Modelling Time Series of Counts in Epidemiology

Abstract

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.

Retrospective time series analysis of veterinary laboratory data: Preparing a historical baseline for cluster detection in syndromic surveillance

“…This proved to be a reasonable assumption for the syndromic time series evaluated in this work, since neither a negative binomial nor zero-inflated models indicated a better fit for the daily counts. If this assumption is not met, models which can account for zero-inflated distributions and/or overdispersion should be explored (Schmidt and Pereira, 2011). By reducing the model variables to key explainable factors, such as day-of-week and month, it was possible to model the baseline behaviour, while preventing adaption to temporal aberrations.…”

Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance

“…The probability of observing n cases given that H 1 is true can be estimated using statistical modeling of baseline data [19]. When the cases are independent (i.e.…”

Predicting US‐ and state‐level cancer counts for the current calendar year

“…The generated predictions are estimates of the posterior of the corresponding predictive distributions. Detailed discussion of the Bayes state space methods with particular emphasis on modeling time series of counts in epidemiology can be found in Schmidt and Pereira 5 .…”

“…The additional models are: (1) the Bayesian State-Space Model 5 , (2) two versions of the Joinpoint Regression Model (based on the permutation test and modified-BIC criteria for selecting the number of joinpoints) 6 , (3) the Nordpred Model 7 , and (4) the Vector Autoregressive Model via Hilbert-Huang Transform 8 .…”

“…In this article, we compare the accuracy of the state‐space model and 4 additional models for 4‐year‐ahead projection of cancer deaths to the current year, nationally and in each state, in order to determine the best method of projection. The additional models are: 1) the Bayesian state‐space model,5 2) 2 versions of the Joinpoint regression model (based on the permutation test and modified‐BIC criteria for selecting the number of joinpoints),6 3) the Nordpred model,7 and 4) the vector autoregressive model via Hilbert‐Huang transform 8…”