Spatial outbreak detection based on inference principles for multivariate surveillance

Abstract

Spatial surveillance is a special case of multivariate surveillance. Thus, in this review of spatial outbreak methods, the relation to general multivariate surveillance approaches is discussed. Different outbreak models are useful for different aims. First, it makes a great difference which spreading pattern is of main interest to detect. We will discuss methods for the detection of (i) spatial clusters of increased incidence; (ii) increased incidence at only one (unknown) location; (iii) simultaneous increase at all locations; and (iv) outbreaks with a time lag between the onsets in different regions. The sufficient reduction was used to find likelihood ratio methods for some of these spreading patterns. Second, an alternative to the common assumption of a step change to an increased incidence level is suggested. The assumption is sometimes too restrictive and errors in the estimation of the baseline have great influence. Instead, a robust nonparametric model is suggested. The seasonal variation of influenza in Sweden is used as an example. Here, the outbreak was characterized by a monotonic increase following the constant non-epidemic level. The semi-parametric generalized likelihood ratio surveillance method used for this application is described. Third, evaluation metrics are discussed. Evaluation in spatial and other multivariate surveillance requires special consideration.

Keywords:

• Monitoring
• influenza
• sufficiency
• semi-parametric
• generalized likelihood
• timeliness
• predicted value

Acknowledgement

The author is grateful to the referees for their constructive comments.

Additional information

Notes on contributors

Marianne Frisén

Marianne Frisén is Professor Emerita in Statistics at the Statistical Research Unit, Department of Economics, University of Gothenburg, Gothenburg, Sweden. She received a Ph.D. in Statistics from that university. She is an elected member of the International Statistical Institute. Her main interests are in statistical surveillance, order restricted inference, robust methods, applied work, and the foundations of statistical inference.