There are several methods of calculating transportation costs. The first step is to determine is how accurate the measure of transportation costs must be. The second step is to choose a method that is feasible and can produce the desired level of accuracy. When transportation costs are very small relative to intervention costs, a reasonably accurate estimate of transportation costs across patients should be sufficient, even if it is known to have error. What methods are feasible will depend on the data available. If transportation distance is directly reported on a study form, then no more information is necessary. If distance must be estimated, the patient's zip code will be needed. Having the full street address will allow the most accurate estimation.

## Transportation: cost or quality adjustment?

There is controversy over whether patient time spent in obtaining medical care should be included as a cost, or in the quality adjustments made to the years of life of survival. Most often they are included as costs. The Public Health Task Force book on cost-effectiveness analysis (Luce et al., 1996) discusses the issue.

## Components of transportation cost

### Cost per mile

Patients may use public or private transportation. The cost of public transportation is the fare. The cost of private transportation is not observed and therefore must be estimated. The simplest method is to multiply the number of miles traveled by a reimbursement rate per mile, such as the amount allowed by the U.S. Internal Revenue Service for business expenses. The rate may be found by searching the agency's web site. In 2012 the rate was 55.5 cents/mile.

Using the IRS rate assumes that every mile costs the same, regardless of the number of miles traveled. The analyst must decide whether these assumptions are reasonable based on the study question and the geographic areas under consideration. Most patients will use the same mode of transportation, and thus incur the same expense for every trip. For this reason, it often suffices to capture transportation details only once. However, in studies where transportation costs are relatively large, or where modes of transportation may change, it may be necessary to collect data on each trip. The investigator should examine this issue carefully; collecting data on each trip can be costly and is usually unnecessary.

### Calculating transportation distance or time

Transportation distance may be measured directly, or it may be inferred from travel time. Travel distance is easier to measure than time. The distance from a patient's residence to a health care facility is fixed, whereas travel time varies with the mode of transportation and traffic conditions. Public transportation, for instance, is often slower than private modes.

As noted earlier, the analyst should also calculate the value of time spent traveling to, and receiving care. If time is measured directly, then the remaining step is to assign a value to it. If distance is measured instead of time, then one must determine a typical time based on the distance traveled.

*Geographic Information System (GIS) programs*

Standardized transportation times are now available for many trips within the U.S. These calculations are derived from geographic information system (GIS) programs. GIS programs can estimate the actual transportation distance with greater accuracy, but there are also errors in these calculations. The distances that GIS programs estimate depend on which roads are included in the transportation network and the logic the program uses to determine transportation routes. GIS programs sometimes choose a route that a traveler with local area knowledge would not normally take.

Using a GIS program to calculate transportation time from a patient's residence to a health care facility requires the complete address for each patient, something unavailable in most secondary healthcare datasets. Furthermore, this level of detail is now harder to obtain, given the privacy requirements of the Health Insurance Portability and Accountability Act (HIPAA). If data on complete addresses are available, it doesn't require much effort to make full use of these data. Modern GIS programs will calculate both the transportation distance and the estimated transportation time between any two points in the U.S. and in many other countries.

If full addresses are not available, the patient's zip code of residence can be used to calculate transportation time with only a small loss of accuracy. In this case the starting point will be the population centroid of the zip code instead of the patient's home.

Many sources offer the latitude and longitude of the population centroid of each zip code within the U.S. VA users may obtain these data from the Planning Systems Support Group (PSSG) intranet page (Intranet-only: http://vaww.pssg.med.va.gov) The PSSG VAST data include a dataset with locations of all VA facilities and the distances from each zip code to the nearest VA inpatient and outpatient facilities. These data also map zip codes without area (zip codes that are only for post office boxes) to the enclosing zip codes.

For Veterans enrolled in VHA, the Planning Systems Support Group (PSSG) maintains a location file that is updated quarterly with information from the US Postal Service National Change of Address file. This file uses geo-coding to estimate travel distances and travel times to the nearest VA facility that provides primary, secondary, and tertiary care. Note, some Veterans will receive care at other facilities, so the distances from this file don’t necessarily correspond to the travel distance/time for specific clinical encounters. For more information about this file, visit the PSSG web site (Intranet-only: http://vaww.pssg.med.va.gov).

