  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.
