Open Collections

Wang, Vinky

University of British Columbia

Hidden Markov models (HMMs), a powerful class of statistical models, can uncover patterns in noisy, incomplete, or indirect data by modelling a sequence of observations as driven by an underlying latent state process. HMMs can infer latent biological rhythms by modelling transitions between states with functions of time that assume fixed, regular cycles. However, rhythms often fluctuate due to internal factors (e.g., diseases, disorders) and external influences (e.g., lifestyle, environment). Current methodologies overlook this and thus do not capture the dynamic nature of rhythms. In this work, I extend HMMs to model “irregular rhythms” that vary in frequency or stability over time. I analyse motor activity data from patients with depression to infer their circadian rhythms, which repeat every 24 hours but often exhibit irregularities. To jointly model state transition probabilities across all patients, accounting for daily behavioural cycles, daily variability, and individual variability, I formulate these probabilities to depend on time-of-day, day, and random effects. I use smooth functions for the time-related covariates to model transition probabilities as varying continuously over time, yielding visually smooth estimates and facilitating the interpretation of state dynamics. This approach provides insights into the regularities and trends of state-switching dynamics, revealing that transition probabilities do not always adhere to a regular daily cycle. Additionally, I calculate summary statistics from circadian research—typically applied to raw actigraph data—directly from the estimated sequence of states, offering clinical interpretations of the state process. Overall, this work advances the modelling of irregular rhythms in HMMs and contributes to a deeper understanding of circadian-related health issues.

Text

2024-10-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/89452

Statistics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/