To avoid obtaining a distance of zero for patients who live in the same zip code as the provider's location, add a small distance to the patient's transportation. One method is to make an adjustment based on the area that the zip code encompasses, which is included in most zip code data files. Assuming that 0.5 times the square root of the area [sqrt (Az)] is an approximation of the radius of a zip code, and that the population will tend to cluster towards the population centroid, 0.125 times the square root of the area of the zip code is one possible adjustment:

Distance within a zip code = .125 * sqrt(Az)

This will avoid assigning any patient-provider pairs with a zero distance, while providing an adjustment to distance that is based on the area of each zip code.

*Straight-line distance*

A straight-line distance often provides sufficient information for estimating patient transportation costs. Phibbs and Luft (1995) found a very high correlation between straight-line distances and actual transportation times for transportation on a road network. They estimated regressions to predict transportation time from distance for distances less then 15 and 30 miles. The resulting formulas were:

For distance < 15 miles: Transportation time (minutes) = 2.75 + 1.78 * distance (miles)

For distance < 30 miles Transportation time (minutes) = 3.42 + 1.70 * distance (miles)

Transportation distance will be somewhat greater than straight-line distance. Based on available information, 1.4 appears to be an appropriate adjustment factor for the short trips that represent most transportation from home to health care providers.

*Calculating distance between two points*

The following is based on information from a web page, "What is the best way to calculate the distance between 2 points?" written by Robert Chamberlain of the Jet Propulsion Laboratory. The formula listed below is what Chamberlain considers as the most appropriate for computing patient transportation costs.

The actual calculation of the distance between two points can be a complex problem influenced by factors such as elevation, curvature of the Earth, and the fact that the Earth is not quite a sphere. The method below is an approximation that works quite well for points fairly close to each other, which is the typical application for transportation for health care.

Presuming a spherical Earth with radius R (see below), and the locations of the two points in spherical coordinates (longitude, latitude) are lon1, lat1 and lon2, lat2, then the Haversine Formula (Sinott 1984) will give mathematically and computationally exact results. The intermediate result c is the great circle distance in radians. The great circle distance d will be in the same units as R. We provide the inverse tangent version of the Haversine Formula:

dlon = lon2 - lon1

dlat = lat2 - lat1

a = (sin(dlat/2))^2 + cos(lat1) * cos(lat2) * (sin(dlon/2))^2

c = 2 * atan2( sqrt(a), sqrt(1-a) )

d = R * c

For R, use 3957 miles (6367 km), which is the radius of curvature at 30° latitude; the use of other possible values results in very small differences. Most computers require the arguments of trigonometric functions to be expressed in radians. To convert lon1, lat1 and lon2, lat2 from degrees, minutes, and seconds to radians, first convert them to decimal degrees. To convert decimal degrees to radians, multiply the number of degrees by:

pi/180 = 0.017453293 radians/degree.

Inverse trigonometric functions return results expressed in radians. To express c in decimal degrees, multiply the number of radians by

180/pi = 57.295780 degrees/radian

(But be sure to multiply the number of radians by R to get d.)

## Other Considerations

There may be transportation costs that are not captured by travel distance alone. These include costs that do not vary with distance, such as parking fees, bridge tolls, and road tolls, and specialized modes of transportation that may be required by persons with disabilities. The analyst should work with clinicians and study site teams to determine whether these will apply. Such information can be gathered from patients using survey forms.

## References

Luce BR, Manning WG, Siegel JE. Estimating costs in cost-effectiveness analysis. In: Gold, M.R., Siegel J.E., Russell L.B., and Weinstein M.B., eds. __Cost-effectiveness in health and medicine__. New York: Oxford University Press, 1996.

Phibbs CS, Luft HS. Correlation of travel time on roads versus straight line distance. Medical Care Research and Review 1995 Nov;52(4):532-542.