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PLoS One. 2016 Jul 15;11(7):e0159312. doi: 10.1371/journal.pone.0159312. eCollection 2016.

# Applications of Extreme Value Theory in Public Health.

### Author information

1
Department of Mathematical Statistics, Chalmers University of Technology-Göteborg, Sweden.
2
Sorbonne Universités, UPMC Univ Paris 06, INSERM, Institut Pierre Louis d'Epidémiologie et de Santé Publique, UMR_S 1136, F-75012, Paris, France.
3
Fogarty International Center, NIH, Washington, DC, United States of America.
4
Department of Epidemiology, School of Public Health, University of Michigan, Ann Arbor, Michigan, United States of America.
5
Service des Urgences, Hôpital Saint-Antoine, Assistance Publique-Hôpitaux de Paris, Paris, France.
6
Geostatistics group, Centre de Géosciences, MINES ParisTech, PSL Research University, Fontainebleau, France.
7
Public Health Unit, Saint-Antoine hospital, AP-HP, F-75012, Paris, France.

### Abstract

#### OBJECTIVES:

We present how Extreme Value Theory (EVT) can be used in public health to predict future extreme events.

#### METHODS:

We applied EVT to weekly rates of Pneumonia and Influenza (P&I) deaths over 1979-2011. We further explored the daily number of emergency department visits in a network of 37 hospitals over 2004-2014. Maxima of grouped consecutive observations were fitted to a generalized extreme value distribution. The distribution was used to estimate the probability of extreme values in specified time periods.

#### RESULTS:

An annual P&I death rate of 12 per 100,000 (the highest maximum observed) should be exceeded once over the next 30 years and each year, there should be a 3% risk that the P&I death rate will exceed this value. Over the past 10 years, the observed maximum increase in the daily number of visits from the same weekday between two consecutive weeks was 1133. We estimated at 0.37% the probability of exceeding a daily increase of 1000 on each month.

#### CONCLUSION:

The EVT method can be applied to various topics in epidemiology thus contributing to public health planning for extreme events.

PMID:
27419853
PMCID:
PMC4946775
DOI:
10.1371/journal.pone.0159312
[Indexed for MEDLINE]
Free PMC Article