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Taylor's power law and the statistical modelling of infectious disease surveillance data
Author(s) -
Enki Doyo Gragn,
Noufaily Angela,
Farrington Paddy,
Garthwaite Paul,
Andrews Nick,
Charlett Andre
Publication year - 2017
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/rssa.12181
Subject(s) - skewness , statistics , infectious disease (medical specialty) , econometrics , statistical power , context (archaeology) , variance (accounting) , outbreak , power analysis , mathematics , power law , geography , medicine , disease , algorithm , economics , archaeology , accounting , pathology , virology , cryptography
Summary 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.