Abstract
Surveillance data collected on several hundred different infectious organisms over 20 years have revealed striking power relationships between their variance and mean in successive time periods. Such patterns are common in ecology, where they are referred to collectively as Taylor's power law. In the paper, these relationships are investigated in detail, with the aim of exploiting them for the descriptive statistical modelling of infectious disease surveillance data. We confirm the existence of variance-to-mean power relationships, with exponent typically between 1 and 2. We investigate skewness-to-mean relationships, which are found broadly to match those expected of Tweedie distributions, and thus confirm the relevance of the Tweedie convergence theorem in this context. We suggest that variance- and skewness-to-mean power laws, when present, should inform statistical modelling of infectious disease surveillance data, notably in descriptive analysis, model building, simulation and interval and threshold estimation, threshold estimation being particularly relevant to outbreak detection.
DOI
10.1111/rssa.12181
Publication Date
2016-02-05
Publication Title
Journal of the Royal Statistical Society, Series A
Volume
180
Issue
1
Publisher
Oxford University Press (OUP)
Embargo Period
2024-11-22
Keywords
Exponential dispersion model, Infectious disease, Power law, Surveillance
First Page
45
Last Page
72
Recommended Citation
Enki, D., Noufaily, A., Farrington, P., Garthwaite, P., & Andrews, N. (2016) 'Taylor’s power law and the statistical modelling of infectious disease surveillance data', Journal of the Royal Statistical Society, Series A, 180(1), pp. 45-72. Oxford University Press (OUP): Available at: https://doi.org/10.1111/rssa.12181
