Travel,Time,and Cost Savings Associated with a University Medical Center's Video Medical Interpreting Program

Abstract

Background:

Patients with limited English proficiency experience disparities in health care access, quality, costs, and outcomes. Providing qualified medical interpreting services (MIS) in the health care setting can reduce these disparities. Unfortunately, health organizations face logistical and financial difficulties in meeting the need for qualified medical interpreters.

Introduction:

This descriptive review evaluated travel, time, and cost savings associated with video interpreting services compared to traditional in-person services.

Materials and Methods:

We conducted a retrospective review of all inpatient and outpatient medical interpreting encounters at a large academic hospital delivered through video and in person between 2006 and 2017. Outcome measures included interpreter travel distance, time, and cost for in-person encounters and savings associated with avoided travel for services provided through video.

Results:

We reviewed 281,701 interpreting encounters, including 249,357 in person and 32,344 by video. Video encounters occurred both for on-site and off-site visits. For on-site encounters, the use of video resulted in an average round trip walking distance saved of 0.75 miles (SD = 0.33) and an average round trip walking time saved of 14.75 min (SD = 6.30) per encounter. For off-site encounters, the use of video resulted in an average round trip driving distance saved of 8.63 miles (SD = 9.13), an average round trip driving time saved of 23.78 min (SD = 9.50), and an average round trip driving cost savings of $4.66 per encounter.

Conclusions:

This single institution review of the travel, time, and cost savings associated with providing MIS through video demonstrates the opportunity for more efficient use of time and resources.

Introduction

More than 63 million people in the United States speak a language other than English at home and more than 25 million people self-identify as having limited English proficiency (LEP) or speaking English “less than very well.”^1,2 Patients with language barriers often face difficulties in the health care setting affecting access to care, satisfaction with care, and health outcomes.^3
–5 Compared to their English-speaking counterparts, patients with LEP are less likely to have a medical home or to use preventative health services.^{3,4,6

–10} Patients with LEP are also more likely to have lower satisfaction with care,^11

–14 higher resource utilization,^15
–17 poorer adherence to medical advice and care plans,¹⁸ increased risk of adverse medical events,^19
–21 and longer lengths of hospital stay.^21,22 As a result, language barriers are associated with increased costs.^15,23

To assist in the provision of health care for patients with LEP, hospitals and health care facilities provide medical interpreting services (MIS). Health care organizations who receive federal funding are legally obligated to provide patients with access to language interpreting services according to three federal laws: (1) Title VI of the Civil Rights Act of 1964, (2) the American with Disabilities Act, and (3) the Affordable Care Act.^24

–27 Changes to the Affordable Care Act in 2016 further appointed that federally-funded health organizations must provide interpreting services that are free to patients, accurate and timely, protect confidentiality, and are provided by qualified interpreters above simply requiring that services be available. Health care organizations use a variety of methods to provide qualified language interpreting services, including staffing in-house interpreters, freelancing interpreters, or using telephone or video on demand services.

Despite federal laws requiring interpreting services, health organizations often encounter logistical and financial difficulties staffing qualified medical interpreters on-site for all languages due to varying and unpredictable demand. In addition, if the appropriate interpreter is available to be dispatched for in-person services, patients and providers are often subjected to lengthy wait times potentially delaying care. Therefore, providing interpreting services through live video—or video MIS—is an efficient way to bring real time, qualified language interpreting services to wherever the patient may be. Studies researching the feasibility of video MIS have shown its ability to increase access to high-quality interpreter services^24,28

–31 while maintaining equivalent patient and provider satisfaction compared with traditional in-person services.^32

–35 However, little is known about the time and cost savings associated with video MIS compared to traditional in-person services. Thus, this study sought to conduct a descriptive analysis of the University of California Davis Health (UCDH) video MIS program evaluating interpreter travel distance, travel time, and travel cost from the health system perspective.

Materials and Methods

STUDY DESIGN AND DATA SOURCE

This study is a retrospective review of all inpatient and outpatient encounters at the UCDH hospital, on-site outpatient clinics, and off-site outpatient clinics receiving language interpreting services from the UCDH MIS program delivered through video or in person between January 1, 2006 and December 31, 2017. UCDH is composed of a single 625-bed multispecialty academic hospital, on-site ambulatory care primary and specialty care outpatient clinics, and a regional network of 17 off-site outpatient clinics. Data were evaluated from the UCDH MIS program administrative database that tracks encounter-level data for all language interpreting services. Variables recorded include service date, start and end time, language, mode of interpreting (video, telephone, or in-person), and location of service provided.

