345 

Appendices 

Bibliography 

Methodological and Technical Notes 
346 
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B. METHODOLOGICAL AND TECHNICAL NOTES

Definition of a County

The data in this report come from more than 15 secondary data sources. Different institutions organize 

their data into a particular universe of spatial units based on their analytical needs. The county-level data 

files provided by these sources—or sub-county data aggregated from source files—were organized to

meet the Appalachian Regional Commission’s standard representation of the United States as consisting 

of 3,113 counties, which adheres to the Bureau of Economic Analysis’s county-level delineation of the 

nation. However, many of the data sources disaggregate the country into 3,143 “county units” (with some 

slight variation around this number). The data from many of these secondary data sources thus have to be 

converted into the 3,113-county universe, and this is done by combining several county-level units. The 

most frequent example of this takes place in Virginia, where independent cities are combined with 

surrounding counties in order to meet the ARC/BEA organizational structure. If source data provided 

numerators and denominators, these values were used to compute figures such as rates and percentages 

for each indicator. When only computed figures were provided, a weighting variable from another source 

(such as the 2014 American Community Survey (ACS) population figures) was used to create a weighted 

average of values. In rare cases, data from source counties were distributed to more than one of the 3,113 

counties. This was most often necessary for five Alaska boroughs/county-equivalents, which were 

recently reallocated from three county-equivalents. In these cases, values from the three countyequivalents were directly assigned to the new areas based on predominate geographic overlap. 

Mapping Procedures 

The measures included in this report are examined at the county level, with national and regional maps for 

each indicator displaying its variation across counties. For ease of interpretation, the maps for each 

variable were designed to have darker colors represent values indicating poor health status, or values for 

social or behavioral factors that contribute to poor health status.

The value groupings used to determine the color categories in both the national and regional maps are 

determined by the national quintiles of each respective indicator: five groupings with equal numbers of 

constituent counties in each category (with some variation due to rounding, clustering, and suppressed 

data values). The quintiles are determined by using the breaks at the 20th, 40th, 60th, and 80th percentiles of 

the national distribution. Since both the national and regional maps use these national groupings, the

national maps will have the same number of counties in each category.8 The maps for the Appalachian 

Region, however, will not necessarily have an equal distribution among categories and colors, as the

quintiles are based on the national data. For example, if the Appalachian Region as a whole performs 

worse than the national average for any particular measure, it is likely that more than 20 percent of the 

Region’s counties will be shaded in the darkest color on the map. 

 8 The number of counties may vary by one between groups. For example, there are 3,113 counties analyzed, which does not 

divide equally into groups of five, meaning for indicators with complete data, three groups will have 623 and two will have 622.
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Age Adjusting Mortality Rates 

Age adjusting mortality rates allows for comparisons among counties with different age distributions. 

Counties with greater numbers of elderly residents can generally expect higher mortality rates than 

counties with less elderly residents. Thus, a county with higher unadjusted (crude) mortality rates, which 

suggest poor health, may actually be relatively healthy but simply have a larger number of older residents

(and thus a higher overall baseline risk of death). Using data from the Compressed Mortality Files from 

CDC, we compared the distributions of county populations by age cohort to the standard population 

distribution for the country as a whole. Using these population distributions by age cohort as a base, the 

mortality rates in this report are age adjusted and standardized based on the Year 2000 Standard Million 

Population (see Table 71). This provides the reader with the ability to accurately compare mortality across 

counties with different age distributions. Only infant mortality is not age adjusted in this report, because 

the age distribution of a population is not relevant to the measure. The YPLL indicator is obtained directly 

from County Health Rankings & Roadmaps, which age-adjusted YPLL prior to publishing.

Table 71: Year 2000 Standard Million Population for the United States

Age 2000 Standard Population 

Distribution

Under 1 year 13,818

1-4 years 55,317

5-9 years 72,533

10-14 years 73,032

15-19 years 72,169

20-24 years 66,478

25-34 years 135,573

35-44 years 162,613

45-54 years 134,834

55-64 years 87,247

65-74 years 66,037

75-84 years 44,841

85 years and over 15,508

All Years 1,000,000

Source: https://wonder.cdc.gov/wonder/help/cmf.html

The formulas to convert crude rates to weighted rates by age cohort and total population age-adjusted are:

(Deaths / pop) x 100,000 = CRUDE RATE

CRUDE RATE x (standard pop in each age cohort / 1,000,000) = WEIGHTED RATE

Sum (WEIGHTED RATES) all cohorts = AGE-ADJUSTED RATE for total population

In this example, the crude data are reported in increments of 100,000 residents.
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For example, consider the crude and age-adjusted mortality rates in two states: Utah and Maine, the 

former of which has a relatively younger population. Table 72 displays the crude and age adjusted rates 

using two sources: CDC Wonder, an interactive web tool that allows users to calculate mortality rates for 

specific queries, and then also the age adjustment process used in this report. The slight differences in the 

mortality rates between these two sources are due to rounding and the inclusion of deaths with unknown 

ages. Table 72 also shows the process of converting from crude mortality rates to age-adjusted mortality 

rates. While Maine has nearly double the crude rate of Utah, once the data are age adjusted, the rates 

become quite similar in all age cohorts. 

