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An effective emergency medical service (EMS) response to emergency medical calls during extreme weather events is a critical public service. Nearly all models for allocating EMS resources focus on normal operating conditions. However, public health risks become even more critical during extreme weather events, and hence, EMS systems must consider additional needs that arise during weather events to effectively respond to and treat patients. This paper seeks to characterize how the volume and nature of EMS calls are affected during extreme weather events with a particular focus on emergency preparedness. In contrast to other studies on disaster relief, where the focus is on delivery of temporary commodities, we focus on the delivery of routine emergency services during blizzards and hurricane evacuations. The dependence of emergency service quality on weather conditions is explored through a case study using real-world data from Hanover County, Virginia. The results suggest that whether it is snowing is significant in nearly all of the regression models. Variables associated with increased highway congestion, which become important during hurricane evacuations, are positively correlated with an increased call volume and the likelihood of high-risk calls. The analysis can aid public safety leaders in preparing for extreme weather events.
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Laura A. McLay, Ed L. Boone, and J. Paul BrooksDepartment of Statistics and Operations Research
Virginia Commonwealth [email protected]
Paper to appear in Socio-Economic Planning Sciences
Analyzing the volume and nature of emergency medical calls during severe
weather
This material is based upon work supported by the National Science Foundation under Award No. CMMI -1054148. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation .
Objective The objective of this research use regression methodologies
to predict the number and nature of emergency medical 911 calls.
This objective is related to an overall goal of optimally allocating scarce EMS resources using optimization methodologies.
Allocating scarce EMS resources during extreme events (such as during hurricanes and blizzards) is important for system performance and patient outcomes.
Hanover County Map
Call Volume by Day of Week
Dependent variables Call data Multiple linear regression
Log response time (measured in minutes) Service time (measured in minutes)
Logistic regression Priority 1 call (binary) No arriving unit (binary) Hospital call (binary) Heart-related call (binary) Seizure/stroke related call (binary)
Call volume data Zero inflated Poisson regression
Number of EMS calls (per six hour unit of time) Number of Fire calls (per six hour unit of time)
EMS/Fire call data was provided for time period June 1, 2009 – May 31, 2010 9218 EMS calls and 2352 Fire calls
Description of Data – Call dataNumerical data Wind speed (miles per hour) Temperature from normal (deviation from current temperature and monthly average, in
Celsius) Precipitation rate (inches per hour) Cloud cover fraction (approximate proportion of the sky that is covered by clouds) Relative humidity (proportion)
Categorical data Priority 1, 2, 3 (Priority 2 is the reference value) Time interval: 12am-6am (reference value), 6am-12pm, 12pm-6pm, 6pm-12am Day of week: Weekday (M-F, reference value) or Weekend(Sa-Su) Season: Fall (reference value), Winter, Spring, Summer District: Ashcake (reference value), Ashland, Rockville/Farrington, Mechanicsville, East
Hanover, West Hanover, North Hanover Holiday (binary)
Description of Data – Call dataCategorical data (continued) Summer weekend (binary) Rain (binary) Snow: yes, no (reference value), within 24 of a snow storm Thunderstorm (binary) Visibility: Normal or low (reference value) High school dances (binary) King’s Dominion open (binary) State fair (binary)
Description of Data – Call volume dataNumerical data Defined the same as call data except all values taken as the average over the six hour time
period Wind speed and precipitation rate consider maximum over the six hour time period
Categorical data Defined the same as call data
Model variables were selected for all regression models based on p-values less than α = 0.05 level
Zero-Inflated Poisson Regression Zero-inflated Poisson regression used to predict the overall
number of calls per six-hour intervals Why zero-inflated Poisson? Usually Poisson regression is used to model count data Poisson assumes mean and variance are equal
Zero-inflated Poisson used as an alternative to Poisson regression when there are excess zeros in the data set
Zero-Inflated Poisson Regression Considers two processes first process is selected for observation i with probability i, second process is selected with probability 1 – i.
Let the second process follow a Poisson random variable with distribution Poisson mean for observation i is given by there are k independent variables with coefficients xj
i = the value of independent variable k for observation i and xi = (xj
i, xji,…,xj
i ) is the vector of independent variable values for observation i.
( ) exp( ) / !,iyi i i ig y y
1exp k i
i j jjx
1 2, ,..., k
Zero-Inflated Poisson Regression Therefore, the distribution associated with the zero-inflated
Poisson regression random variable for observation i is
Yi is the random variable associated with the number of calls zi is the vector of zero-inflated covariates
Model adequacy tested by Log-likelihood ratio test for testing whether or not the zero-
inflation component is needed Comparing the fitted model to the corresponding standard
Poisson regression model using the Vuong Non-Nested Hypothesis Test
* Both types of tests yield significant p-values for both models
(1 )exp( ), 0( | , ) ~
(1 ) exp( ) / !, 0i
i i i ii i i i y
i i i i i
yP Y y x z
y y
Multiple Linear Regression
Used to estimate average log response time and average service time
Let y denote the dependent variable independent variables x1, x2,…,xk. The error is assumed to be normally distributed with mean
0 and variance 2.