UCDH MIS PROGRAM

UCDH MIS program provides interpreting services in over 18 languages by telephone, video, or in person 24 h a day, 7 days a week. For languages not provided by the UCDH MIS program, a contracted telephone-based service is used. However, data on these encounters are not internally documented and thus not included in the present analysis. In 2002, the UCDH MIS program began providing interpreting services over videoconferencing in addition to the traditional in-person and telephone interpreting services. Currently, there are 76 MIS video-enabled units throughout the hospital, ambulatory care clinics, and off-site network clinics. At UCDH, the mode of interpretation (in-person, telephone, or video) is determined at the time of the request for services considering several factors, including medical provider(s) preference, patient/family preference, location of need, day/time of request, and interpreter availability.

PRIMARY OUTCOME MEASURES

The primary outcome measures include the interpreter travel distance, travel time, and travel cost (when a car was needed) for in-person encounters and the interpreter travel distance, travel time, and travel cost savings (when the need for a car was obviated) associated with avoided travel for video encounters. For on-site encounters, the assumed method of travel for the interpreter was walking, and for off-site encounters, the assumed method of travel for the interpreter was driving.

Travel distance savings, defined as the interpreter's round trip distance savings resulting from the use of video, was calculated as the round trip driving or walking distance from the MIS office to the location the interpreter would have traveled for an in-person encounter.

Travel time savings, defined as the interpreter's round trip travel time savings resulting from the use of video, was calculated as the round trip driving or walking time required to drive from the MIS office to the location the interpreter would have traveled for an in-person encounter.

Travel cost savings, calculated only for off-site encounters, defined as the round trip cost savings resulting from the use of video, was calculated by multiplying the IRS mileage reimbursement rate by the round trip driving distance the interpreter would have traveled for an off-site in-person encounter.

TRAVEL DISTANCE AND TRAVEL TIME CALCULATIONS

The location of the interpreting encounter was defined as the location of the patient and provider (i.e., where the clinical encounter physically took place). Encounter addresses were identified using the MIS database location of the requesting clinic (in-person or video). Stata³⁶ was used to geocode addresses. For off-site encounters, a proprietary geolocation application programming interface was used to calculate driving distance and driving time under normal driving conditions.³⁷ For on-site encounters, Google Maps was used to calculate walking distance and walking time. Round trip distances were calculated by doubling the one-way walking or driving distance from the UCDH MIS office to the interpreting location. Round trip travel time was calculated by doubling the one-way walking or driving time from the MIS office to the interpreting location.

TRAVEL COST CALCULATION

At UCDH, MIS interpreters use their personal vehicles to drive to the interpreting location and are reimbursed per miles driven at the IRS mileage reimbursement rate as per a University of California policy. Encounter-level travel costs were calculated for all off-site encounters by multiplying the UCDH mileage reimbursement rate ($0.54/mile) by the round trip driving distance.

STATISTICAL ANALYSES

Stata was used to edit and merge data sets, generate frequency distributions, and perform statistical comparisons using χ² tests for categorical variables and Student's t tests for continuous variables. This study was reviewed and approved as nonhuman subject research by the Institutional Review Board at University of California Davis.

Results

A total of 475,071 individual language interpreting encounters were documented in the UCDH MIS database between January 1, 2006 and December 31, 2017. Of those, 615 encounters (0.13%) were excluded because they did not have location or address information and 4,442 encounters (0.94%) were excluded because they did not have mode of interpretation (i.e., in-person, video, or phone). Of the remaining 470,014 encounters, 249,357 (53.05%) were completed in person, 188,313 (40.07%) were completed over telephone, and 32,344 (6.88%) were completed over video.

There were 281,701 encounters that used either video or in-person MIS; 249,357 (88.52%) encounters were provided in person and 32,344 (11.48%) encounters were provided over video. Interpreting services were provided in 23 different languages (Table 1) with a majority provided in Spanish (56.07%). Two hundred sixty-three thousand ten (93.4%) encounters were provided to locations on the UCDH campus, including to the main hospital and to on-site outpatient clinics, with the remaining 18,691 (6.6%) provided to off-site outpatient network clinics. Among video encounters during the study period, 25,212 (77.9%) were provided remotely to on-site locations, while the remaining 7,132 (22.1%) were provided to off-site outpatient network clinics. Among in-person encounters during the study period, 237,798 (95.4%) were provided to on-site locations, and the remaining 11,559 (4.6%) were provided to off-site outpatient network clinics where the interpreter drove to the location of the provider and patient.

