title: Bayesian hierarchical Poisson models with a hidden Markov structure for the detection of influenza epidemic outbreaks.
abstract: Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epidemic phase. To do so, we propose a hidden Markov model in which the transition between both phases is modelled as a function of the epidemic state of the previous week. Different options for modelling the rates are described, including the option of modelling the mean at each phase as autoregressive processes of order 0, 1 or 2. Bayesian inference is carried out to provide the probability of being in an epidemic state at any given moment. The methodology is applied to various influenza data sets. The results indicate that our methods outperform previous approaches in terms of sensitivity, specificity and timeliness.
authors.affiliation: Departament d'Estadística i Investigació Operativa, Universitat de València, C/ Dr. Moliner 50, 46100 Burjassot (Valencia), Spain. david.v.conesa@uv.es.
authors.forename: D
authors.initials: D
authors.lastname: Conesa
authors.affiliation: Centro Superior de Investigación en Salud Pública, Generalitat Valenciana, Av. Cataluña 21, 46021 Valencia, Spain.
authors.forename: M A
authors.initials: MA
authors.lastname: Martínez-Beneito
authors.affiliation: Centro Superior de Investigación en Salud Pública, Generalitat Valenciana, Av. Cataluña 21, 46021 Valencia, Spain. Departamento de Ciencias Físicas, Matemáticas y Computación, Universidad Cardenal Herrera-CEU, Ed. Seminario, 46113 Moncada (Valencia), Spain.
authors.forename: R
authors.initials: R
authors.lastname: Amorós
authors.affiliation: Departament d'Estadística i Investigació Operativa, Universitat de València, C/ Dr. Moliner 50, 46100 Burjassot (Valencia), Spain.
authors.forename: A
authors.initials: A
authors.lastname: López-Quílez
mesh_terms: D001499:Bayes Theorem; D056808:Biostatistics; D004196:Disease Outbreaks; D058872:Epidemics / Q000706:statistics & numerical data; D006801:Humans; D015994:Incidence; D007251:Influenza, Human / Q000453:epidemiology*; D020407:Internet; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D016012:Poisson Distribution; D011336:Probability; D057386:Search Engine; D018571:Sentinel Surveillance; D013030:Spain / Q000453:epidemiology