MetSim: A Simulation Decision Support Tool using Meteorological

Information for Short-Term Planning of Hospital Services

Paul Harper

, John Minty

, Sujit Sahu

, Bernard Baffour

and Christophe Sarran

School of Mathematics, Cardiff University, Cardiff, U.K.

School of Mathematics, University of Southampton, Southampton, U.K.

Met Office, Exeter, U.K.

Keywords: Forecasting Demand, Hospital Capacity Management, Weather, Simulation.

Abstract: Improved short-term predictions of hospital admissions and bed occupancy offer the potential to plan

resource needs more accurately and effectively. The MetSim project explores the relationship between

weather and health, building novel Bayesian models that are more sensitive to fluctuations in weather.

Short-term forecasts of the numbers of admissions, categorised by age, gender and medical condition, are

produced. In turn, coupled with predictions on length of stay and information on current occupancy,

MetSim uses hazard ratios embedded within a simulation framework to provide forecasts of short-term bed

needs. MetSim is a collaboration between Cardiff University, the University of Southampton, and the Met

Office. Cardiff and Vale University Health Board and Southampton University Hospitals NHS Trust have

guided the development of MetSim, provided data and piloted the tool.

1 INTRODUCTION

More than 2,000 years ago, Hippocrates first

recognised that epidemics were related to seasonal

changes in weather. However, it was only during

the 1970s that research into connecting weather and

health was taken seriously and, for the first time,

meteorological variables were investigated to gain

insight into the causes of increased mortality in

winter and smaller increases in unusually hot

weather (Keatinge 2002). Since then, the interest in

the effects of weather on health has grown

substantially, helped to some extent by raised

awareness of global warming and concern about the

public health impact of climate change. Knowledge

on the influence of weather on health is valuable,

and has the ability to contribute greatly to our

understanding of epidemiology, the occurrence of

accidents and injuries, and of public health issues.

Examples of weather-health research from the

literature include those relating to: extreme weather

events (WMO, 2003); sunshine, such as skin cancer

(Cancer Research UK, 2012) and Seasonal Affective

Disorder (Garland, 2003); temperature, such as cold

weather and mortality (Hajat et al., 2002);

Thunderstorms, such as lightning strikes (Elsom,

2001) and leading to increased asthma attacks

(Venables 1997, Dales et al. 2003, New Scientist,

February 2006); and snow/ice leading to fractures

(Smith and Nelson, 1998).

The ability to predict weather offers the potential

to provide valuable information that can be used in

planning health services. For example, imagine a

short-term hospital planning tool that was able to

predict fluctuations in demand and bed occupancy

for different specialities by including meteorological

predictions alongside other known information such

as day of the week. The relationship between

weather and health is immediately evident in some

specialities, for example respiratory medicine.

Figure 1 shows respiratory admissions data from

Southampton General Hospital. The top graph

shows temperature over a five year period. The

remaining graphs show admissions and discharges in

black and occupancy in red. We observe that low

temperatures lead to an increased number of

admissions. Similar plots have been produced with

data from other UK hospitals.

The MetSim project is a multidisciplinary

collaboration involving academics (from OR and

Statistics), meteorologists from the Met Office, and

managers and consultants from hospitals.

It is beneficial for managers of hospitals to have

short-term forecasts of demand and occupancy. Of

543

Harper P., Minty J., Sahu S., Baffour B. and Sarran C..

MetSim: A Simulation Decision Support Tool using Meteorological Information for Short-Term Planning of Hospital Services.

DOI: 10.5220/0004161805430547

In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (HA-2012), pages

543-547

ISBN: 978-989-8565-20-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Respiratory patient flows at Southampton

General Hospital.

particular interest is the number of non-elective

(emergency) patients. Our particular focus is on

patients who are admitted into hospital, as opposed

to attending Accident and Emergency. The

objectives of the MetSim project are:

• To describe hospital occupancy in two parts:

rate of admissions and length of stay.

• To explore relationship between weather

patterns and hospital admissions.

• To describe different lengths of stay for

different classes of patient.

• To build a web-based tool which provides

hospitals with short-term (7-day) predictions on

demand and corresponding bed occupancy.

Figure 2 presents a high-level schematic of the

component parts of the MetSim tool and

corresponding responsibilities. These components

are discussed in subsequent sections of this paper.

Figure 2: MetSim schematic.

2 DATA

Anonymized patient admission and discharge data

from participating hospitals have been linked to

meteorological data provided by the Met Office. We

summarise the data types below.

2.1 Historic Hospital Data

For every admission/discharge of a patient over the

course of a year the hospital records the age at

admission, gender, broad class of treatment

(medicine, surgery, trauma, paediatric or other), date

of admission, and date of discharge. Hour of

admission and discharge is optional. Ideally, the

year of observation should be from 14 months ago to

2 months ago.

2.2 Current Hospital Data

For some day during the last week, the hospital

gives a census of all prevalent patients. The items

recorded are as for historic data except that there is,

perforce, no date of discharge.

2.3 Meteorological Data

Over the entire time period, historic, current and

forecast, the Met Office records the mean

temperature on a given day and the minimum one

week ago.

2.4 Temporal Data

Other variables needed are school holidays, public

holidays, and day of the week. The historic hospital

dataset is used to select models and estimate

parameters. The current and forecast temperatures

are then used to forecast admissions. The current

hospital data are used only to simulate occupancy.