Table 1.

Characteristics of In-Person and Video Medical Interpreting Encounters

ENCOUNTER-LEVEL VARIABLES	IN-PERSON (N = 249,357)	VIDEO (N = 32,344)	ALL (N = 281,701)
Language of encounter, n (%)^a
American sign language	17,667 (7.1)	198 (0.6)	17,865 (6.3)
Cantonese	9,834 (3.9)	929 (2.9)	10,763 (3.8)
Hmong	8,444 (3.4)	889 (2.7)	9,333 (3.3)
Korean	8,537 (3.4)	410 (1.3)	8,947 (3.2)
Lao	2,527 (1.0)	175 (0.5)	2,702 (1.0)
Mandarin	4,454 (1.8)	419 (1.3)	4,873 (1.7)
Mien	12,122 (4.9)	1,274 (3.9)	13,396 (4.8)
Russian	30,126 (12.1)	3,570 (11.0)	33,696 (12.0)
Spanish	135,572 (54.4)	22,377 (69.2)	157,949 (56.1)
Vietnamese	11,268 (4.5)	1,372 (4.2)	12,640 (4.5)
Other languages	8,806 (3.5)	731 (2.3)	9,537 (3.4)
Location of encounter, n (%)
On-site	237,798 (95.4)	25,212 (77.9)	263,010 (93.4)
Off-site	11,559 (4.6)	7,132 (22.1)	18,691 (6.6)
Time of encounter (start time), n (%)^b
Business hours (9am to 5pm)	190,785 (86.0)	25,818 (91.1)	216,603 (86.5)
After hours (5pm to 9am)	31,178 (14.0)	2,520 (8.9)	33,698 (13.5)
Duration of encounter, mean (SD)^c
Average duration, min	41.72 (36.1)	30.72 (26.0)	40.48 (35.3)

Top 10 languages out of 23 representing at least 1% of the total sample are shown above; all others lumped into “Other languages.”

Due to missing data, sample size differs for time of encounter: In-person (N = 221,963), video (N = 28,338), all (N = 250,301).

Due to missing data, sample size differs for duration of encounter: In-person (N = 221,471), video (N = 28,265), all (N = 249,736).

SD, standard deviation.

On-site travel distance and time—actual (from in-person encounters) and saved (from video encounters)—are depicted in Table 2. Among on-site in-person encounters where the interpreter was assumed to have walked, the average round trip distance traveled by the interpreter per encounter was 0.60 miles (SD = 0.47) and the average round trip walking time traveled by the interpreter per encounter was 11.94 min (SD = 9.30). Over the 12-year study period, on-site in-person interpreting resulted in an average annual travel distance of 11,824.80 miles and an average annual travel time of 236,563.33 min (3,942.72 h or 164.28 days). Among on-site video encounters where the interpreter did not have to walk, the average round trip walking distance saved per encounter was 0.75 miles (SD = 0.33) and the average walking time saved per encounter was 14.75 min (SD = 6.30). Over the 12-year study period, video interpreting provided to on-site locations resulted in an average annual travel distance savings of 1,574.50 miles and an average annual travel time savings of 30,988.67 min (516.48 h or 21.52 days).

Table 2.

On-Site Walking Distance and Time: Average per Encounter, Annual, and Total

	PER-ENCOUNTER AVERAGE (SD)	ANNUAL AVERAGE	TOTAL
Round trip walking from in-person encounters (N = 237,798)
Walking distance (miles)	0.60 (0.47)	11,824.80	141,897.60
Walking time (min)	11.94 (9.30)	236,563.33	2,838,760.00
Round trip walking saved through video encounters^a (N = 25,212)
Walking distance saved (miles)	0.75 (0.33)	1,574.50	18,894.00
Walking time saved (min)	14.75 (6.30)	30,988.67	371,864.00

Walking saved: In-person walking distance and time saved by providing services over video.

