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Modelling Time Series of Counts in Epidemiology
Author(s) -
Schmidt Alexandra M.,
Pereira João Batista M.
Publication year - 2011
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2010.00123.x
Subject(s) - poisson distribution , mathematics , count data , statistics , series (stratigraphy) , bayesian probability , poisson regression , generalized linear model , population , paleontology , demography , sociology , biology
Summary We review generalized dynamic models for time series of count data. Usually temporal counts are modelled as following a Poisson distribution, and a transformation of the mean depends on parameters which evolve smoothly with time. We generalize the usual dynamic Poisson model by considering continuous mixtures of the Poisson distribution. We consider Poisson‐gamma and Poisson‐log‐normal mixture models. These models have a parameter for each time t which captures possible extra‐variation present in the data. If the time interval between observations is short, many observed zeros might result. We also propose zero inflated versions of the models mentioned above. In epidemiology, when a count is equal to zero, one does not know if the disease is present or not. Our model has a parameter which provides the probability of presence of the disease given no cases were observed. We rely on the Bayesian paradigm to obtain estimates of the parameters of interest, and discuss numerical methods to obtain samples from the resultant posterior distribution. We fit the proposed models to artificial data sets and also to a weekly time series of registered number of cases of dengue fever in a district of the city of Rio de Janeiro, Brazil, during 2001 and 2002.