: all the active covariates of $$$ \boldsymbol{\beta} $$$ are generated from Unif(1.5, 3). …”

“…Following simulation settings in Cao et al [11], we investigate the behavior of proposed methods under small and large signals for the true coefficient vector 𝜷…”

“…These challenges are partially addressed by explicitly formulating a loss function that yields a sparse solution to the estimation problem. The sparse solution restricts the number of important covariates to be small [9, 10] thereby providing interpretability, computational efficiency, and stability of inference [4, 11]. Consequently, in large $$$ k $$$, small $$$ n $$$ settings, variable selection is often the first step towards dimension reduction.…”

“…These methods have demonstrated excellent performance in a low dimensional setting [14], but may not work well for high dimensional data classification, especially when the objective function is not convex and/or when it is difficult to choose a penalty function [15]. Common Bayesian methods, that can be used as alternatives to the frequentist ones to overcome the issue of the curse of dimensionality, include Bayesian LASSO [16], spike and slab (SSL) priors [11], and global-local (GL) shrinkage priors [17].…”

Seleção Bayesiana de variáveis para modelos de mistura de regressão logística com variáveis latentes Pólya-Gamma

“…Under this specification, we update only those regression coefficients β it for which γ it = 1 at each MCMC iteration, because β it = 0 by definition when γ it = 0. This method has been widely applied in Bayesian variable selection (GEORGE; MCCULLOCH, 1997;WU, 2016;CAO;HUANG, 2020). Figure 3 shows an example of how we update the regression coefficients at each iteration considering their indicators.…”