Off-site travel distance, time, and costs—actual (from in-person encounters) and saved (from video encounters)—are depicted in Table 3. Among off-site in-person encounters where the interpreter drove from the MIS office to the location of the patient and provider, the average round trip driving distance traveled by the interpreter per encounter was 10.41 miles (SD = 13.16), the average round trip driving time traveled by the interpreter per encounter was 23.92 min (SD = 14.48), and the average round trip cost per encounter was $5.62. Over the 12-year study period, off-site in-person interpreting resulted in an average annual travel distance of 10,029.13 miles, an average annual travel time of 23,045.64 min (384.09 h or 16.00 days), and an average annual travel cost of $5,413.47. Among the off-site video encounters where the interpreter did not have to drive, the average round trip distance saved per encounter was 8.63 miles (SD = 9.13), the average round trip time saved per encounter was 23.78 min (SD = 9.50), and the average round trip cost saved per encounter was $4.66. Over the 12-year study period, video interpreting provided to off-site locations resulted in an average annual travel distance savings of 5,126.19 miles, an average annual travel time savings of 14,132.16 min (235.54 h or 9.81 days), and an average annual cost savings of $2,769.59.

Table 3.

Off-Site Driving Distance, Time, and Cost: Average per Encounter, Annual, and Total

	PER-ENCOUNTER AVERAGE (SD)	ANNUAL AVERAGE	TOTAL
Round trip driving from in-person encounters (N = 11,559)
Driving distance (miles)	10.41 (13.16)	10,029.13	120,349.60
Driving time (min)	23.92 (14.48)	23,045.64	276,547.70
Driving cost ($)	5.62	5,413.47	64,961.58
Round trip driving saved through video encounters^b (N = 7,132)
Driving distance saved (miles)	8.63 (9.13)	5,126.19	61,514.22
Driving time saved (min)	23.78 (9.50)	14,132.16	169,585.90
Driving cost saved ($)^a	4.66	2,769.59	33,235.12

Travel cost: round trip miles X reimbursement rate ($0.54/mile).

Travel saved: In-person travel saved by providing services over video.

Discussion

This retrospective review of in-person and video language interpreting encounters at a large university hospital system over a 12-year period demonstrates significant travel-related distance, time, and cost savings associated with providing language services through video. Savings from avoiding interpreter travel on-site using video produced an average annual walking savings of over 1,574 miles and 30,988 min (or more than 21 full days). Savings from avoiding interpreter travel off-site using video produced an average annual driving savings of over 5,126 miles, 14,132 min (or more than 9 full days), and $2,769 in driving costs. Although video language interpreting services made up only 11.5% of all services provided, we still found important travel-related savings. These results also highlight the opportunity to increase potential savings and interpreting capacity by increasing the proportion of services provided over video.

Technological advances over the past decade have increased the variety of methods health care organizations can provide qualified language interpreting services to their patients. For example, health care organizations can staff in-house interpreters to deliver services in person, by telephone, or by video or contract with an external on-demand interpreter service utilizing different modalities. Previous research has not only demonstrated the feasibility of video medical interpreting^24,28

–31 but also has shown comparable quality and patient and provider satisfaction to traditional in-person services.^32

–35 Literature comparing MIS travel-related time, distance, and costs by mode of delivery is very limited. A time-motion study conducted at a large health system in Delaware quantified interpreter travel time for in-person encounters over a 50-h period for the system's two most commonly serviced languages, Spanish and Mandarin. Results showed that their interpreters spent more than 11% of their time traveling to and from the service location and an average of 4.55 min per encounter.³⁸

To our knowledge, this is the first study to review travel (both driving and walking) distance, time, and cost savings resulting from the use of video medical interpreting. There are several limitations of our study to be noted. First, this was a single-institution study assessing a video MIS program at an academic hospital and health care system. Thus, these results may not be generalizable to other institutions or health systems where the volume of MIS, travel time, and travel distance may be either more or less. Second, we were limited to the variables available in the MIS database, which did not include time waiting for interpreter, interpreter travel method for in-person encounters, or the use of third-party interpreting services. We were not able to factor in the time a provider and patient spent waiting for the appropriate interpreter once dispatched for either in-person encounters or video encounters. Nor we were able to factor in the time the interpreter may have spent parking and walking within large buildings. For interpreter travel method, we made the assumption that interpreters walked or would have walked for on-site encounters and drove or would have driven for off-site encounters. However, it is possible that interpreters used different travel methods which could result in the travel time and travel distance estimated in this study to be an over- or underestimate. Similarly, the database only tracks internal, UCDH MIS interpreting encounters; therefore, we were not able to compare the use of outside telephone or video on-demand services. Third, we did not include telephone MIS encounters in the present study and chose to compare in-person with video MIS only. We decided to not include telephone encounters due to not being able to differentiate in the database between telephone calls made for providing interpreting services to patients and their provider versus telephone calls made to provide interpreting services for the purposes of billing, scheduling, or pharmacy-related calls that would not have replaced an in-person encounter. Finally, we were not able to factor into our analysis the vast technological advances over the 12-year study period. The significant advances in internet connections, software, and hardware enabling live video MIS over the study period should be recognized.

