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Technology, Computing, and Simulation: Original Clinical Research Report

Determination of Geolocations for Anesthesia Specialty Coverage and Standby Call Allowing Return to the Hospital Within a Specified Amount of Time

Epstein, Richard H. MD*; Dexter, Franklin MD, PhD; Diez, Christian MD, MBA*; Potnuru, Paul MD*

Author Information
doi: 10.1213/ANE.0000000000003320
  • Free

Abstract

KEY POINTS

  • Question: What are the postal codes around a hospital within which anesthesia standby call personnel can be located and return to the hospital within a specified interval during all call hours?
  • Findings: Calculations must consider the longest driving times during all call hours, not simply distances from the hospital, because the latter does not incorporate traffic congestion by time of day and varying access to highways.
  • Meaning: When anesthesia personnel are contemplating where to live or places where they will be located while on standby call, driving times to return to the hospital should be considered.

Staffing requirements needed to perform procedures during nonregular hours (ie, nights, weekends, holidays) can be determined using historical data from operating room or anesthesia information management systems.1–4 For emergent procedures (eg, cesarean delivery for nonreassuring fetal heart rate, laparotomy to control bleeding after trauma), in-house teams are needed to provide immediate care. However, for many procedures, there is sufficient time to mobilize a team from home without increasing patient morbidity (eg, open fracture, solid organ transplant, appendectomy).5,6 For such procedures, standby call from home is a reasonable option and is a financial, not a medical, decision.3 Additionally, even when in-house call is provided, personnel taking backup call from home are also usually assigned to be available in case the workload is too great for the in-house person to handle. For hospitals using subspecialty teams to improve patient outcomes during regular hours (eg, pediatric anesthesia, neurosurgical anesthesia), providing similar care during nonregular hours would increase the need for standby call from home.7

A requirement to return to the hospital during nonregular hours within a locally established interval of time after notification has implications as to where members of such teams can be located when on call. A requirement when taking standby call to return to the hospital within a given amount of time after notification may be written into employment contracts. This may affect decisions as to where to purchase or rent a home, or the places where one can be located when taking such call. Because urgent cases occur at unpredictable times, one needs to consider conservative travel times at any hour during periods when standby call is taken. Such travel times can vary substantively, depending on local traffic patterns (eg, rush hour in large urban areas, road closures). Determining the locations around a hospital permitting timely return is not a trivial exercise due to the many combinations of days of the week, hours of the day, and hundreds of potential locations (eg, postal codes within a given radius of the hospital). Automating this process would be of substantial benefit to anesthesia departments, as nearly all have some call teams that do not take in-house call.

In this study, we developed an automated methodology based on the travel times available using the Google Maps Distance Matrix Application Program Interface (Distance API). We supply computer code that can be used for implementation (see Supplemental Digital Content, File Description, http://links.lww.com/AA/C288, or go to http://FDshort.com/CallReturnTime to access the latest version of the computer code). A hospital can use nearby postal codes (eg, United States Zip Codes) to determine a perimeter within which members of such standby call teams can be located and still satisfy the established return-to-hospital requirements. We also present a manual method, using the online Google Map application, that can be used to check specific addresses in areas that are close to the limit of acceptable return times.

METHODS

The complete methodology is provided as comments in the computer code in Supplemental Digital Content, File Description, http://links.lww.com/AA/C288. The principal points are included here in the Methods.

Software and Data Sources

We obtained a free key online from Google and created a billing account to use their Distance API (Google, Mountain View, CA).8 A key currently allows up to 2500 free calls per day to the API, with additional volume charged at a rate of $0.50 per 1000 requests.

The main entrance to the University of Miami Hospital is located at latitude 25.789269, longitude −80.215937, as determined using Google Maps. This geolocation was used for all distance calculations to the hospital. The latitudes and longitudes of the centroids for all other Florida zip code tabulation areas were obtained from the US Census Bureau.9 Zip code tabulation areas are generalized area representations of United States Zip Codes.10a For convenience, these are hereafter referred to as “postal codes” to align with terminology used elsewhere throughout the world, as our method is generalizable.

Screening for Candidate Postal Codes Within Range of the University of Miami Hospital

To reduce the computational burden of calculating driving times at all hours of the day and days of the week from the postal codes surrounding the hospital, we first determined the great circle (“straight line”) distances from the global positioning satellite (GPS) coordinates corresponding to all postal codes in the state of Florida9 to the hospital using the haversine formula.11 We considered only those postal codes within 60 miles of the hospital. Because driving distances are always longer than great circle distances, this range included all postal codes within a 60-minute drive to the hospital (based on an average driving speed of 60 miles per hour). This approach automated the (cumbersome) manual process of drawing a circle around the hospital with a radius equal to 60 miles and then tabulating the postal codes from a map with overlaid postal codes.

