EMS Performance Targets and Travel Times EMS Planning Conference, August 2008 Armann Ingolfsson 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

Let’s do this for a location in Twin Brooks, Edmonton Pick a location in the city 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) Using a Map to Predict Performance

Closest Station: Terwillegar Call location Closest station

How Far is it? Take 1 Call location Closest station 4.5 km As the crow flies “Euclidean distance”

How Far is it? Take 2 Call location Closest station 5.8 km North-south and east-west travel only “Manhattan metric” “Rectilinear distance”

How Far is it? Take km Using Google Maps “Network distance”

OK, so I Measured the Distance What’s Next? Distance Different ways to measure Station locations Ambulance availability Zone sizes Response Time When to start and stop the clock Variability “Outcome” Less or more than 8:59? Medical outcome? Psychological outcome? Transform Traffic conditions Driver behaviour Construction Pre-travel and post-travel … Paramedic training Patient’s condition … What we’ll do next

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 Time Speed acceleration cruising speed deceleration A long trip:

A Simpler Approach Time Speed A short trip:

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 tripsLong 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. = × (distance in km) Twin Brooks: × (8.6 km) = 7:42 min. 8:59 min.  10.8 km Twin Brooks is covered!

Not coveredCovered! Is Twin Brooks Really Covered? Terwillegar stationTwin Brooks 8:597:42 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 stationTwin Brooks 8:597:42

Probability of Coverage Curve Implications for deployment: 3 km is twice as good as 11 km vs. 11 km bad

Probability of Coverage Map 0% 20% 40% 60% 80% 100% Prob. of Coverage Created using probability of coverage curve, for all locations in a city

The Formulas Travel time = (  (distance) + f(time of day)) × exp(  (distance)  )  (distance)  avg. travel time curve  (distance)  next slide f(time of day)  the slide after that  ~ t distribution with 3.3 d.f.

Coefficient of Variation:  (distance)

Time-of-day Effect ~ 5 PM Afternoon rush hour ~ 4 AM ??

How About Medical Outcomes instead of % in 8:59? Distance Different ways to measure Station locations Ambulance availability Zones sizes Response Time When to start and stop the clock Variability “Outcome” Less or more than 8:59? Medical outcome? Psychological outcome? Transform Traffic conditions Driver behaviour Construction Pre-travel and post-travel … Paramedic training Patient’s condition …

Out-of-hospital Cardiac Arrest Survival Rates Survival rate 100% Time from cardiac arrest 10 min. CPR Defibrillation Adapted from Eisenberg et al, 1979 Advanced cardiac life support

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: “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 Arrest to CPR time Arrest to defibrillation time

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 bad

Sensitivity Analysis: Avg. Access Time, Un-Witnessed Arrest

“Optimal” Allocation of Ambulances to Stations 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 Incorporation of uncertainty NoneResponse times Ambulance availability Both Min. avg. response time Max. avg. coverage Max. avg. lives saved809

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 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 Ambulance deployment for maximum survival. Naval Research Logistics Budge, S., A. Ingolfsson, D. Zerom. Empirical Analysis of Ambulance Travel Times (ready later this month)

Questions?