Linking Covariates to State Durations in Dynamic Brain Networks via Hidden Semi-Markov Models

Hidden semi-Markov models (HSMMs) provide a flexible framework for studying dynamic functional connectivity because they represent brain activity as transitions between latent network states with explicit dwell time distributions. Although dwell times are often associated with behavioral and demographic variables, these associations are typically assessed only after model fitting using indirect group comparisons, limiting formal covariate modeling and the simultaneous inclusion of multiple predictors. In this work, we extend the HSMM framework by introducing covariate-dependent dwell time distributions through a regression-based formulation, allowing expected state duration to vary with subject-level covariates and enabling direct inference on how these factors relate to state persistence. Model parameters are estimated with an expectation-maximization algorithm, and uncertainty in the dwell-time regression coefficients is quantified using a subject-level nonparametric bootstrap. In simulations, the proposed model accurately recovered covariate effects under both shifted-Poisson and Gamma dwell time specifications, with low bias and variability. We applied the method to resting-state fMRI data from 1,000 UK Biobank participants and found that age and sex were associated with dwell times in a subset of brain states. Together, these results show that modeling dwell-time behavior directly provides a more flexible framework for studying individual differences in brain dynamics, revealing not only which states occur, but also how long individuals remain in them.