Analyzing the volume and nature ofemergency medical calls during severe               weather                             ...
Objective The objective of this research use regression methodologies  to predict the number and nature of emergency medi...
Hanover County Map
Call Volume by Day of Week
Dependent variables Call data    Multiple linear regression       Log response time (measured in minutes)       Servic...
Description of Data – Call dataNumerical data Wind speed (miles per hour) Temperature from normal (deviation from curren...
Description of Data – Call dataCategorical data (continued) Summer weekend (binary) Rain (binary) Snow: yes, no (refere...
Description of Data – Call volume dataNumerical data Defined the same as call data except all values taken as the average...
Zero-Inflated Poisson Regression Zero-inflated Poisson regression used to predict the overall  number of calls per six-ho...
Zero-Inflated Poisson Regression Considers two processes   first process is selected for observation i with probability ...
Zero-Inflated Poisson Regression Therefore, the distribution associated with the zero-inflated  Poisson regression random...
Multiple Linear Regression Used to estimate average log response time and average  service time    y   0  1 x1   2 ...
Logistic regression Used to estimate the likelihood of the nature of the calls The logistic function outputs the expecte...
Zero-inflated Poisson Regression Number of EMS CallsZero-inflation Variable   Estimate   Standard Error   T-value   p-valu...
Zero-inflated Poisson Regression    Number of Fire CallsZero-inflation Variable   Estimate   Standard Error   T-value   p-...
Linear RegressionLog Response Times                                        Log Response Time (log min)                    ...
Linear Regression  Service Times                                            Service Time (min)                            ...
Logistic RegressionPriority 1 calls                                               Standard               Variable         ...
Logistic RegressionNo arriving unit                                        Standard                Variable     Estimate  ...
Logistic Regression       Patient transported to hospital                                               Hospital variables...
Logistic Regression    Heart-related calls                                  Standard        Variable       Estimate    Err...
Logistic Regression  Seizure/stroke-related calls            Variable   Estimate   Standard Error   T-value   p-valueInter...
Results from 10 fold cross-validation for each model that         report Mean Square Predictive Error (MSPE) for numeric  ...
Parameter values for blizzard and hurricane evacuation scenarios                  Parameter                               ...
Dependent variable values for blizzard    and hurricane evacuation scenarios                                              ...
Conclusions Planning for extreme weather events is the first step toward  improving patient outcomes during these times ...
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Analyzing the Volume and Nature of Emergency Medical Calls during Severe Weather Events

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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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Analyzing the Volume and Nature of Emergency Medical Calls during Severe Weather Events