Software Development for Determination of Driving Times and Distances and Mapping

Computer code requesting the distances and driving times in traffic from the postal code’s GPS coordinates to the GPS coordinates of the hospital using the Distance API was written in the open source programming language Python v 3.4.1 (Python Software Foundation, Beaverton, OR). Departure dates were selected that were several months in the future to eliminate contributions from current traffic conditions that would otherwise be included in the time estimates if the current date were used. Rather, the range of such differences in driving times is incorporated into the historical data used for the calculations. Manual determinations of driving times and distances (for the same future dates as for the Distance API) were made using the free Google Maps web application (https://www.google.com/maps).

The online software package Map Business Online (SpatialTEQ a division of Software Technologies, Taganrog, Russia) was used to produce the maps identifying the postal codes within the 60-minute specified return time to the hospital.12

Determination of the Longest Driving Time for Return to the Hospital

Google’s calculated “pessimistic” driving times are based on historical data for the time of day and represent a value “longer than the actual traffic time on most days, through occasional days with particularly bad traffic may exceed this value.”13 An average or “expected” driving time would not be appropriate for the purpose of determining return times because this would result in substantive failures to meet the department’s service commitment to provide coverage for urgent cases within a specified interval after notification.

Driving times were determined for each hour of departure on each day of the week using the pessimistic driving times provided by the Distance API.b The longest estimated driving time was then determined for each day of the week for the following 108 ranges of departure times: Monday to Friday from 6 pm to 6 am, and for the 24-hour period starting on Saturday and Sunday at 6 am. The 108 call hours = 5 days × 12 hours/day + 2 days × 24 hours/day.

Statistical Analysis

Systat v13 (Systat Software, San Jose, CA) was used for the comparison of the longest driving times among the 108 call hours for each combination of the 7 days of the week and the 136 postal codes. Next, 21 paired t tests were performed between days of the week, with each paired t test having N = 136 postal codes. The 21 comparisons were for Sunday versus Monday, Sunday versus Tuesday,…, Friday versus Saturday. Holm-Bonferroni adjustments of the P values were made for the 21 comparisons (Table). A post hoc P value <.01 was required to claim statistical significance.

Table.
Table.:
Differences Among Days of the Week for the Average of the Longest Return Times Among the N = 138 Postal Codes During Nonregular Hours to Return to the Hospital

Linear regression with a 0 intercept was used to minimize the sum of the mean absolute percentage differences between the driving distances (x-axis) and the longest pessimistic driving times (y-axis) among the 108 call hours per week. This calculation of the slope m of the regression line was performed on the N = 136 numbers (ie, 1 data point per postal code) using the add-in Solver function in Excel (Microsoft, Redmond, WA).

RESULTS

Findings From the Google Map API

Great circle distances, driving distances, and driving times were calculated for the shortest distances between the University of Miami Hospital and postal codes within 60 miles.c

Figure 1.
Figure 1.:
Bland Altman plot of the differences between the driving distances calculated using the Google Maps Distance Matrix Application Program Interface (“gold standard”) and the great circle distances for the N = 136 postal codes within 60 miles of the University of Miami Hospital. The figure shows a systematic increase in the error between the driving and great circle distance as the driving distance increased (Spearman rank correlation ρ = 0.69, P < .0001).
Figure 2.
Figure 2.:
Relationship between the driving distance and the maximum of the longest pessimistic driving times during nonregular hours reported by the Google Maps Distance Matrix Application Program Interface. The driving times were determined for each of the 108 hourly times between 6 pm and 6 am on weekdays and 6 am and 6 am on weekends and represent an estimate of the longest time to return to the hospital after notification. There was wide scatter among postal codes between the linear regression line for the driving time as a function of the driving distance (mean absolute percent error = 25.1% ± 19.3%; N = 136 postal codes). Some notable outliers for relatively close distances but long travel times include locations in South Beach (red diamond), Fisher Island (purple diamond), the University of Miami Coral Gables Campus (black diamond), Bal Harbor (green diamond), and Sunny Isles (orange diamond). These locations all involve travel on congested highways and/or travel on a causeway over an intercostal waterway. The Fisher Island location is notable in that access requires travel on a ferry.

