A statistical framework for the analysis of multivariate infectious disease surveillance counts

A framework for the statistical analysis of counts from infectious disease surveillance databases is proposed. In its simplest form, the model can be seen as a Poisson branching process model with immigration. Extensions to include seasonal effects, time trends and overdispersion are outlined. The model is shown to provide an adequate fit and reliable one-step-ahead prediction intervals for a typical infectious disease time series. In addition, a multivariate formulation is proposed, which is well suited to capture space-time dependence caused by the spatial spread of a disease over time. An analysis of two multivariate time series is described. All analyses have been done using general optimization routines, where ML estimates and corresponding standard errors are readily available.

[1]  Noel Cressie,et al.  Hierarchical statistical modelling of influenza epidemic dynamics in space and time , 2002, Statistics in medicine.

[2]  B. Jørgensen,et al.  A state-space model for multivariate longitudinal count data , 1999 .

[3]  Peter J. Diggle,et al.  On-line Monitoring of Public Health Surveillance Data , 2004 .

[4]  Dankmar Böhning,et al.  Empirical Bayes estimators and non‐parametric mixture models for space and time–space disease mapping and surveillance , 2003 .

[5]  L Knorr-Held,et al.  Modelling risk from a disease in time and space. , 1998, Statistics in medicine.

[6]  Brian D. Ripley,et al.  Modern applied statistics with S, 4th Edition , 2002, Statistics and computing.

[7]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[8]  Nick Andrews,et al.  A Statistical Algorithm for the Early Detection of Outbreaks of Infectious Disease , 1996 .

[9]  Charles J. Mode,et al.  Multitype branching processes;: Theory and applications , 1971 .

[10]  S. Zeger,et al.  Markov regression models for time series: a quasi-likelihood approach. , 1988, Biometrics.

[11]  S. Zeger.  A regression model for time series of counts , 1988 .

[12]  Bryan T Grenfell,et al.  A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks. , 2002, Biostatistics.

[13]  Sylvia Richardson,et al.  A hierarchical model for space–time surveillance data on meningococcal disease incidence , 2003 .

[14]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[15]  Refik Soyer,et al.  Bayesian Methods for Nonlinear Classification and Regression , 2004, Technometrics.

[16]  C Montomoli,et al.  Spatial correlation in ecological analysis. , 1993, International journal of epidemiology.