Applications of Extreme Value Theory in Public Health

Abstract

ObjectivesWe present how Extreme Value Theory (EVT) can be used in public health to predict future extreme events.MethodsWe 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.ResultsAn 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.ConclusionThe EVT method can be applied to various topics in epidemiology thus contributing to public health planning for extreme events.

Extreme value theory of evolving phenomena in complex dynamical systems: Firing cascades in a model of a neural network

“…the review book [1] and references therein), has so far mainly considered low dimensional systems in a very simple setting that we will describe momentarily. To the contrary, its statistical ancestor, the socalled extreme value theory (EVT) [2], has been fruitfully applied to phenomena like earthquakes, floods, epidemics [3,4], that all involve complex, many dimensional interactions that operate for a certain period of time and are otherwise silent. It is the purpose of this paper to develop a theoretical framework to extend the dynamical treatment of extreme events to this kind of systems.…”

Operating at the extreme: estimating the upper yield boundary of winter wheat production in commercial practice

“…Other applications include engineering [18,19] and toxicology [20]. More recently, extreme value analysis has been used in epidemiology to estimate the probability of severe pneumonia and influenza epidemics [21], and in the field of demography with a discussion of whether there is a finite upper bound on human lifespan [22]. Applications of extreme value analysis in the agricultural sciences have so far concentrated on financial aspects, for instance commodity price fluctuations [23,24], rather than agronomic factors such as yield.…”

How climate affects extreme events and hence ecological population models

“…Ecological examples include hurricanes (Jagger and Elsner ), wildfires (Moritz ), and disease spread (Thomas et al. ). Many times in ecology, extreme events are modeled as random “catastrophes” (e.g., Lande ); these models only include event frequency.…”

“…Extreme events are rare large deviations from average conditions (Coles 2001) that often have significant impacts. Ecological examples include hurricanes (Jagger and Elsner 2006), wildfires (Moritz 1997), and disease spread (Thomas et al 2016). Many times in ecology, extreme events are modeled as random "catastrophes" (e.g., Lande 1993); these models only include event frequency.…”