(Mostly) Vindicated: Euclidean measures of distance are just as good as high priced, fancy measures

DistancePlotsITNIn my seminal paper, “Distance to health services influences insecticide-treated net possession and use among six to 59 month-old children in Malawi,” I indicated that Euclidean (straight line) measures of distance were just as good as more complicated, network based measures.

I didn’t include the graph showing how correlated the two were, but I wish I had and I can’t find it here my computer.

Every time I’ve done presentations of research of the association of distances to various things and health outcomes, someone inevitably asks why I didn’t use a more complex measure of actual travel paths. The idea is that no one walks in a straight line anywhere, but rather follows a road network, or even utilizes a number of transportation options which might be lost in a simple measure.

I always respond that a straight line distance is as good as any other when investigating relationships on a coarse scale. Inevitably, audiences are never convinced.

A new paper came out today, “Methods to measure potential spatial access to delivery care in low- and middle-income countries: a case study in rural Ghana” which compared the Euclidean measure with a number of more complex measurements.

The conclusion confirmed what I already knew, that the Euclidean measure is just as good in most cases, and the pain and cost of producing sexy and complicated ways of calculating distance just isn’t worth it.

It’s a pretty decent paper, but I wish they had put some graphs in to illustrate their points. It would be good to see exactly where the measures disagree.

Background
Access to skilled attendance at childbirth is crucial to reduce maternal and newborn mortality. Several different measures of geographic access are used concurrently in public health research, with the assumption that sophisticated methods are generally better. Most of the evidence for this assumption comes from methodological comparisons in high-income countries. We compare different measures of travel impedance in a case study in Ghana’s Brong Ahafo region to determine if straight-line distance can be an adequate proxy for access to delivery care in certain low- and middle-income country (LMIC) settings.

Methods
We created a geospatial database, mapping population location in both compounds and village centroids, service locations for all health facilities offering delivery care, land-cover and a detailed road network. Six different measures were used to calculate travel impedance to health facilities (straight-line distance, network distance, network travel time and raster travel time, the latter two both mechanized and non-mechanized). The measures were compared using Spearman rank correlation coefficients, absolute differences, and the percentage of the same facilities identified as closest. We used logistic regression with robust standard errors to model the association of the different measures with health facility use for delivery in 9,306 births.

Results
Non-mechanized measures were highly correlated with each other, and identified the same facilities as closest for approximately 80% of villages. Measures calculated from compounds identified the same closest facility as measures from village centroids for over 85% of births. For 90% of births, the aggregation error from using village centroids instead of compound locations was less than 35 minutes and less than 1.12 km. All non-mechanized measures showed an inverse association with facility use of similar magnitude, an approximately 67% reduction in odds of facility delivery per standard deviation increase in each measure (OR = 0.33).

Conclusion
Different data models and population locations produced comparable results in our case study, thus demonstrating that straight-line distance can be reasonably used as a proxy for potential spatial access in certain LMIC settings. The cost of obtaining individually geocoded population location and sophisticated measures of travel impedance should be weighed against the gain in accuracy.

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About Pete Larson

Assistant Professor of Epidemiology at the Nagasaki University Institute for Tropical Medicine

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