There was a systematic increase in the discrepancy between the great circle distance and the driving distance within 60 miles of the University of Miami Hospital (Figure 1). There was wide scatter between the driving distances and the longest driving times for a return to the hospital (mean absolute percentage error = 25.1% ± 1.7% SE; Figure 2; N = 136 postal codes). Great circle distances also correlated poorly with the driving times (mean absolute percentage error = 28.3% ± 1.9% SE). Among the 74 postal codes beyond a driving distance of 20 miles, only 16 (21.6%) would allow a reliable return to the hospital within 60 minutes. However, the use of driving distances should not be used to limit locations where standby call can be taken (eg, by drawing a circle around the hospital) because some postal codes beyond a given threshold distance have sufficient access to high-speed highways to meet the service commitment of a return within 60 minutes.

Use of the Google Maps Web Application to Estimate Future Driving Times

Figure 3 displays a map of the postal codes surrounding the hospital flagged according to the capability to return to the hospital within 60 minutes during all 108 nonregular hours on any day of the week. Postal codes that were considered, but were far beyond the perimeter of unacceptable locations, are not shown.

Figure 3.
Figure 3.:
Map of centroid locations (green balls) from the US Census Bureau zip code tabulation areas surrounding the University of Miami Hospital (blue ball) where the estimated longest time to return to the hospital among all nonregular hours of the week is ≤60 min. Areas outside this zone are noted with red balls.

We next sought to determine for the University of Miami Hospital if there were a time and day of the week with the longest estimated driving times so that subsequent manual use could be limited to that time. This might be convenient for an individual wanting to manually check if a specific home address would allow for timely return when taking standby call, as all days and times would not have to be investigated. Among the 136 postal codes tested, the longest return times occurred on Fridays for N = 80 postal codes, Thursdays for N = 42 postal codes, and Tuesdays for N = 14 postal codes. However, 13 of the 14 postal codes on Tuesdays had the longest return times, which were <3 minutes longer than the corresponding longest return times on Fridays, with 1 outlier of 18 minutes (median = 0.7 minutes, 90th percentile = 2.6 minutes). The postal code for the outlier would not have qualified as an acceptable location from which to take standby call, making the difference moot. Comparing the longest return times on Thursdays to Fridays and for which the Thursday values were greater, all 42 were within 8 minutes of the Friday values (median = 1.6 minutes, 90th percentile = 5.6 minutes). Overall, the average difference among the 136 postal codes between the longest return times from the Friday return time at 6 pm and the longest return time during all 108 hours of nonregular hours per week (including Fridays) was −0.03 ± 0.15 minutes (standard deviation). Thus, for the University of Miami Hospital, 6 pm on Friday would be a reasonable surrogate to estimate the return time from any surrounding location.

From the preceding results, an individual wishing to determine if living at a specific address would allow for timely return to the University of Miami Hospital could use the Google Maps web application, select a departure of Friday at 6 pm, and determine the estimated minimum driving time among the various proposed routes. Neither great circle distances nor driving distances are relied on with this method. However, at other hospitals, such simplification would require first knowing which, if any, day of the week and departure hour had the longest return driving time (ie, after a full analysis was done).

Generalizability of Findings to a Hospital in a Rural State

To assess the generalizability of our findings, we applied our method to the University of Iowa Hospital, a large (761-bed) public teaching hospital in the state of Iowa, located at latitude 41.659263, longitude −91.548094. Iowa City had an estimated population of 74,398 as of July 1, 2016, and the state of Iowa population was 3,134,693.14 In contrast, the estimated population of the City of Miami on June 1, 2016, was 453,579, with Miami-Dade County, in which Miami is located, home to 2,496,435 people.13 Two major interstates, east-west I-80 and north-south I-380, intersect adjacent to Iowa City. The region lacks the geographic barriers (ie, water) affecting driving times in Miami. However, farmland results in a transportation network that is less dense than that surrounding Miami.

Figure 4.
Figure 4.:
Map of centroid locations (green balls) from the US Census Bureau zip code tabulation areas surrounding the University of Iowa Hospital (blue ball), where the estimated longest time to return to the hospital among all nonregular hours of the week is ≤60 min. Areas outside this zone are noted with red balls.

There was better correlation between driving distances and driving times using the Iowa data than the Miami data; the mean absolute percent error was 12.1% ± 1.3% SE (P < .0001, N = 136 postal codes). The correlation was also better compared to Miami for the driving times and the great circle distances, with a mean absolute percent error of 18.1% ± 1.6% (P < .0001). However, in contrast to the situation in Miami, there was no time on a day of the week that could be used as a surrogate for calculating the longest estimated driving times using the Distance API. A map of locations within the range of returning to the hospital within 60 minutes, and those just beyond this interval, is displayed in Figure 4.

