Endocrinologist data
The NPI Registry is part of the Health Insurance Portability and Accountability Act of 1996 Administrative Simplifications standard which is issued by the Centers for Medicare and Medicaid Services through the National Plan and Provider Enumeration System [15]. Since December 2012, the NPI Registry data is released and updated weekly and provides timely information for individual physician and physician group practices. It has a unique 10-digit identification number for each covered health care provider regardless of whether he/she is in individual practice or in a group practice.
This study used NPI Registry data released on July 9, 2012 using health care taxonomy code Endocrinology, Diabetes & Metabolism 207RE0101X and Pediatric Endocrinology 2080P0205X [16]. After excluding physicians practicing in US territories and outside the US, the study included 6,501 adult endocrinologists with practice locations in the 50 states and the District of Columbia (DC). There were only 1,203 pediatric endocrinologists in 47 states and DC and no pediatric endocrinology practices were identified in Idaho, Montana and Wyoming in 2012. Each endocrinologist was geocoded to his/her practice location’s street address.
Population counts
Population counts at the census block level were obtained from Census 2010 Summary File 1. The US census block is the smallest geographic census unit [17], which is typically bounded by visible features such as streets, roads, and streams, or by nonvisible boundaries such as selected property lines and city, township, school district, and county limits [18]. We used the census block as the initial geographic unit to calculate potential population geographic access to an endocrinologist and were able to aggregate data to higher geographic levels (census tract, county, state, national, and areas defined by urban/rural status). We retained 6,207,027 out of 11,155,486 census blocks in the analysis and excluded 4,948,459 uninhabited (44.4 %) census blocks in the 2010 US Census. Urbanized areas have been defined by the Census Bureau as areas consisting of multiple census blocks with combined populations equal to or greater than 50,000; urban clusters as areas with populations of at least 2,500 and less than 50,000; and rural areas as all other remaining areas [19]. Each census block is identified by the Census Bureau as belonging to an urbanized area, urban cluster, or rural area.
Census block internal geometric centroids were used to calculate distances to endocrinologist practice locations. The population counts of blocks were also stratified into three age groups: 0–17, 18–64 and ≥65 years. Those population counts were linked with their corresponding census block centroids. Because we did not have data on the proportion of pediatric patients who were treated by adult endocrinologists, we only used pediatric endocrinologists to estimate the accessibility to pediatric endocrinologists for children 0–17 years old, following the example of Lee (2008).
Buffer zones around endocrinologist practice locations
Our general approach to estimating population geographic access to endocrinologists is broadly similar to that used in floating catchment area (FCA) spatial accessibility metrics [20–24]. The FCA metric most closely aligned to our approach is the two-step floating catchment area (2SFCA) [20]. 2SFCA provides a flexible approach to quantify population access to spatial opportunities within a predefined distance searching boundary. An important difference in our approach is that we used Euclidean distance between census block-level populations and endocrinologists to measure geographic accessibility. 2SFCA most commonly uses driving distances or driving times, but because our study was national and the basic unit of analysis was the census block level, this particular network analysis approach was computationally impractical. Instead, we chose to use the simpler Euclidean distance. By using each endocrinologist practice location as a center, we used a specific radius to create a circular area as a buffer zone (Fig. 1) and to identify the total population residing within that buffer zone. Extensions of the 2SFCA, such as the Enhanced 2SFCA [21], the Kernel Density 2SFCA [22], the Three Step FCA [23], and the Modified 2SFCA [24], specifically acknowledge variations in travel likelihood due to increased distances, and account for this by incorporating distance decay functions as weights. All these FCA methods adopted a single predefined distance search boundary, such as 15 miles or 30 or 60 travel/driving minutes. Considering variations in distance decay and population density across the US, particularly given the nature of urban/rural landscapes, we used a series of radii (5, 10, 15, 20, 30, and 50 miles) around each endocrinologist practice location to account for different transportation modes used to access endocrinologists. We assumed 5-mile and 10-mile distances to be reasonable proxies for travel by public transportation in urban areas; 15-mile and 20-mile distances to be approximate 20–30 min travel time by automobile; and a 50-mile distance to be approximately equal to 1 h of travel time by automobile, which may be more typical of travel time from a rural area to a regional medical center. If a census block’s centroid was inside a specific buffer zone of an endocrinologist’s location, all (100 %) of the population in that block was assumed to have access to that endocrinologist.