In this use case, video MIS saved interpreters more than 516 h or 21 days' worth of walking and more than 235 h or almost 10 days' worth of driving each year. The resulting travel-related savings demonstrate from the health system perspective the potential for more efficient use of interpreters' time and increased capacity for language interpreting services. Future research is needed to evaluate and quantify increased interpreter productivity and service provision at lower overall costs associated with video MIS compared to in-person MIS. Further research quantifying the costs and benefits of video MIS is also needed to provide evidence that will drive more widespread investment in and adoption of video MIS in the future.

Footnotes

Disclosure Statement

No competing financial interests exist.

Funding Information

No funding was received for this article.

References

United States Census Bureau. Detailed languages spoken at home and ability to speak English for the population 5 years and over: 2009–2013. 2015. Available at: https://www.census.gov/data/tables/2013/demo/2009-2013-lang-tables.html (last accessed March 8, 2019 ).

Pandya

, McHugh

, Batalova

. Limited English proficient individuals in the United States: Number, share, growth, and linguistic diversity. Washington, DC: Migration Policy Institute, 2011.

Jacobs

, Chen

, Karliner

, Agger-Gupta

, Mutha

. The need for more research on language barriers in health care: A proposed research agenda. Milbank Q, 2006; 84:111–133.

Fiscella

, Franks

, Doescher

, Saver

. Disparities in health care by race, ethnicity, and language among the insured: Findings from a national sample. Med Care, 2002; 40:52–59.

Kim

, Kim

, Paasche-Orlow

, Rose

, Hanchate

. Disparities in hypertension associated with limited English proficiency. J Gen Intern Med, 2017; 32:632–639.

Flores

, Abreu

, Tomany-Korman

. Limited English proficiency, primary language at home, and disparities in children's health care: How language barriers are measured matters. Public Health Rep, 2005; 120:418–430.

, Flores

. Pay now or pay later: Providing interpreter services in health care. Health Aff (Millwood), 2005; 23:435–444.

Regenstein

, Trott

, West

, Huang

. In any language: improving the quality and availability of language services in hospitals. Princeton, NJ: Robert Wood Johnson Foundation, 2008.

DuBard

, Gizlice

. Language spoken and differences in health status, access to care, and receipt of preventive services among US Hispanics. Am J Public Health, 2008; 98:2021–2028.

10.

Jacobs

, Karavolos

, Rathouz

, Ferris

, Powell

. Limited English proficiency and breast and cervical cancer screening in a multiethnic population. Am J Public Health, 2005; 95:1410–1416.

11.

Morales

, Cunningham

, Brown

, Liu

, Hays

. Are Latinos less satisfied with communication by health care providers?. J Gen Intern Med, 1999; 14:409–417.

12.

Menendez

, Loeffler

, Ring

. Patient satisfaction in an outpatient hand surgery office: A comparison of English- and Spanish-speaking patients. Qual Manag Health Care, 2015; 24:183–189.

13.

Carrasquillo

, Orav

, Brennan

, Burstin

. Impact of language barriers on patient satisfaction in an emergency department. J Gen Intern Med, 1999; 14:82–87.

14.

Baker

, Hayes

, Fortier

. Interpreter use and satisfaction with interpersonal aspects of care for Spanish-speaking patients. Med Care, 1998; 36:1461–1470.

15.

Hampers

, Cha

, Gutglass

, Binns

, Krug

. Language barriers and resource utilization in a pediatric emergency department. Pediatrics, 1999; 103(Pt 1):1253–1256.

16.

Njeru

, St Sauver

, Jacobson

, et al. Emergency department and inpatient health care utilization among patients who require interpreter services. BMC Health Serv Res, 2015; 15:214.

17.

