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International Biometric Society
COUNT TIME SERIES MODELS FOR SYNDROMIC SURVEILLANCE AND OUTBREAK DETECTION
Xanthi Pedeli1 and Dimitris Karlis1
1
Department of Statistics, Athens University of Economics, 76 Patission str, Athens 10434,
Greece
Reliable surveillance models are an important tool in public health because they contribute
significantly in the detection of disease outbreaks, identify when and where outbreaks occur
and predict future occurrences. Even though various statistical models have been used for
syndromic surveillance purposes, important practical goals of good sensitivity and
specificity, proper use of covariate information and inclusion of spatio-temporal information
are rarely simultaneously met. Moreover, surveillance data usually consist of multiple time
series of counts of infectious diseases. Data for a single disease are typically reported in
several strata defined through administrative geographical areas and/or age groups. Also
disease counts from different pathogens often present dependencies that have to be taken
into account (Paul and Held, 2011).
The focus of this paper is on the application of multivariate count time series models on
syndromic surveillance data for early event detection. In particular, we consider the class of
integer-valued autoregressive (INAR) models, introduced by McKenzie (1985) and Al-Osh
and Alzaid (1987) as a discrete counterpart of the standard autoregressive (AR) process.
Recently, Pedeli and Karlis (2011, 2013) suggested an extension of the simple INAR(1)
model to the multi-dimensional space. The introduced process is flexible allowing for both
serial and cross correlation between the series and can easily accommodate overdispersion
and covariate information. Moreover, its structure implies a natural decomposition into an
endemic and an epidemic component, a common distinction in dynamic models for
infectious disease counts (see e.g. Finkenstädt et al., 2002 and Paul et al., 2008). We
propose the application of multivariate INAR processes to the analysis of multivariate
(bio)surveillance data. The suggested approach is compared with already established
surveillance models and emphasis is placed on the detection of disease outbreaks using the
theory of change point detection (Franke et al., 2012).
References
Al-Osh, M.A., and Alzaid, A.A. (1987). First–Order Integer–Valued Autoregressive Process.
Journal of Time Series Analysis, 8, 261–275.
Finkenstädt, B.F., Bjørnstad, O.N., and Grenfell, B.T. (2002). A stochastic model for
extinction and recurrence of epidemics: estimation and inference for measles outbreaks.
Biostatistics, 3, 493–510.
Franke, J., Kirch, C. and Kamgaing, J.T. (2012). Changepoints in times series of counts.
Journal of Time Series Analysis, 33, 757-770.
McKenzie, E. (1985). Some Simple Models for Discrete Variate Time Series. Water
Resources Bulletin, 21, 645–650.
Paul, M. and Held, L. (2011). Predictive assessment of a non-linear random effects model for
multivariate time series of infectious disease counts. Statistics in Medicine, 30, 1118-1136.
Pedeli, X. and Karlis, D. (2011). A bivariate INAR(1) process with application. Statistical
Modelling, 11, 325–349.
Pedeli, X. and Karlis, D. (2013). On composite likelihood estimation of a multivariate INAR(1)
model. Journal of Time Series Analysis, 34, 206–220.
International Biometric Conference, Florence, ITALY, 6 – 11 July 2014