Geographic access to an endocrinologist
We used three methods to calculate/illustrate geographic access to an endocrinologist. The first method was to estimate the coverage rate – the percentage of population within a geographic area (i.e., county, state, nation, or urban/rural area) that was within a specific radius distance or buffer zone for at least one endocrinologist. The second method was to estimate the total number of endocrinologists for a specified census block. And the third method was to calculate the population-to-endocrinologist ratio in a geographic area.
Estimating the coverage rate
For the first metric, we accounted for geographic access to endocrinologists, regardless of the political boundaries, with the only consideration being distance to endocrinologist practice locations. The circular buffer zone approach was used to estimate the number of the population with access to each endocrinologist within a defined geographic area [25] . We identified the population within and outside of a specific buffer zone to calculate the percentage of the population who had access to at least one endocrinologist for defined geographic areas (e.g., state, county, nation, urban/rural areas).
Estimating total number of endocrinologists for a specified census block
For the second metric, we equally divided an endocrinologist by the total number of persons (Pi) in an endocrinologist-identified circular buffer zone; thus each person in that circular buffer zone has 1/Pi share of that particular endocrinologist. This step is conceptually the same as calculating the supply-to-demand ratio of the 2SFCA. Each person can be covered by multiple individual circular buffer zones of endocrinologists (i = 1, 2, 3, …, n), so the total number of endocrinologists covering a particular person at a block centroid location (Eb) is the sum of 1/Pi of conjoined buffer zones, which is a measure of individual spatial accessibility to endocrinologists. This step is mathematically equivalent to the second step of the 2SFCA. Here, we aggregated for each census block all the buffers that contain that census block’s centroid. Since the census block is the smallest unit of census geography, the total number of shares of the endocrinologist for a census block will be the sum of the individual share multiplied by the total number of population Pb in that census block. For any geographic area (a) above the census block (e.g., county, state, or nation), the total number of endocrinologists is the sum of endocrinologists of all the blocks (b = 1, 2, 3… m) in that geographic area (Fig. 1).1).
$$ \begin{array}{l}{\mathrm{E}}_{\mathrm{b}}={\mathrm{P}}_{\mathrm{b}}\times {\sum}_{\mathrm{i}=1}^{\mathrm{n}}\left(\frac{1}{{\mathrm{P}}_{\mathrm{i}}}\right)\\ {}{\mathrm{E}}_{\mathrm{a}}={\sum}_{\mathrm{b}=1}^{\mathrm{m}}{\mathrm{E}}_{\mathrm{b}}\end{array} $$
a: specified geographic area (county, state, national, or urban/rural area)
b: specified census block
Pi: total persons in a circular buffer zone around each endocrinologist
Pb: total number of persons in a specified census block
Eb: number of endocrinologists for a specified census block
Ea: number of endocrinologists within a specified geographic area
n: number of endocrinologist buffer zones
m: number of blocks within a specified geographic area
Ratio of population to endocrinologist
Because our research is situated in public health practice, with a focus on the population, we calculated the population-to-endocrinologist ratio (Ra). This ratio is the count of covered population per each endocrinologist for each geographic area within a specific circular buffer zone. More formally, it is the total covered population of a geographic area (Pa) divided by the total number of the endocrinologists within that geographic area (i.e., Ra = Pa/Ea). In this study, we used this approach to examine the ratio by state, county, urban/rural areas, and distance or radius within specified buffer zones.
ArcGIS version 10.0 (Esri, Redlands, CA) with ArcGIS Online 10.0 North America Geocode Service was used to obtain the geographic coordinates (latitudes and longitudes) of endocrinologist practice locations, to calculate the access metrics, and to map the final results.
Ethics statement
This study used only publically available data and did not constitute human subjects research.