Statistics and Its Interface

Volume 16 (2023)

Number 2

Special issue on recent developments in complex time series analysis – Part II

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

Approximate hidden semi-Markov models for dynamic connectivity analysis in resting-state fMRI

Pages: 259 – 277

DOI: https://dx.doi.org/10.4310/22-SII730

Authors

Mark B. Fiecas (Division of Biostatistics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Christian Coffman (Division of Biostatistics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Meng Xu (Division of Biostatistics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Timothy J. Hendrickson (Informatics Institute, University of Minnesota, Minneapolis, Minn., U.S.A.)

Bryon A. Mueller (Department of Psychiatry & Behavioral Sciences, University of Minnesota, Minneapolis, Minn., U.S.A.)

Bonnie Klimes-Dougan (Department of Psychology, University of Minnesota, Minneapolis, Minn., U.S.A.)

Kathryn R. Cullen (Department of Psychiatry & Behavioral Sciences, University of Minnesota, Minneapolis, Minn., U.S.A.)

Abstract

Motivated by a study on adolescent mental health, we conduct a dynamic connectivity analysis using resting-state functional magnetic resonance imaging (fMRI) data. A dynamic connectivity analysis investigates how the interactions between different regions of the brain, represented by the different dimensions of a multivariate time series, change over time. HiddenMarkov models (HMMs) and hidden semi-Markov models (HSMMs) are common analytic approaches for conducting dynamic connectivity analyses. However, existing approaches for HSMMs are limited in their ability to incorporate covariate information. In this work, we approximate an HSMM using an HMM for modeling multivariate time series data. The approximate HSMM (aHSMM) model allows one to explicitly model dwell-time distributions that are available to HSMMs, while maintaining the theoretical and methodological advances that are available to HMMs. We conducted a simulation study to show the performance of the aHSMM relative to other approaches. Finally, we used the aHSMM to conduct a dynamic connectivity analysis, where we showed how dwell-time distributions vary across the severity of non-suicidal self-injury (NSSI) in adolescents. The aHSMM allowed us to identify states that have greater dwell-times for those with moderate or severe NSSI.

Keywords

dynamic functional connectivity, fMRI, hidden Markov models, hidden semi-Markov models, multivariate time series

2010 Mathematics Subject Classification

Primary 62M05, 62M10. Secondary 62P10.

Full Text (PDF format)

Received 1 March 2021

Accepted 17 February 2022

Published 13 April 2023