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Methods Inf Med 1991; 30(03): 206-209
DOI: 10.1055/s-0038-1634838
Data Analysis
Schattauer GmbH

Poisson Approximation to a Negative Binomial Process in the Surveillance of Rare Health Events

G. Gallus
1   Institute of Biometry and Medical Statistics, University of Milan, Milan, Italy
,
G. Radaelli
1   Institute of Biometry and Medical Statistics, University of Milan, Milan, Italy
,
M. Marchi
2   Institute of Clinical Physiology of C.N.R., Pisa, Italy
› Author Affiliations
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Publication History

Publication Date:
08 February 2018 (online)

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Abstract

The Poisson approximation to a negative binomial process is evaluated regarding the surveillance of rare health events in the framework of the “Sets” scheme. This scheme defines an alarm in terms of “distance” between consecutive events of interest. The system’s parameters are determined by minimizing the expected delay for an alarm when a given increase in the event rate has occurred, subject to a restriction on the rate of false alarms. It is shown that the main consequence of the Poisson approximation lies in an increase of the false alarm probability with respect to the assigned one, whilst influence on the expected delay for a true alarm is lower. It is, however, found that over a large range of practical instances, the Poisson assumption provides a reasonable description of the negative binomial process.

Key-Words

Bernoulli Trial - Negative Binomial Process - Poisson Process - Sets Scheme - Health Surveillance
 

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