Twenty-five years of the binary power law for characterizing heterogeneity of disease incidence

L. V. Madden*, G. Hughes, W. Bucker Moraes, X. M. Xu, W. W. Turechek

*Corresponding author for this work

Research output: Contribution to journalReview article

1 Citation (Scopus)

Abstract

Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor’s power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.

Original languageEnglish
Pages (from-to)656-680
Number of pages25
JournalPhytopathology
Volume108
Issue number6
Early online date26 Feb 2018
DOIs
Publication statusPrint publication - 1 Jun 2018

Fingerprint

disease incidence
sampling
plant diseases and disorders
data analysis
synthesis
prediction
crops
methodology

Cite this

Madden, L. V. ; Hughes, G. ; Moraes, W. Bucker ; Xu, X. M. ; Turechek, W. W. / Twenty-five years of the binary power law for characterizing heterogeneity of disease incidence. In: Phytopathology. 2018 ; Vol. 108, No. 6. pp. 656-680.
@article{b6461fdb57ec4d79b664cf8b49247f36,
title = "Twenty-five years of the binary power law for characterizing heterogeneity of disease incidence",
abstract = "Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor’s power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.",
author = "Madden, {L. V.} and G. Hughes and Moraes, {W. Bucker} and Xu, {X. M.} and Turechek, {W. W.}",
year = "2018",
month = "6",
day = "1",
doi = "10.1094/PHYTO-07-17-0234-RVW",
language = "English",
volume = "108",
pages = "656--680",
journal = "Phytopathology",
issn = "0031-949X",
publisher = "American Phytopathological Society",
number = "6",

}

Twenty-five years of the binary power law for characterizing heterogeneity of disease incidence. / Madden, L. V.; Hughes, G.; Moraes, W. Bucker; Xu, X. M.; Turechek, W. W.

In: Phytopathology, Vol. 108, No. 6, 01.06.2018, p. 656-680.

Research output: Contribution to journalReview article

TY - JOUR

T1 - Twenty-five years of the binary power law for characterizing heterogeneity of disease incidence

AU - Madden, L. V.

AU - Hughes, G.

AU - Moraes, W. Bucker

AU - Xu, X. M.

AU - Turechek, W. W.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor’s power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.

AB - Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor’s power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.

U2 - 10.1094/PHYTO-07-17-0234-RVW

DO - 10.1094/PHYTO-07-17-0234-RVW

M3 - Review article

C2 - 29148964

AN - SCOPUS:85047328810

VL - 108

SP - 656

EP - 680

JO - Phytopathology

JF - Phytopathology

SN - 0031-949X

IS - 6

ER -