Biostatistics (2001), 2, 4, pp. 433–444 Printed in Great Britain
Bayesian analysis of a time series of counts with covariates: an application to the control of an infectious disease J. L. HAY∗ Department of Social and Preventive Medicine, University of Queensland, Princess Alexandra Hospital, Brisbane, Queensland, 4102, Australia
[email protected] A. N. PETTITT Centre in Statistical Science and Industrial Mathematics, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, 4001, Australia S UMMARY This paper presents a Bayesian analysis of a time series of counts to assess its dependence on an explanatory variable. The time series represented is the incidence of the infectious disease ESBLproducing Klebsiella pneumoniae in an Australian hospital and the explanatory variable is the number of grams of antibiotic (third generation) cephalosporin used during that time. We demonstrate that there is a statistically significant relationship between disease occurrence and use of the antibiotic, lagged by three months. The model used is a parameter-driven model in the form of a generalized linear mixed model. Comparison of models is made in terms of mean square error. Keywords: Bayesian hierarchical model; Count data; Klebsiella pneumoniae; Markov chain Monte Carlo; Parameter driven model; Time series effects.
1. I NTRODUCTION In epidemiological studies, the reported occurrences of a disease are often expressed as daily, weekly or monthly counts. Studies that model these counts and their associations with other variables provide important information leading to better understanding of the disease and, hopefully, better control measures. When the counts are relatively large, methods based on transformation and consequent use of