We study possible relations between the structure of the connectome, white matter connecting different regions of brain, and Alzheimer disease. Regression models in covariates including age, gender and disease status for the extent of white matter connecting each pair of regions of brain are proposed. Subject We study possible relations between the Alzheimers disease progression and the structure of the connectome, white matter connecting different regions of brain. Regression models in covariates including age, gender and disease status for the extent of white matter connecting each pair of regions of brain are proposed. Subject inhomogeneity is also incorporated in the model through random effects with an unknown distribution. As there are large number of pairs of regions, we also adopt a dimension reduction technique through graphon (Lovasz and Szegedy (2006)) functions, which reduces functions of pairs of regions to functions of regions. The connecting graphon functions are considered unknown but assumed smoothness allows putting priors of low complexity on them. We pursue a nonparametric Bayesian approach by assigning a Dirichlet process scale mixture of zero mean normal prior on the distributions of the random effects and finite random series of tensor products of B-splines priors on the underlying graphon functions. Markov chain Monte Carlo techniques, for drawing samples for the posterior distributions are developed. The proposed Bayesian method overwhelmingly outperforms similar ANCOVA models in the simulation setup. The proposed Bayesian approach is applied on a dataset of 100 subjects and 83 brain regions and key regions implicated in the changing connectome are identified.
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