Multi-subject Stochastic Blockmodels for adaptive analysis of individual differences in human brain network cluster structure
Dragana M. Pavlović,
Bryan R.L. Guillaume,
Emma K. Towlson,
Nicole M.Y. Kuek,
Soroosh Afyouni,
Petra E. Vértes,
B.T. Thomas Yeo,
Edward T. Bullmore,
Thomas E. Nichols
Affiliations
Dragana M. Pavlović
Big Data Institute, Nuffield Department of Population Health, University of Oxford, Oxford, United Kingdom; Department of Electrical and Computer Engineering, Clinical Imaging Research Centre, N.1 Institute for Health and Memory Networks Programme, National University of Singapore, Singapore; Corresponding author. Big Data Institute, Nuffield Department of Population Health, University of Oxford, Oxford, United Kingdom.
Bryan R.L. Guillaume
Big Data Institute, Nuffield Department of Population Health, University of Oxford, Oxford, United Kingdom; Department of Biomedical Engineering, National University of Singapore, Singapore
Emma K. Towlson
Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA, United States; Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA, United States
Nicole M.Y. Kuek
Department of Electrical and Computer Engineering, Clinical Imaging Research Centre, N.1 Institute for Health and Memory Networks Programme, National University of Singapore, Singapore
Soroosh Afyouni
Big Data Institute, Nuffield Department of Population Health, University of Oxford, Oxford, United Kingdom
Petra E. Vértes
Behavioural and Clinical Neuroscience Institute, Department of Psychiatry, University of Cambridge, Cambridge, United Kingdom
B.T. Thomas Yeo
Department of Electrical and Computer Engineering, Clinical Imaging Research Centre, N.1 Institute for Health and Memory Networks Programme, National University of Singapore, Singapore
Edward T. Bullmore
Behavioural and Clinical Neuroscience Institute, Department of Psychiatry, University of Cambridge, Cambridge, United Kingdom; Cambridgeshire and Peterborough National Health Service Foundation Trust, Cambridge, United Kingdom; GlaxoSmithKline, Clinical Unit Cambridge, Addenbrooke's Hospital, Cambridge, United Kingdom
Thomas E. Nichols
Big Data Institute, Nuffield Department of Population Health, University of Oxford, Oxford, United Kingdom; Warwick Manufacturing Group, University of Warwick, Coventry, United Kingdom
There is considerable interest in elucidating the cluster structure of brain networks in terms of modules, blocks or clusters of similar nodes. However, it is currently challenging to handle data on multiple subjects since most of the existing methods are applicable only on a subject-by-subject basis or for analysis of an average group network. The main limitation of per-subject models is that there is no obvious way to combine the results for group comparisons, and of group-averaged models that they do not reflect the variability between subjects. Here, we propose two new extensions of the classical Stochastic Blockmodel (SBM) that use a mixture model to estimate blocks or clusters of connected nodes, combined with a regression model to capture the effects of subject-level covariates on individual differences in cluster structure. The proposed Multi-Subject Stochastic Blockmodels (MS-SBMs) can flexibly account for between-subject variability in terms of homogeneous or heterogeneous covariate effects on connectivity using subject demographics such as age or diagnostic status. Using synthetic data, representing a range of block sizes and cluster structures, we investigate the accuracy of the estimated MS-SBM parameters as well as the validity of inference procedures based on the Wald, likelihood ratio and permutation tests. We show that the proposed multi-subject SBMs recover the true cluster structure of synthetic networks more accurately and adaptively than standard methods for modular decomposition (i.e. the Fast Louvain and Newman Spectral algorithms). Permutation tests of MS-SBM parameters were more robustly valid for statistical inference and Type I error control than tests based on standard asymptotic assumptions. Applied to analysis of multi-subject resting-state fMRI networks (13 healthy volunteers; 12 people with schizophrenia; n=268 brain regions), we show that Heterogeneous Stochastic Blockmodel (Het-SBM) identifies a range of network topologies simultaneously, including modular and core structures.
