On the application of integer-valued time series models for the analysis of disease incidence

Statistics in Medicine

Volumn 18, Issue 15, 1999, Pages 2025-2039

  Cardinal, Mitsi ^a   Roy, Roch ^a   Lambert, Jean ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; FORECASTING; HUMAN; INCIDENCE; MENINGOCOCCOSIS; MORBIDITY; PUBLIC HEALTH; STATISTICAL MODEL; TIME;

COMMUNICABLE DISEASES; DISEASE NOTIFICATION; DISEASE OUTBREAKS; FORECASTING; HUMANS; INCIDENCE; MENINGITIS, MENINGOCOCCAL; MODELS, BIOLOGICAL; PUBLIC HEALTH; REGRESSION ANALYSIS; TIME FACTORS;

EID: 0033566585     PISSN: 02776715     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0258(19990815)18:15<2025::AID-SIM163>3.0.CO;2-D     Document Type: Article

References (38)

1. Thacker, S. B., Berkelman, R. L. and Stroup, D. F. 'The science of public health surveillance', Journal of Public Health Policy, 10, 187-203 (1989).
2. Watier, L., Richardson, S. and Hubert, B. 'A time series construction of an alert threshold with application to S. bovismorbificans in France', Statistics in Medicine, 10, 1493-1509 (1991).
3. Stroup, D. F., Thacker, S. B. and Herndon, J. L. 'Application of multiple time series analysis to the estimation of pneumonia and influenza mortality by age 1962-1983', Statistics in Medicine, 7, 1045-1059 (1988).
4. Box, G. E. P. and Jenkins, G. M. Time Series Analysis: Forecasting and Control, revised edition, Holden Day, San Francisco, 1976.
5. Anderson, R. M. and Grenfell, B. T. 'Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: time series analysis', Journal of Hygiene, 93, 587-608 (1984).
6. Choi, K. and Thacker, S. B. 'An evaluation of influenza mortality surveillance, 1962-1979: I. Time series forecasts of expected pneumonia and influenza deaths', American Journal of Epidemiology, 113, 215-226 (1981).
7. Choi. K. and Thacker, S. B. 'An evaluation of influenza mortality surveillance, 1962-1979: II. Percentage of pneumonia and influenza deaths as an indicator of influenza activity', American Journal of Epidemiology, 113, 227-235 (1981).
8. Helfenstein, U. 'Box-Jenkins modelling of some viral infectious diseases', Statistics in Medicine, 5, 37-47 (1986).
9. Schnell, D., Zaidi, A. and Reynolds, G. 'A time series analysis of gonorrhea surveillance data', Statistics in Medicine, 8, 343-352 (1989).
10. Zaidi, A. A., Schnell, D. J. and Reynolds, G. H. 'Time series analysis of syphilis surveillance data', Statistics in Medicine, 8, 353-362 (1989).
11. Al-Osh, M. A. and Alzaid, A. A. 'First-order integer-valued autoregressive (IN AR(1)) process', Journal of Time Series Analysis, 8, 261-275 (1987).
12. Alzaid, A. A. and Al-Osh, M. A. 'An integer-valued pth order autoregressive structure (IN AR(p)) process', Journal of Applied Probability, 27, 314-324 (1990).
13. Du, J. G. and Li, Y. 'The integer-valued autoregressive (IN AR(p)) model', Journal of Time Series Analysis, 12, 129-142 (1991).
14. Gauthier, G. and Latour, A. 'Convergence forte des estimateurs des paramètres d'un processus GENAR(p)', Annales des Sciences Mathématiques du Québec, 18, 49-71 (1994).
15. Dion, J. -P., Gauthier, G. and Latour, A. 'Branching processes with immigration and integer-valued time series', Serdica, 21, 123-136 (1995).
16. Latour, A. 'Existence and stochastic structure of non-negative integer-valued autoregressive processes', Journal of Time Series Analysis, 19, 439-455 (1998).
17. Latour, A. 'The multivariate GINAR(p) process', Advances in Applied Probability, 29, 228-248 (1997).
18. Zeger, S. L. 'A regression model for time series of counts', Biometrika, 61, 439-447 (1988).
19. Zeger, S. L. and Qaqish, B. 'Markov regression models for time series: a quasi-likelihood approach', Biometrics, 44, 1019-1031 (1988).
20. Cox, D. R. 'Statistical analysis of time series: some recent developments', Scandinavian Journal of Statistics, 8, 93-115 (1981).
21. Blais, M., MacGibbon, B. and Roy, R. 'Limit theorems for regression models of time series of counts', Statistics and Probability Letters, (1999), in press.
22. Diggle, P. J. Time Series: A Biostatistical Introduction, Oxford University Press, Oxford, 1990.
23. Wei, W. W. S. Time Series Analysis: Univariate and Multivariate Methods, Addison-Wesley, Redwood City, 1990.
24. McKenzie, E. 'Some ARMA models for dependent sequences of Poisson counts', Advances in Applied Probability, 20, 822-835 (1988).
25. Steutel, F. W. and van Harn, K. 'Discrete analogues of self-decomposability and stability', Annals of Probability, 7, 898-899 (1979).
26. Lawless, J. F. 'Negative binomial and mixed Poisson regression', Canadian Journal of Statistics, 15, 209-225 (1987).
27. McCullagh, P. and Nelder, J. A. Generalized Linear Models, 2nd edn, Chapman and Hall, London, 1983.
28. Lambert, J., Ranger, N. and Roy, R. 'INAR, XINAR and INARG PROGRAMS: User's Guide (UNIX and DOS Versions)', Technical Report, Départment de médecine sociale et préventive de l'Université de Montréal, Montreal, 1993.
29. Franke, J. and Seligmann, T. 'Conditional maximum likelihood estimates for INAR(1) processes and their application to modeling epileptic seizure counts', in Subba Rao, T. (ed.), Developments in Time Series Analysis, Chapman and Hall, London, 1993, pp. 310-330.
30. Efron, B. and Tibshirani, R. An Introduction to the Bootstrap, Chapman and Hall, New York, 1993.
31. Benenson, A. S. (ed.), Control of Communicable Diseases in Man, 15th edn, APHA, Washington D.C., 1990.
32. Ljung, G. M. and Box, G. E. P. 'On a measure of lack of fit in time series models', Biometrika, 65, 297-303 (1978).
33. Brookmeyer, R. and Damiano, A. 'Statistical methods for short-term projections of AIDS incidence', Statistics in Medicine, 8, 23-34 (1989).
34. Lui, K.-J. and Rudy, R. K. 'An application of a mathematical model to adjust for time lag in case reporting', Statistics in Medicine, 8, 259-262 (1989).
35. Zeger, S. L., See, L. -C. and Diggle, P. J. 'Statistical methods for monitoring the AIDS epidemic', Statistics in Medicine, 8, 3-21 (1989).
36. Karon, J. M., Devine, O. J. and Morgan, W. M. 'Predicting AIDS incidence by extrapolating from recent trends', in Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomathematics, 83, Springer Verlag, Heidelberg, 1989, pp. 58-88.
37. Frisén, M. 'Evaluations of methods for statistical surveillance', Statistics in Medicine, 11, 1489-1502 (1992).
38. Thacker, S. B., Parrish, R. G., Trowbridge, F. L. and the Surveillance Coordination Group. 'A method for evaluating systems of epidemiological surveillance', World Health Statistics Quarterly, 41, 11-18 (1988).