  1. 1. Analyzing the volume and nature ofemergency medical calls during severe weather Laura A. McLay, Ed L. Boone, and J. Paul Brooks Department of Statistics and Operations Research Virginia Commonwealth University lamclay@vcu.edu Paper to appear in Socio-Economic Planning SciencesThis 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 theviews of the National Science Foundation .
  2. 2. 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.
  3. 3. Hanover County Map
  4. 4. Call Volume by Day of Week
  5. 5. 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
  6. 6. 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)
  7. 7. 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)
  8. 8. 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 periodCategorical 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
  9. 9. 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
  10. 10. 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 g ( yi )  exp(  i ) iy / yi !, i  Poisson mean for observation i is given by i  exp  k  j 1  j xij   there are k independent variables with coefficients 1 ,  2 ,...,  k  xji = the value of independent variable k for observation i  and xi = (xji, xji,…,xji ) is the vector of independent variable values for observation i.
  11. 11. Zero-Inflated Poisson Regression Therefore, the distribution associated with the zero-inflated Poisson regression random variable for observation i is  i  (1  i ) exp( i ), yi  0  P(Yi  yi | xi , zi ) ~    (1  i ) exp(  i ) iyi / yi !, yi  0  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
  12. 12. Multiple Linear Regression Used to estimate average log response time and average service time y   0  1 x1   2 x2  ...   k xk   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.
  13. 13. 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, 1 f ( z)  1  e z Where z   0  1 x1   2 x2  ...   k xk
  14. 14. Zero-inflated Poisson Regression Number of EMS CallsZero-inflation Variable Estimate Standard Error T-value p-valueIntercept -6.568 0.959 -6.850 <0.001Time: 12am – 6am 3.2534 1.003 3.241 0.001Count model variableIntercept 1.823 0.023 78.972 <0.001Temperature from normal 0.007 0.002 3.162 0.002Windspeed 0.005 0.002 2.882 0.004Season: Spring -0.123 0.0288 -4.272 <0.001Season: Summer -0.279 0.037 -7.535 <0.001Day of Week: Weekend -0.172 0.027 -6.338 <0.001Summer Weekend: Yes 0.190 -0.045 4.231 <0.001Snow: Yes 0.522 0.0840 6.214 <0.001King’s Dominion: Yes 0.385 0.029 13.400 <0.001State Fair: Yes 0.140 0.066 2.133 0.033
  15. 15. Zero-inflated Poisson Regression Number of Fire CallsZero-inflation Variable Estimate Standard Error T-value p-valueIntercept -0.5021 0.148 -3.395 <0.001Time: 6am – 12pm -1.941 0.411 -4.725 <0.001Time: 12pm – 6pm -3.246 1.025 -3.166 0.002Time: 6pm – 12am -1.958 0.370 -5.299 <0.001Count model variableIntercept 0.550 0.064 8.631 <0.001Relative Humidity 0.107 0.018 5.828 <0.001Windspeed 0.026 0.003 7.689 <0.001Season: Summer -0.286 0.060 -4.776 <0.001Season: Winter -0.140 0.061 -2.289 0.022Thunderstorm: Yes 1.385 0.084 16.399 <0.001Snow: Yes 0.402 0.188 2.140 0.032Precipitation: Yes -0.171 0.062 -2.786 0.005Visibility: normal -0.230 0.054 -4.302 <0.001King’s Dominion: Yes 0.260 0.058 4.493 <0.001
  16. 16. Linear RegressionLog Response Times Log Response Time (log min) Standard Variable Estimate 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
  17. 17. Linear Regression Service Times Service Time (min) Standard Variable Estimate Error T-value p-valueIntercept 78.137 0.902 86.588 <0.001Priority 1 3.654 0.684 5.346 <0.001Time: 12pm – 6pm 1.804 0.830 2.173 0.030Time: 6pm – 12am 2.236 0.915 2.444 0.015District: Ashland 7.272 1.027 7.080 <0.001District: Rockville/Farrington 34.152 1.800 18.970 <0.001District: Mechanicsville -12.013 0.900 -13.34 <0.001District: Central Hanover 10.877 1.499 7.258 <0.001District: West Hanover 42.420 1.402 30.259 <0.001Snow: Yes 13.196 3.440 3.836 <0.001Windspeed -0.113 0.053 -2.119 0.034
  18. 18. Logistic RegressionPriority 1 calls Standard Variable Estimate 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
  19. 19. Logistic RegressionNo arriving unit Standard Variable Estimate 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
  20. 20. Logistic Regression Patient transported to hospital Hospital variables Standard Variable Estimate Error T-value p-valueIntercept 0.544 0.055 9.895 <0.001Priority 3 -0.221 0.049 -4.484 <0.001Time: 6am – 12pm -0.013 0.057 4.897 <0.001District: Ashland -0.257 0.0608 -4.225 <0.001District: Mechanicsville 0.227 0.053 4.298 <0.001District: Rockville/Farrington -0.647 0.097 -6.639 <0.001Temperature from Normal -0.014 0.005 -2.994 0.003Snow: Yes -0.891 0.181 -4.91 <0.001Snow: Post-Snow -0.602 0.226 -2.660 0.008Visibility: normal 0.177 0.050 3.533 <0.001Season: Winter 0.187 0.057 3.283 0.001
  21. 21. Logistic Regression Heart-related calls Standard Variable Estimate Error T-value p-valueIntercept -2.661 0.182 -14.610 <0.001Time: 6am – 12pm -0.573 0.200 -2.861 0.004Time: 12pm – 6pm -1.349 0.214 -6.300 <0.001Time: 6pm – 12am -0.617 0.207 -2.980 0.003Cloud Cover Fraction -0.555 0.138 -4.01 <0.001Day of Week: Weekend -1.033 0.162 -6.393 <0.001Summer Weekend: Yes 1.576 0.171 9.236 <0.001King’s Dominion: Yes 1.708 0.131 13.036 <0.001Visibility: normal -0.494 0.121 -4.071 <0.001
  22. 22. Logistic Regression Seizure/stroke-related calls Variable Estimate Standard Error T-value p-valueIntercept -3.376 0.192 -17.599 <0.001Time: 6am – 12pm -0.957 0.244 -3.920 <0.001Time: 12pm – 6pm -1.341 0.248 -5.410 <0.001Time: 6pm – 12am -1.130 0.251 -4.500 <0.001District: Ashland -0.664 0.195 -3.403 <0.001Cloud Cover Fraction -0.562 0.161 -3.490 <0.001King’s Dominion: Yes 2.334 0.165 14.163 <0.001
  23. 23. 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 PCCRResponse time model 1.52 Priority 1 model 0.5449Service time model 26.66 Arriving unit model 0.9248EMS call volume model (zero-inflated Poisson model) 3.41 Hospital model 0.6712EMS call volume model (corresponding Poisson model) 3.44 Heart-related model 0.6148Fire call volume model (zero-inflated Poisson model) 2.01 Seizure/stroke-related model 0.5319Fire call volume model (corresponding Poisson model) 2.02
  24. 24. Parameter values for blizzard and hurricane evacuation scenarios Parameter Base Case Blizzard Hurricane EvacIndependent Wind speed, measured in miles per hour. 0 10 30variable 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
  25. 25. Dependent variable values for blizzard and hurricane evacuation scenarios HurricaneModel Base Case Blizzard evacuationEMS call count (count per six hours) 5.20 8.21 12.30Fire call count (count per six hours) 1.16 2.51 3.59Response time (min) 5.47 7.57 5.47Service Time (min) 83.6 95.7 80.2Priority 1 (probability) 0.404 0.255 0.404No unit arriving (probability) 0.033 0.092 0.033Hospital transport (probability) 0.614 0.397 0.571Heart-related patient (probability) 0.003 0.004 0.09Seizure/stroke-related patient (probability) 0.007 0.005 0.05Offered Load (EMS) 5.12 6.78 11.24Offered Load (Fire) 0.48 1.12 1.48Offered Load (Total) 5.60 7.90 12.72The total offered load increases by 41% and 127% for the blizzard andhurricane evacuation scenarios, respectively.
  26. 26. 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

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