BAYESIAN HIDDEN MARKOV MODELS FOR LONGITUDINAL COUNTS

Abstract

Summary This paper describes a Bayesian approach to modelling carcinogenity in animal studies where the data consist of counts of the number of tumours present over time. It compares two autoregressive hidden Markov models. One of them models the transitions between three latent states: an inactive transient state, a multiplying state for increasing counts and a reducing state for decreasing counts. The second model introduces a fourth tied state to describe non-zero observations that are neither increasing nor decreasing. Both these models can model the length of stay upon entry of a state. A discrete constant hazards waiting time distribution is used to model the time to onset of tumour growth. Our models describe between-animal-variability by a single hierarchy of random effects and the within-animal variation by first-order serial dependence. They can be extended to higher-order serial dependence and multi-level hierarchies. Analysis of data from animal experiments comparing the influence of two genes leads to conclusions that differ from those of Dunson (2000). The observed data likelihood defines an information criterion to assess the predictive properties of the three- and four-state models. The deviance information criterion is appropriately defined for discrete parameters.