EMS Performance Targets and Travel Times EMS Planning
- Slides: 35
EMS Performance Targets and Travel Times EMS Planning Conference, August 2008 Armann Ingolfsson armann. ingolfsson@ualberta. ca Academic Director Centre for Excellence in Operations School of Business, University of Alberta Based on joint work with S. Budge, E. Erdogan, E. Erkut, and D. Zerom and using data from Calgary EMS and Edmonton EMS
Typical EMS Performance Targets: Coverage • US EMS Act, 1973: 95% in 10 min. • North America, current: 90% of urgent urban calls in 8: 59 min. • UK: – 75% of all calls in 8 min. – 95% of urban calls in 14 min. – 95% of rural calls in 19 min. • Germany: – 95% in X min. – X varies across the country from 10 to 15 min. • Questions: – What are targets based on? – How can we predict compliance to these targets, using a map? – Are there better targets?
What are Coverage Targets Based on? • Cardiac Arrest Survival Studies • Focus on limiting the longest possible response time – As opposed to average response time • Consistency: it’s what other operators do – Although the details vary widely • Simple to interpret and compute
Using a Map to Predict Performance • • • Let’s do this for a location Pick a location in the city in Twin Brooks, Edmonton Find closest station Predict performance for that location Repeat for all locations in the city Colour-code the map Compute weighted average performance for the whole city – Weights = call volumes • (What we’re leaving out: ambulance availability)
Closest Station: Terwillegar Closest station Call location
How Far is it? Take 1 Closest station 4. 5 km As the crow flies “Euclidean distance” Call location
How Far is it? Take 2 Closest station 5. 8 km North-south and east-west travel only “Manhattan metric” “Rectilinear distance” Call location
How Far is it? Take 3 8. 6 km Using Google Maps “Network distance”
OK, so I Measured the Distance What’s Next? Distance Response Time Different ways to measure Transform What we’ll do next Station locations When to start and stop the clock Variability Traffic conditions Zone sizes Driver behaviour Construction Transform Ambulance availability Pre-travel and post-travel … “Outcome” Paramedic training Less or more than 8: 59? Patient’s condition Medical outcome? … Psychological outcome?
Distance Travel Time • 8. 6 km ? min. • Google Maps says 14 min. • Better: use historical call data to compute average speed • Even better (? ) compute different average speeds for: – – – Downtown vs. elsewhere Different road types Urgent vs. non-urgent Rush hour vs. other times Winter vs. summer And so on … Complicated! Is there a simpler approach that is useful?
A Simpler Approach A long trip: Speed cruising speed acceleration deceleration Time
A Simpler Approach A short trip: Speed Time
The Simpler Approach vs. Reality Long trip Short trip Good enough to estimate average travel time, but lots of variability around the average
(Average) Travel Time Curve Short trips Long trips Estimates from Edmonton and Calgary data: • Cruising speed: 100 kph. • Acceleration: 5 min. (4. 2 km) to reach cruising speed
Travel time Formula • Short trips (< 4. 2 km): Travel time in min. = 2. 45 × SQRT(distance in km) • Long trips (> 4. 2 km): Travel time in min. = 2. 5 + 0. 6 × (distance in km) • Twin Brooks: 2. 5 + 0. 6 × (8. 6 km) = 7: 42 min. • 8: 59 min. 10. 8 km • Twin Brooks is covered!
Is Twin Brooks Really Covered? Terwillegar station Twin Brooks Covered! Not covered 7: 42 8: 59 But travel times are not always the same: • Traffic • Driver behaviour • Construction Twin Brooks may be covered on average, but it would be useful to know the probability of coverage Terwillegar station Twin Brooks 7: 42 8: 59
Probability of Coverage Curve Implications for deployment: 3 km is twice as good as 11 km vs. < 11 km good, > 11 km bad
Probability of Coverage Map Created using probability of coverage curve, for all locations in a city Prob. of Coverage 0% 20% 40% 60% 80% 100%
The Formulas • Travel time = (m(distance) + f(time of day)) × exp(s(distance) e) • m(distance) avg. travel time curve • s(distance) next slide • f(time of day) the slide after that • e ~ t distribution with 3. 3 d. f.
