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Hidden Markov models for zero‐inflated Poisson counts with an application to substance use
Author(s) -
DeSantis Stacia M.,
Bandyopadhyay Dipankar
Publication year - 2011
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4207
Subject(s) - covariate , count data , poisson distribution , statistics , zero inflated model , econometrics , bayesian probability , poisson regression , craving , hidden markov model , zero (linguistics) , mathematics , markov chain , psychology , computer science , addiction , medicine , artificial intelligence , population , psychiatry , linguistics , philosophy , environmental health
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.