Hidden Markov models for zero-inflated Poisson counts with an application to substance use
Article first published online: 2 MAY 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 30, Issue 14, pages 1678–1694, 30 June 2011
How to Cite
DeSantis, S. M. and Bandyopadhyay, D. (2011), Hidden Markov models for zero-inflated Poisson counts with an application to substance use. Statist. Med., 30: 1678–1694. doi: 10.1002/sim.4207
- Issue published online: 2 JUN 2011
- Article first published online: 2 MAY 2011
- Manuscript Accepted: 3 JAN 2011
- Manuscript Received: 17 SEP 2009
- hidden Markov model;
- Markov chain Monte Carlo;
- zero inflation
Paradigms for substance abuse cue-reactivity research involve pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine-dependent subjects. It is unclear as to whether stress induced from participation in such studies increases drug-seeking behavior. We propose a 2-state Hidden Markov model to model the number of cocaine abuses per week before and after participation in a stress-and cue-reactivity study. The hypothesized latent state corresponds to ‘high’ or ‘low’ use. To account for a preponderance of zeros, we assume a zero-inflated Poisson model for the count data. Transition probabilities depend on the prior week's state, fixed demographic variables, and time-varying covariates. We adopt a Bayesian approach to model fitting, and use the conditional predictive ordinate statistic to demonstrate that the zero-inflated Poisson hidden Markov model outperforms other models for longitudinal count data. Copyright © 2011 John Wiley & Sons, Ltd.