Coefficient of Variation: s(distance)
Time-of-day Effect ~ 4 AM ? ? ~ 5 PM Afternoon rush hour
How About Medical Outcomes instead of % in 8: 59? Distance Response Time Different ways to measure Transform Station locations When to start and stop the clock Variability Traffic conditions Zones sizes Driver behaviour Construction Transform Ambulance availability Pre-travel and post-travel … “Outcome” Paramedic training Less or more than 8: 59? Patient’s condition Medical outcome? … Psychological outcome?
Out-of-hospital Cardiac Arrest Survival Rates Adapted from Eisenberg et al, 1979 Survival rate 100% CPR Defibrillation Advanced cardiac life support 10 min. Time from cardiac arrest
Casino Study (Valenzuela et al, 2000) • Casino security officers trained in CPR and defibrillation • Time of collapse from videotapes • Response times ≈ 3 min – much shorter than most EMS calls • Survival rates: – 74% when response time < 3 min. – 49% when response time > 3 min.
Estimated Survival Functions • Here’s one of four that we found: Arrest to CPR time Arrest to defibrillation time • “Response time” is nowhere to be seen! • Need to make assumptions so can “average over” non-response-time factors • A good thing – allows calibration of a function estimated in one city for use in another city with a different EMS system
Calibrating Survival Functions: Assumptions • Is collapse witnessed? 61% yes, average access time = 1. 2 min 39% no, average access time = 30 min • Bystander CPR: 64%, 1 min after 911 • Response time: Average pre-travel delay = 3 min + Average travel time (based on distance) • EMS arrival to defibrillation: 2 min
Add Variability around the Averages, Stir, and Bake, to get … … a probability of survival curve Implications for deployment: 2 km is twice as good as 11 km vs. < 11 km good, > 11 km bad
Sensitivity Analysis: Avg. Access Time, Un-Witnessed Arrest
“Optimal” Allocation of Ambulances to Stations Incorporation of uncertainty None Response times Ambulance availability Both Min. avg. response time 697 745 Max. avg. coverage 762 809 809 Max. avg. lives saved 809 809 • Change target from avg. response time to coverage: save 65 lives • Account for uncertainty about coverage: save 47 lives • Change target from coverage to survival (but ignore uncertainty): save 47 lives
Observations • Survival rates vs. response time: – Out-of-hospital cardiac arrest survival rates have been studied extensively – These are the most “saveable lives” • Possible to incorporate survival rates based on medical research into planning models • Coverage is a poor proxy for survival rates … – … but consideration of uncertainty improves it
Why does Maximizing Survival Rates and Maximizing Expected Coverage give Similar Results?
Potential Reasons to Focus on Survival Rates instead of Coverage • Coverage is an imperfect proxy for survival rates … – … assuming that’s the real objective • Abstract units – $ or lives saved get more attention than “% in 8: 59” • All of the following are arbitrary and vary among EMS systems: – The time standard – The percentage goal – When the clock starts and stops
Potential Problems (and Solutions) with a Focus on Survival Rates • Only know survival rates for cardiac arrest – Do more studies of non-cardiac arrest patients – Use coverage target for other patients? • Insufficient data to calibrate survival functions – Maybe the data should be collected anyway for cardiac arrest patients? – Plans to collect the data in some cities • “ 90% covered” sounds better than “ 8% survived” – Important to include benchmarks: 2% survival without EMS? – Focus on “lives saved” instead of “% survival”? • ? – ?
For More Information • Erkut, E. , A. Ingolfsson, G. Erdoğan. 2008. Ambulance deployment for maximum survival. Naval Research Logistics 55 42 -58 • Budge, S. , A. Ingolfsson, D. Zerom. Empirical Analysis of Ambulance Travel Times (ready later this month) • Armann. ingolfsson@ualberta. ca • www. business. ualberta. ca/aingolfsson/publications. htm
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