Bayesian scalar-on-image regression with application to association between intracranial DTI and cognitive outcomes

- We analyze the relationship between cognitive outcomes and DTI predictors.
- We jointly model the predictive status and the regression coefficient.
- We induce the sparsity and promote spatial continuity in the model.
- The model is estimated through a Gibbs sampler, which is computationally efficient.
- The model can be carried out over a large and irregular brain region.

Diffusion tensor imaging (DTI) measures water diffusion within white matter, allowing for in vivo quantification of brain pathways. These pathways often subserve specific functions, and impairment of those functions is often associated with imaging abnormalities. As a method for predicting clinical disability from DTI images, we propose a hierarchical Bayesian “scalar-on-image” regression procedure. Our procedure introduces a latent binary map that estimates the locations of predictive voxels and penalizes the magnitude of effect sizes in these voxels, thereby resolving the ill-posed nature of the problem. By inducing a spatial prior structure, the procedure yields a sparse association map that also maintains spatial continuity of predictive regions. The method is demonstrated on a simulation study and on a study of association between fractional anisotropy and cognitive disability in a cross-sectional sample of 135 multiple sclerosis patients.