Ngai

, Grudzen

, Lee

, Tong

, Richardson

, Fernandez

. The association between limited English proficiency and unplanned emergency department revisit within 72 hours. Ann Emerg Med, 2016; 68:213–221.

18.

Wilson

, Chen

, Grumbach

, Wang

, Fernandez

. Effects of limited English proficiency and physician language on health care comprehension. J Gen Intern Med, 2005; 20:800–806.

19.

Cohen

, Rivara

, Marcuse

, McPhillips

, Davis

. Are language barriers associated with serious medical events in hospitalized pediatric patients?. Pediatrics, 2005; 116:575–579.

20.

Divi

, Koss

, Schmaltz

, Loeb

. Language proficiency and adverse events in US hospitals: A pilot study. Int J Qual Health Care, 2007; 19:60–67.

21.

Lion

, Rafton

, Shafii

, et al. Association between language, serious adverse events, and length of stay among hospitalized children. Hosp Pediatr, 2013; 3:219–225.

22.

Lindholm

, Hargraves

, Ferguson

, Reed

. Professional language interpretation and inpatient length of stay and readmission rates. J Gen Intern Med, 2012; 27:1294–1299.

23.

Waxman

, Levitt

. Are diagnostic testing and admission rates higher in non-English-speaking versus English-speaking patients in the emergency department?. Ann Emerg Med, 2000; 36:456–461.

24.

Masland

, Lou

, Snowden

. Use of communication technologies to cost-effectively increase the availability of interpretation services in healthcare settings. Telemed J E Health, 2010; 16:739–745.

25.

Chen

, Youdelman

, Brooks

. The legal framework for language access in healthcare settings: Title VI and beyond. J Gen Intern Med, 2007; 22(Suppl 2):362–367.

26.

Betancourt

, Renfrew

, Green

, Lopez

, Wasserman

. Improving patient safety systems for patients with limited English proficiency: A guide for hospitals. Rockville, MD: Agency for Healthcare Research and Quality, 2012.

27.

Justice UDo. Title VI of the Civil Rights Act of. 1964. 42 USC §2000D ET SEQ; Overview of Title VI of the Civil Rights Act of 1964. Vol. 2018. Available at https://www.justice.gov/crt/fcs/TitleVI-Overview (last accessed March 8, 2019 ).

28.

Nápoles

, Santoyo-Olsson

, Karliner

, O'Brien

, Gregorich

, Pérez-Stable

. Clinician ratings of interpreter mediated visits in underserved primary care settings with ad hoc, in-person professional, and video conferencing modes. J Health Care Poor Underserved, 2010; 21:301–317.

29.

Jones

, Gill

, Harrison

, Meakin

, Wallace

. An exploratory study of language interpretation services provided by videoconferencing. J Telemed Telecare, 2003; 9:51–56.

30.

Karliner

, Mutha

. Achieving quality in health care through language access services: Lessons from a California public hospital. Am J Med Qual, 2010; 25:51–59.

31.

Jacobs

, Fu

, Rathouz

. Does a video-interpreting network improve delivery of care in the emergency department?. Health Serv Res, 2012; 47(Pt 2):509–522.

32.

Locatis

, Williamson

, Gould-Kabler

, et al. Comparing in-person, video, and telephonic medical interpretation. J Gen Intern Med, 2010; 25:345–350.

33.

Lion

, Brown

, Ebel

, et al. Effect of telephone vs video interpretation on parent comprehension, communication, and utilization in the pediatric emergency department: A randomized clinical trial. JAMA Pediatr, 2015; 169:1117–1125.

34.

Gany

, Leng

, Shapiro

, et al. Patient satisfaction with different interpreting methods: A randomized controlled trial. J Gen Intern Med, 2007; 22(Suppl 2):312–318.

35.

Schulz

, Leder

, Akinci

, Biggs

. Improvements in patient care: Videoconferencing to improve access to interpreters during clinical consultations for refugee and immigrant patients. Aust Health Rev, 2015; 39:395–399.

36.

StataCorp LLC. Stata statistical software: Release 15 [computer program]. College Station, TX: StataCorp LLC, 2017.

37.

Weber

, Péclat

. A simple command to calculate travel distance and travel time. The Stata Journal, 2017; 17:962–971.

38.

Chiam

, Hoover

, Mosby

, et al. Meeting demand: A multi-method approach to optimizing hospital language interpreter staffing. J Hosp Admin, 2017; 6:21.