A coupled hidden Markov model for disease interactions

• Published in: Journal of the Royal Statistical Society Vol. 62; no. 4; pp. 609 - 627
• Main Authors: Sherlock, Chris, Xifara, Tatiana, Telfer, Sandra, Begon, Mike
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 01.08.2013; John Wiley & Sons Ltd; Oxford University Press
• Subjects: Adaptive Markov chain Monte Carlo sampling; Applied statistics; Bartonella; Covariance; Datasets; Discrete time; Disease; Disease models; Diseases; Economic theory; Forward-backward algorithm; Gibbs sampler; Hidden Markov models; Immune response; Infections; Inference; Logistic regression; Logistics; Longitudinal studies; Markov chains; Markov models; Markovian processes; Mathematical models; Medical research; Monte Carlo simulation; Original; Parasites; Population (statistical); Probability; Public health; Regression analysis; Samples; Sampling; Statistical analysis; Studies; Transition probabilities; Voles; Zoonosis; Gibbs sampler; Zoonosis; Adaptive Markov chain Monte Carlo sampling; Hidden Markov models; Forward–backward algorithm
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/rssc.12015

To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session, leading to incomplete profiles for all subjects. We use a discrete time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, which cycles through each of the diseases, first using an adaptive Metropolis–Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters. We find evidence for interactions between several pairs of parasites and of an acquired immune response for two of the parasites.