2.5 Historiography

We initially analysed datasets much larger than the

ones in the final version of the model. The

hospitals’ historic datasets included the method of

admission, full episodic progression of patient-spells

and destination on discharge. The meteorological

datasets included humidity, pressure, vapour

pressure, rainfall and wind speed.

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3 FORECASTING ADMISSIONS

As anticipated, age is a significant explanatory

variable; we partitioned patients into 0-17 as

paediatric, 18-74 as adult and 75+ as elderly (on

guidance from the hospitals). We used gender, as

much for logistic (planning for single sex wards) as

statistical reasons. Temperature is a significant

explanatory variable as is current day of the week.

Figure 3 illustrates that admissions are higher during

weekdays than at weekends.

Figure 3: Boxplots of admissions by day.

3.1 Transformation

The data reveal that the number of daily admissions

is naturally positively skewed. To overcome this in

modelling, it is sufficient to take a square-root

transformation. Having fitted a large number of

models to the historic hospital dataset we reached

the following conclusions:

• A model which includes age, sex, day of the

week, whether the day is a school holiday, mean

daily temperature and minimum temperature a

week ago is the best main effects model

according to both the R

and AIC. Such a model

is very parsimonious.

• This is improved by adding two-factor

interaction terms, namely age-gender and

interaction between age and minimum

temperature a week ago. In fact, it explains

over 80% of the variation in daily admissions.

This is the model which will be adopted

henceforth.

• Age alone explains a remarkable 74% of the

variation in the number of admissions.

3.2 Weather Forecasting: Uncertainty

The model is found from historic data with observed

weather temperatures. When predicting future

admissions, we rely on weather forecasts.

Accordingly, we regard actual future temperature as

some linear function of forecast temperature, putting

Bayesian uncertainty on the coefficients of the linear

relation

4 LENGTH OF STAY

The length of stay is a problem in survival analysis,

where “survival” is not leaving the hospital, whether

by discharge, transfer or death. We regard the

length of stay as a non-negative discrete number of

days n≥0. Let h(n) denote the hazard rate and let

Gamma denote the log-odds of the hazard rate.

Figure 4: Log-odds of hazard rates for Southampton.

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Figure 4 shows how Gamma evolves and depends

also on age and current day of the week.

To model the log-odds of the hazard rates, we

include the explanatory variables age, gender, day of

week together with a broad grouping of the patients’

specialities: medicine, surgery, trauma or other.

Even in the least favourable cases about 70% of the

variation is explained; it is often much higher.

5 SIMULATION STRUCTURE

We are now in a position to describe the flow of

patients. It is too difficult to model analytically, so we

simulate. We use a discrete timeline in days. We first

use the historic weather data together with the historic

hospital data to model admissions. From such a model,

we use current and forecast weather data to simulate

streams of admissions over the next few days (Figure

5). Next we model length of stay. We also simulate

the specialities of newly admitted patients (Figure 6).

Finally, we use data on current patients together with

streams of hypothetical admissions to simulate streams

of discharges (Figure 7).

Figure 5: Simulation of admissions.

Figure 6: Simulation of length of stay.

We thus obtain forecasts for admissions,

discharges, occupancy and change in occupancy.

For example, Figure 8 shows a forecast of

admissions for the next week, with 80% and 95%

confidence intervals.

The projected is currently being piloted. Cardiff

and Southampton hospitals are submitting datasets

to the Met Office where our code is implemented.

The Met Office returns the forecasts to the hospitals.

Figure 7: Simulation of patient flow.

Figure 8: Illustrative MetSim output: Forecasted

admissions (non-paediatric).

6 DISCUSSION

This paper outlines the underpinning methodology

of the MetSim tool, designed to support hospital

managers in predicting short-term demand and bed

occupancy. Initially a Bayesian statistical model

(full details are not included in this proceedings

paper in the interests of space and rather the focus

on the simulation components) is used to forecast

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demand for different categories/conditions of

admissions. This tool is currently being piloted at

two hospitals: Cardiff and Southampton, and results

at the time of writing this paper are promising. For

example, over a period April 25

2011 to January

2012, the Root Mean Square Error (RMSE) of

7-day ahead forecasts was just 4.8.

Demand forecasts are then fed into a simulation

framework to produce corresponding bed occupancy

predictions over the planning horizon. To do this,

we simulate length of stay for the predicted

admissions using hazard rates (such that the time a

patient spends in hospital is modelled using

‘survival’ analysis techniques).

The simulation is coded in C++ and sits on the

server at the Met Office, Exeter, UK. A number of

routines are run (as shown diagrammatically for

simplicity in Figures 5-7) typically for 1000’s of

iterations (and thanks to the power of the

supercomputer at the Met Office, are executed

within seconds), thus participating hospitals are

provided on a daily basis with forecasts and

associated confidence intervals.

Over the next few months we will streamline the

system to have a web interface for ease of use.

Further piloting is also taking place with more

hospitals across the UK.

ACKNOWLEDGEMENTS

This work is supported by the UK Engineering and

Physical Sciences Research Council (EPSRC), grant

EP/H010637/1.

The authors thank Patrick Sachon from the UK

Met Office; Ben Hendy and Alison Gray from

Southampton University Hospital Trust; Steve Tarr,

Andrew Nelson and John Peters from the Cardiff

and Vale University Health Board. These persons

provided the data used here and shared their many

helpful insights.

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