COMPSTAT pp 41-52 | Cite as

Spatio-temporal hierarchical modeling of an infectious disease from (simulated) count data

  • Noel Cressie
  • Andrew S. Mugglin


An infectious disease spreads through “contact” between an individual who has the disease and one who does not. However, modeling the individual-level mechanism directly requires data that would amount to observing (imperfectly) all individuals’ disease statuses along their space-time lines in the region and time period of interest. More likely, data consist of spatio-temporal aggregations that give small-area counts of the number infected during successive, regular time intervals. In this paper, we give a spatially descriptive, temporally dynamic hierarchical model to be fitted to such data. The dynamics of infection are described by just a few parameters, which can be interpreted. We take a Bayesian approach to the analysis of these space-time count data, using Markov chain Monte Carlo to compute Bayes estimates of all parameters of interest. As a “proof of concept,” we simulate data from the model and investigate how well our approach recovers important hidden features.


small-area counts multivariate autoregression Markov chain Monte Carlo Markov random field 


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  1. Carlin, B.P. and Louis, T.A. (1996). Bayes and Empiricial Bayes Methods for Data Analysis. Chapman and Hall, London.Google Scholar
  2. Cressie, N. (1993). Statistics for Spatial Data, revised edition. Wiley, NY.Google Scholar
  3. Cressie, N., Stern, H.S., and Wright, D.R. (2000). Mapping rates associated with polygons. Journal of Geographical Systems, 2, forthcoming.Google Scholar
  4. Gelman, A. and Rubin, D.B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, pp. 457–511.CrossRefGoogle Scholar
  5. (ed.) Gilks, W.R., Richardson, S., and Spiegelhalter, D.J. (1996). Markov chain Monte Carlo in Practice. Chapman and Hall, London.MATHGoogle Scholar
  6. Keeling, M.J., Rand, D.A., and Morris, A.J. (1997). Correlation models for childhood epidemics. Proceedings of the Royal Society of London, 264, pp. 1149–1156.CrossRefGoogle Scholar
  7. Knorr-Held, L. and Besag, J.E. (1998). Modelling risk from a disease in time and space. Statistics in Medicine, 17, pp. 2045–2060.CrossRefGoogle Scholar
  8. Lilienfeld, D.E. and Stolley, P.D. (1994). Foundations of Epidemiology, third edition. Oxford, NY.Google Scholar
  9. Lawson, A.B. and Leimich, P. (2000). Approaches to space-time modelling of infectious disease behavior. IMA Journal of Mathematics Applied to Medicine and Biology, 17, pp. 1–13.MATHCrossRefGoogle Scholar
  10. Mugglin, A.S., Cressie, N., and Gemmell, I. (2000). Hierarchical statistical modeling of influenza-epidemic dynamics in space and time (Tentative title), in preparation.Google Scholar
  11. Rhodes, C.J. and Anderson, R.M. (1996). Power laws governing epidemics in isolated populations. Nature, 381, pp. 600–602.CrossRefGoogle Scholar
  12. Stern, H.S. and Cressie, N. (1999). Inference for extremes in disease mapping in A. Lawson, A. Biggeri, D. Bohning, E. Lesaffre, J-F Viel, and R. Bertollini, eds. Disease Mapping and Risk Assessment for Public Health. Wiley, Chichester, pp. 63–84.Google Scholar
  13. Waller, L.A., Carlin, B.P., Xia, H., and Gelfand, A.E. (1997). Hierarchical spatio-temporal mapping of disease rates. Journal of the American Statistical Association, 92, pp. 607–617.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Noel Cressie
    • 1
  • Andrew S. Mugglin
    • 1
  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA

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