DISCUSSION

Implications

This study provides a simple methodology for determining geolocations surrounding a hospital from which anesthesia providers taking standby call can return to the hospital during nonregular hours within a specified interval after notification. The results demonstrate that neither a straight line nor driving distances can be used for such determinations; rather, the driving times need to be calculated. The method also applies to nurses, scrub technicians, anesthesia technicians, perfusionists, and other hospital employees who take call from home.

In Supplemental Digital Content, File Description, http://links.lww.com/AA/C288, we supply computer code written in Python and full instructions that will allow an individual with programming ability to implement our process with minimal effort. The third-party software required is readily available online and is either free (Python, Google Maps) or low cost (Google Distance Matrix API). We also provide an Excel workbook (Microsoft, Redmond, WA) with embedded software (Visual Basic for Applications) that allows automated processing of the Google travel time data (Supplemental Digital Content, File Description, http://links.lww.com/AA/C288). Languages other than Python could be used (eg, R, Javascript), with sample code specified in the Google guide for developers.8 The mapping software used for creation of the figures is unnecessary for implementation; the display could be prepared with a map of the area surrounding the hospital and a highlighter to mark the boundaries from which timely return to the hospital would be possible.

We emphasize that we do not intend to imply that a return time of 60 minutes is appropriate for standby call teams. The appropriate interval depends on types of procedures to be performed and time ahead when there is knowledge of the procedure to be performed. For example, there may be multiple hours of notice for patients receiving a solid organ transplant. In addition, if the expectation were that the returning provider will be available in the operating room by the specified service interval, rather than simply having arrived at the hospital, a driving time somewhat less than the interval would need to be ensured (eg, for parking). Another consideration is the potential presence of in-house anesthesia providers (eg, resident or nurse anesthetist) who can begin preparing the patient for surgery (eg, complete the preoperative evaluation, place intravenous lines) before the anesthesiologist arrives. For departments where some individuals only take certain categories of standby call allowing longer return times than the usual situation, a greater distance from the hospital may be possible. This would involve expanding the potential range of locations and using a different cutoff value for the return time.

If an anesthesia department or hospital specifies as a matter of policy a time interval within which personnel on standby call are expected back after notification, then this will restrict the potential locations where such personnel can be located when on call. Such restrictions can influence decisions when inclement weather may affect travel or there are local events attracting large numbers of people near the hospital. For example, the University of Iowa Hospital is located adjacent to a football stadium with a capacity of 70,585 spectators. There can be value to staying relatively close to the hospital when an urgent case might present itself. This is especially relevant for hospitals in urban areas with considerable variability in driving times due to traffic congestion. Under some circumstances, consideration may need to be given to providing in-house call rather than standby call from home.

Figure 5.
Figure 5.:
Google Map web application, which can be used to determine estimated future driving times. After entering the origin and destination for the trip, a future date and time can be entered, and several routes with estimated driving time ranges are displayed. The optimal route is the one with the shortest upper limit of driving time. Dates and times can be changed be selecting new values from a drop-down list below each parameter or by clicking on the arrows to the right of the time and date. Estimated driving times for a future data and time are returned by entering departure and arrival locations and specifying the departure time. The shortest upper limit of the driving time ranges is used as the predicted driving time to return to the hospital after notification. This tool can be used to determine the suitability of a location during standby call over the duration of the potential recall window. Similar web-based software from other vendors (eg, Microsoft’s Bing Maps, Verizon’s Mapquest) could also be used.

We think it would be practical for an anesthesia department or hospital to determine a list of postal codes surrounding the hospital where timely return within a specified interval can reasonably be ensured, along with those that are on the perimeter of acceptability (ie, not surrounded by other acceptable postal codes). An employee considering a residence in a perimeter postal code (perhaps from considerations of housing costs) could investigate the potential return times at peak travel hours during the week. This can easily be done using the Google Map online tool (Figure 5). For some locations (eg, Miami), there may be a single day and time that can be used for the evaluation; however, this is not generalizable, as shown by our results for the University of Iowa Hospital in Iowa City.

Limitations

Although we used the pessimistic driving times from the Google Distance Matrix API, these times can be exceeded on days with exceptionally high traffic. Furthermore, the analysis presumes that providers returning to the hospital would use a real-time traffic tool (eg, Google Maps, Waze) to provide guidance for the optimal route. Such real-time mapping tools could also be used by the call person to determine, for example, if having dinner at a nearby restaurant would allow a timely return to the hospital. To the extent that such software is not used, actual driving times may be longer than predicted by the modeling. Thus, the results of our method are optimistic with respect to the driving times. An implication of these limitations is that an anesthesia department might want to require a driving time somewhat shorter than the return interval specified in its service agreement with the hospital.