0 1 1 2 2 ... k ky x x x
Logistic regression Used to estimate the likelihood of the nature of the calls The logistic function outputs the expected probability of a
dichotomous event occurring given its input z,
Where
1( )1 zf z
e
0 1 1 2 2 ... k kz x x x
Zero-inflated Poisson RegressionNumber of EMS Calls
Zero-inflation Variable Estimate Standard Error T-value p-value
Intercept -6.568 0.959 -6.850 <0.001
Time: 12am – 6am 3.2534 1.003 3.241 0.001
Count model variable
Intercept 1.823 0.023 78.972 <0.001
Temperature from normal 0.007 0.002 3.162 0.002
Windspeed 0.005 0.002 2.882 0.004
Season: Spring -0.123 0.0288 -4.272 <0.001
Season: Summer -0.279 0.037 -7.535 <0.001
Day of Week: Weekend -0.172 0.027 -6.338 <0.001
Summer Weekend: Yes 0.190 -0.045 4.231 <0.001
Snow: Yes 0.522 0.0840 6.214 <0.001
King’s Dominion: Yes 0.385 0.029 13.400 <0.001
State Fair: Yes 0.140 0.066 2.133 0.033
Zero-inflated Poisson RegressionNumber of Fire Calls
Zero-inflation Variable Estimate Standard Error T-value p-value
Intercept -0.5021 0.148 -3.395 <0.001
Time: 6am – 12pm -1.941 0.411 -4.725 <0.001
Time: 12pm – 6pm -3.246 1.025 -3.166 0.002
Time: 6pm – 12am -1.958 0.370 -5.299 <0.001
Count model variable
Intercept 0.550 0.064 8.631 <0.001
Relative Humidity 0.107 0.018 5.828 <0.001
Windspeed 0.026 0.003 7.689 <0.001
Season: Summer -0.286 0.060 -4.776 <0.001
Season: Winter -0.140 0.061 -2.289 0.022
Thunderstorm: Yes 1.385 0.084 16.399 <0.001
Snow: Yes 0.402 0.188 2.140 0.032
Precipitation: Yes -0.171 0.062 -2.786 0.005
Visibility: normal -0.230 0.054 -4.302 <0.001
King’s Dominion: Yes 0.260 0.058 4.493 <0.001
Linear RegressionLog Response Times
Log Response Time (log min)
Variable Estimate
Standard
Error T-value p-value
Intercept 2.051 0.0174 118.2 <0.001
Priority 1 -0.128 0.0124 -10.34 <0.001
Priority 3 0.263 0.0137 19.24 <0.001
Time: 6am – 12pm -0.220 0.0172 -12.76 <0.001
Time: 12pm – 6pm -0.224 0.0168 -13.39 <0.001
Time: 6pm – 12am -0.250 0.0175 -14.24 <0.001
District: Ashland -0.0641 0.0132 -4.857 <0.001
District: Rockville/Farrington 0.408 0.0232 17.56 <0.001
District: Central Hanover 0.335 0.0209 16.04 <0.001
District: West Hanover 0.198 0.0211 9.410 <0.001
Snow: Yes 0.326 0.0447 7.29 <0.001
Snow: Post-snow 0.237 0.0516 4.59 <0.001
Linear RegressionService Times
Service Time (min)
Variable Estimate
Standard
Error T-value p-value
Intercept 78.137 0.902 86.588 <0.001
Priority 1 3.654 0.684 5.346 <0.001
Time: 12pm – 6pm 1.804 0.830 2.173 0.030
Time: 6pm – 12am 2.236 0.915 2.444 0.015
District: Ashland 7.272 1.027 7.080 <0.001
District: Rockville/Farrington 34.152 1.800 18.970 <0.001
District: Mechanicsville -12.013 0.900 -13.34 <0.001
District: Central Hanover 10.877 1.499 7.258 <0.001
District: West Hanover 42.420 1.402 30.259 <0.001
Snow: Yes 13.196 3.440 3.836 <0.001
Windspeed -0.113 0.053 -2.119 0.034
Logistic RegressionPriority 1 calls
Variable Estimate
Standard
Error T-value p-value
Intercept -0.387 0.0296 -13.10 <0.001
District: Mechanicsville 0.286 0.0462 6.194 <0.001
District: Rockville/Farrington 0.299 0.0950 3.145 0.002
District: West Hanover 0.175 0.080 2.204 0.028
Snow: Yes -0.684 0.197 -3.474 <0.001
Logistic RegressionNo arriving unit
Variable Estimate
Standard
Error T-value p-value
Intercept -2.389 0.762 -31.32 <0.001
Priority 1 -0.999 0.118 -8.474 <0.001
Priority 3 -0.415 0.114 -3.636 <0.001
District: Ashland -0.361 0.132 -2.747 0.006
Temperature from Normal 0.031 0.008 3.730 <0.001
Snow: Yes 1.104 0.274 4.036 <0.001
Logistic RegressionPatient transported to hospital
Hospital variables
Variable Estimate
Standard
Error T-value p-value
Intercept 0.544 0.055 9.895 <0.001
Priority 3 -0.221 0.049 -4.484 <0.001
Time: 6am – 12pm -0.013 0.057 4.897 <0.001
District: Ashland -0.257 0.0608 -4.225 <0.001
District: Mechanicsville 0.227 0.053 4.298 <0.001
District: Rockville/Farrington -0.647 0.097 -6.639 <0.001
Temperature from Normal -0.014 0.005 -2.994 0.003
