Measuring the severity of disease clustering using Tango's index

Richard J. Kryscio; Claude Lefèvre

doi:10.1016/0025-5564(91)90007-6

Measuring the severity of disease clustering using Tango's index

Richard J. Kryscio, Claude Lefèvre

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Abstract

Tango [Biometrics 40:15 (1984)] proposed an index for detecting disease clustering in time applicable to grouped data obtained from a population that remains fairly stable over the study period. This index has received considerable attention in the literature including the suggestion that it be used to detect the space-time clustering of diseases and the suggestion to use similar test statistics to detect disease clustering in space and/or time while accounting for a changing population size over the study period. This paper concerns the related question of measuring the severity of the disease clustering once it has been determined that cases are not randomly distributed over space and/or time. A family of alternatives to randomness is proposed in which space and/or time versions of Tango's index are sufficient statistics for the parameters measuring the severity of the clustering. For the special case of temporal clustering, an unbiased estimator of the clustering parameter and its sampling variance is derived, and a particularly simple interpretation of this estimator is suggested. These latter results are based on some asymptotic approximations due to Tango [Biometrics 46:351 (1990)]. An application to the trisomy data given by Wallenstein [Am. J. Epidemiol. 111:367 (1980)] is discussed.

Original language	English
Pages (from-to)	235-247
Number of pages	13
Journal	Mathematical Biosciences
Volume	107
Issue number	2
DOIs	https://doi.org/10.1016/0025-5564(91)90007-6
State	Published - Dec 1991

Bibliographical note

Funding Information:
This research was partially supported by a NATO travel grant for intema-tional collaboration. The work of Richard J. Kvscio was also partially supported by the NSF-Kentucky EPSCoR grant RII-861 0671. We thank Professor Toshiro Tango for allowing us to see a preprint of his 1990 paper. We also thank Dr. Goeffrey M. Jacquez for a critical reading of this paper and for his suggestions, which led to a much improved discussion section.

Funding

This research was partially supported by a NATO travel grant for intema-tional collaboration. The work of Richard J. Kvscio was also partially supported by the NSF-Kentucky EPSCoR grant RII-861 0671. We thank Professor Toshiro Tango for allowing us to see a preprint of his 1990 paper. We also thank Dr. Goeffrey M. Jacquez for a critical reading of this paper and for his suggestions, which led to a much improved discussion section.

Funders	Funder number
NSF-Kentucky EPSCoR	RII-861 0671
North Atlantic Treaty Organization

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

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title = "Measuring the severity of disease clustering using Tango's index",

abstract = "Tango [Biometrics 40:15 (1984)] proposed an index for detecting disease clustering in time applicable to grouped data obtained from a population that remains fairly stable over the study period. This index has received considerable attention in the literature including the suggestion that it be used to detect the space-time clustering of diseases and the suggestion to use similar test statistics to detect disease clustering in space and/or time while accounting for a changing population size over the study period. This paper concerns the related question of measuring the severity of the disease clustering once it has been determined that cases are not randomly distributed over space and/or time. A family of alternatives to randomness is proposed in which space and/or time versions of Tango's index are sufficient statistics for the parameters measuring the severity of the clustering. For the special case of temporal clustering, an unbiased estimator of the clustering parameter and its sampling variance is derived, and a particularly simple interpretation of this estimator is suggested. These latter results are based on some asymptotic approximations due to Tango [Biometrics 46:351 (1990)]. An application to the trisomy data given by Wallenstein [Am. J. Epidemiol. 111:367 (1980)] is discussed.",

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note = "Funding Information: This research was partially supported by a NATO travel grant for intema-tional collaboration. The work of Richard J. Kvscio was also partially supported by the NSF-Kentucky EPSCoR grant RII-861 0671. We thank Professor Toshiro Tango for allowing us to see a preprint of his 1990 paper. We also thank Dr. Goeffrey M. Jacquez for a critical reading of this paper and for his suggestions, which led to a much improved discussion section.",

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N2 - Tango [Biometrics 40:15 (1984)] proposed an index for detecting disease clustering in time applicable to grouped data obtained from a population that remains fairly stable over the study period. This index has received considerable attention in the literature including the suggestion that it be used to detect the space-time clustering of diseases and the suggestion to use similar test statistics to detect disease clustering in space and/or time while accounting for a changing population size over the study period. This paper concerns the related question of measuring the severity of the disease clustering once it has been determined that cases are not randomly distributed over space and/or time. A family of alternatives to randomness is proposed in which space and/or time versions of Tango's index are sufficient statistics for the parameters measuring the severity of the clustering. For the special case of temporal clustering, an unbiased estimator of the clustering parameter and its sampling variance is derived, and a particularly simple interpretation of this estimator is suggested. These latter results are based on some asymptotic approximations due to Tango [Biometrics 46:351 (1990)]. An application to the trisomy data given by Wallenstein [Am. J. Epidemiol. 111:367 (1980)] is discussed.

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Measuring the severity of disease clustering using Tango's index

Abstract

Bibliographical note

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ASJC Scopus subject areas

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