A Bayesian hierarchical approach to jointly model structural biomarkers and covariance networks

Estimation of structural biomarkers and covariance networks from MRI have provided valuable insight into the morphological processes and organisation of the human brain. State-of-the-art analyses such as linear mixed effects (LME) models and pairwise descriptive correlation networks are usually performed independently, providing an incomplete picture of the relationships between the biomarkers and network organisation. Furthermore, descriptive network analyses do not generalise to the population level. In this work, we develop a Bayesian generative model based on wombling that allows joint statistical inference on biomarkers and connectivity covariance structure. The parameters of the wombling model were estimated via Markov chain Monte Carlo methods, which allow for simultaneous inference of the brain connectivity matrix and the association of participants' biomarker covariates. To demonstrate the utility of wombling on real data, the method was used to characterise intrahemispheric cortical thickness and networks in a study cohort of subjects with Alzheimer's disease, mild-cognitive impairment and healthy ageing. The method was also compared with state-of-the-art alternatives. Our Bayesian modelling approach provided posterior probabilities for the connectivity matrix of the wombling model, accounting for the uncertainty for each connection. This provided superior inference in comparison with descriptive networks. On the study cohort, there was a loss of connectivity across diagnosis levels from healthy to Alzheimer's disease for all network connections (posterior probability >= 0.7). In addition, we found that wombling and LME model approaches estimated that cortical thickness progressively decreased along the dementia pathway. The major advantage of the wombling approach was that spatial covariance among the regions, as such, global cortical thickness estimates could be estimated. Joint modelling of biomarkers and covariance networks using our novel wombling approach allowed accurate identification of probabilistic networks and estimated biomarker changes that took into account spatial covariance. The wombling model provides a novel tool to address multiple brain features, such as morphological and connectivity changes facilitating a better understanding of disease pathology