Snow: Yes -0.891 0.181 -4.91 <0.001
Snow: Post-Snow -0.602 0.226 -2.660 0.008
Visibility: normal 0.177 0.050 3.533 <0.001
Season: Winter 0.187 0.057 3.283 0.001
Logistic RegressionHeart-related calls
Variable Estimate
Standard
Error T-value p-value
Intercept -2.661 0.182 -14.610 <0.001
Time: 6am – 12pm -0.573 0.200 -2.861 0.004
Time: 12pm – 6pm -1.349 0.214 -6.300 <0.001
Time: 6pm – 12am -0.617 0.207 -2.980 0.003
Cloud Cover Fraction -0.555 0.138 -4.01 <0.001
Day of Week: Weekend -1.033 0.162 -6.393 <0.001
Summer Weekend: Yes 1.576 0.171 9.236 <0.001
King’s Dominion: Yes 1.708 0.131 13.036 <0.001
Visibility: normal -0.494 0.121 -4.071 <0.001
Logistic RegressionSeizure/stroke-related calls
Variable Estimate Standard Error T-value p-value
Intercept -3.376 0.192 -17.599 <0.001
Time: 6am – 12pm -0.957 0.244 -3.920 <0.001
Time: 12pm – 6pm -1.341 0.248 -5.410 <0.001
Time: 6pm – 12am -1.130 0.251 -4.500 <0.001
District: Ashland -0.664 0.195 -3.403 <0.001
Cloud Cover Fraction -0.562 0.161 -3.490 <0.001
King’s Dominion: Yes 2.334 0.165 14.163 <0.001
Results from 10 fold cross-validation for each model that report Mean Square Predictive Error (MSPE) for numeric variables and Predicted Correct Classification Rate (PCCR) for dichotomous variables.
Model RMSPE Model PCCR
Response time model 1.52 Priority 1 model 0.5449
Service time model 26.66 Arriving unit model 0.9248
EMS call volume model (zero-inflated
Poisson model) 3.41 Hospital model 0.6712
EMS call volume model (corresponding
Poisson model) 3.44 Heart-related model 0.6148
Fire call volume model (zero-inflated
Poisson model) 2.01 Seizure/stroke-related model 0.5319
Fire call volume model (corresponding
Poisson model) 2.02
Parameter values for blizzard and hurricane evacuation scenarios
Parameter Base Case Blizzard Hurricane Evac
Independent Wind speed, measured in miles per hour. 0 10 30
variable values Temperature from normal (Celsius) 0 0 0
Precipitation rate (inches per hour) 0 0.75 1
Cloud cover fraction 0.5 1.0 1.0
Priority 1 1 1
Relative humidity 0.7 0.9 1
Time interval 12am – 6pm 12am – 6pm 12am – 6pm
Day of week Weekend Weekend Weekend
Season Fall Winter Fall
District Ashcake Ashcake Ashcake
Holiday No No Yes
Summer weekend. No No Yes
Rain No No Yes
Snow No Yes No
Thunderstorm No No No
Visibility Low Low
King’s Dominion No No Yes
State Fair No No Yes
Dependent variable values for blizzard and hurricane evacuation scenarios
Model Base Case Blizzard
Hurricane
evacuation
EMS call count (count per six hours) 5.20 8.21 12.30
Fire call count (count per six hours) 1.16 2.51 3.59
Response time (min) 5.47 7.57 5.47
Service Time (min) 83.6 95.7 80.2
Priority 1 (probability) 0.404 0.255 0.404
No unit arriving (probability) 0.033 0.092 0.033
Hospital transport (probability) 0.614 0.397 0.571
Heart-related patient (probability) 0.003 0.004 0.09
Seizure/stroke-related patient (probability) 0.007 0.005 0.05
Offered Load (EMS) 5.12 6.78 11.24
Offered Load (Fire) 0.48 1.12 1.48
Offered Load (Total) 5.60 7.90 12.72
The total offered load increases by 41% and 127% for the blizzard and hurricane evacuation scenarios, respectively.
Conclusions Planning for extreme weather events is the first step toward
improving patient outcomes during these times We are continuing to improve the models Introducing new information sources Remove obvious sources of colinearity Variables may not be significant due to having too few observations
Models can be used to assess the impact of weather variables on EMS operations in other settings Not clear if the model results can generalize
Can we predict the volume and nature of EMS calls? Can we include the impact of weather forecasts? Regression may not be the right tool for extreme weather events, but
preliminary findings suggest that regression outperforms machine learning models in their predictive ability
We are building reliability models with this research to assess staffing levels