Shorter than predicted driving times would be possible if the person returning exceeded posted speed limits and otherwise drove aggressively. However, we think it unwise to incorporate an expectation for such behavior to allow return within a specified interval of time.

We only considered driving times in our calculations as compared with walking or public transportation times. However, we do not think our approach is necessary to compute the time to return by foot to the hospital, as those times do not vary much by time or day of the week. Although the Distance API can return information on the time to return to the hospital using public transit, the time reported does not include potential delays until the next bus or train will arrive. For example, if a call person received notice at 2 am to return to the hospital for an urgent case, but the next available nearby bus was not scheduled to leave until 3:00 am, the full time would not be reported by the API, only the interval to walk to the bus stop, the interval for the bus to get to the stop nearest to the hospital, and the interval to walk from that stop to the hospital. Thus, we think our methodology would not be suitable for calculations of return times to the hospital via public transportation. For the 2 hospitals studied, as in most cities, public transportation running on a frequent schedule at all hours and days of the week is generally unavailable (eg, midnight to 5 am).

The examples presented are for 2 hospitals in the United States. The specific results are not generalizable due to considerations of geography and transportation networks. Nonetheless, the methodology described applies to the many countries supported by the Google Distance Matrix API.15 Postal codes are ubiquitous throughout the world, and GPS coordinates can easily be determined for hospital locations. However, this would exclude the few locations where Google does not provide travel time and distance information or where public access to the Internet is blocked by the government (eg, North Korea).

Google does not provide information publicly on how it calculates the pessimistic times reported by its API or the driving times displayed in the online map application. Thus, we were unable to perform a statistical analysis of the relationship between the pessimistic driving times supplied by the Distance API and the upper driving time limits from Google Maps.

Our method is not restricted to the Google’s Distance API, as similar query string interfaces are available from other vendors (eg, Bing Maps API, MapQuest API, OpenRouteService). Each returns responses in the JavaScript Object Notation (JSON) format, as does Google. Yandex is another source of map information, but its distance API is based on Javascript, and thus not compatible with our software solution. The code we provide in Supplemental Digital Content, File Description, http://links.lww.com/AA/C288, can be modified for other vendors’ API to send the request and parse the reply. However, because we did not test alternative products, we cannot comment on their accuracy or performance during automated processing. Other commercial software packages are available to estimate driving times (eg, ArcGIS Network Analyst, Esri, Redlands, CA). These packages are more expensive and complicated to use than the solution presented in this technical report.

CONCLUSIONS

The ability for providers taking standby call to ensure a return to the hospital within a specified interval should incorporate calculation of the longest of conservative estimated driving times over the entire range of call hours. A simple method using the Google Distance Matrix API and an associated Excel workbook to process the data is provided. This will allow anesthesia departments and hospitals to calculate nearby postal codes for location during call hours where such service requirements can be satisfied. The Google Maps online application can be used to determine the suitability of specific locations allowing for such timely return and is recommended for perimeter areas.

DISCLOSURES

Name: Richard H. Epstein, MD.

Contribution: This author helped design the study, conduct the study, analyze the data, and write the article.

Name: Franklin Dexter, MD, PhD.

Contribution: This author helped design the study, conduct the study, analyze the data, and write the article.

Name: Christian Diez, MD, MBA.

Contribution: This author helped write the article.

Name: Paul Potnuru, MD.

Contribution: This author helped write the article and validate the software.

This manuscript was handled by: Maxime Cannesson, MD, PhD.

FOOTNOTES

aMost locations within a zip code tabulation areas (ZCTA) have the same value as the zip code corresponding to the location, but some ZCTAs include zip codes adjacent to the principal zip code in the ZCTA. The centroid location is the latitude and longitude of the center point of the polygon defined by the border of the ZCTA.

bExamination of the predicted pessimistic driving times from the Distance Application Program Interface for various days of the week throughout 2018 indicated that results among the same day of the week over the course of the year were the same. Thus, a single week could be analyzed for the driving times for each day of the week.

cThese postal codes were located in Miami-Dade County, Broward County, and the southernmost region of Palm Beach County.

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10. US Census Bureau. Available at: https://www2.census.gov/geo/pdfs/education/brochures/ZCTAs.pdf. Accessed September 13, 2017.
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13. Google. Distance Matrix API Developer’s Guide. Available at: https://developers.google.com/maps/documentation/distance-matrix/intro Accessed September 12, 2017.
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Supplemental Digital Content

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