Table 72: Comparison of Crude and Age-Adjusted Mortality Rates for Utah and Maine

Age

Cohort in

Years

Standard 

Million

Population

Utah (Younger Population State) Maine (Older Population State)

Deaths Population Crude 

Rate

Wtd 

Rate Deaths Population CrudeRate

Wtd 

Rate

Under 1 13,818 4,383 840,336 522 7.2 1,345 229,045 587 8.1

1–4 55,317 886 3,256,680 27 1.5 227 947,922 24 1.3

5–9 72,533 501 3,862,337 13 0.9 170 1,291,131 13 1.0

10–14 73,032 600 3,669,490 16 1.2 206 1,427,186 14 1.1

15–19 72,169 1,972 3,698,192 53 3.8 843 1,520,896 55 4.0

20–24 66,478 3,047 4,021,230 76 5.0 1,166 1,314,897 89 5.9

25–34 135,573 6,974 6,764,886 103 14.0 2,568 2,537,252 101 13.7

35–44 162,613 9,417 5,545,348 170 27.6 5,060 3,157,287 160 26.1

45–54 134,834 16,789 4,839,035 347 46.8 12,660 3,540,842 358 48.2

55–64 87,247 25,609 3,575,069 716 62.5 23,653 2,888,520 819 71.4

65–74 66,037 36,825 2,198,826 1,675 110.6 37,485 1,868,337 2,006 132.5

75–84 44,841 62,962 1,308,643 4,811 215.7 61,595 1,160,897 5,306 237.9

85 and 

over 15,508 72,608 475,018 15,285 237.0 70,676 462,785 15,272 236.8

All Years 1,000,000 242,573 44,055,090 550.6 733.8 217,654 22,346,997 974.0 788.0

Table 73: Comparison of Calculated Age-Adjusted Rates with CDC Wonder Reported Rates

State Utah Maine

Data Type Crude AgeAdjusted Crude AgeAdjusted

Calculated Rates 550.6 733.8 974.0 788.0

CDC Wonder 550.7 734.1 974.0 788.0
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Data Suppression and Smoothing 

Accommodations for Suppressed Values

The National Center for Health Statistics of the Centers for Disease Control and Prevention prohibits the 

reporting of death counts and death rates when the unit is fewer than ten cases. This results in rates that 

are suppressed for many counties in the Appalachian Region, as well as elsewhere in the United States. 

To account for this issue, data for counties with deaths below this threshold were augmented by

incorporating data from nearby counties. To calculate the augmented rate for any particular county, a

proportion of deaths (numerator) and population (denominator) from nearby counties were added to the 

base numbers for the target county. The proportion of a nearby county’s information that was added to the 

target’s decreases with increasing distance between the two.

This technique is called smoothing. In addition to overcoming suppression issues, it helps correct for 

unstable measures resulting from small population sizes. When small populations lead to even smaller

numerators—such as occurs in counties with fewer than ten poisoning deaths in a given year—rates can 

be smoothed to eliminate statistical instability. The ten-death criteria for spatial adjustment was applied 

not only for the total number of deaths for any given mortality measure, but for individual age cohorts, as 

well.

Overview of Smoothing Process

The smoothing process applies weights to counties surrounding the county with the suppressed value, the 

“county of interest” in Figure 189 below. The process results in an augmented value resulting from the 

combination of actual data from the county of interest with weighted values from nearby counties. The 

degree to which a nearby county contributes to the augmented value depends on the distance from the 

county of interest to any given nearby county. Figure 189 below demonstrates this principle. The county 

of interest receives a weight of 1.0 and is fully shaded. Closer counties (e.g., the small, dark gray county 

directly to the southeast) have darker shading and higher weights than more distant counties (e.g., the

large, white county further to the southeast). For each county, the number of deaths and populations in 

each age category then multiplies the weights. These numbers are then aggregated across counties by age 

category, and ultimately an age-adjusted rate for the county of interest is calculated.
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Figure 189: Example of Weighting Counties for Smoothing Based on Distance
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Technical Detail

This approach is one we have used in the past (Ricketts & Holmes, 2007). First, we specified the general 

form of the weighting function:

WEIGHT = exp (λ * MILES)

where MILES is the straight-line distance between two county centroids. The parameter λ is constrained 

to be negative, so the weighting function is equal to one if MILES equals zero, is decreasing in MILES,

and is bounded from below by zero. Values of λ that are closer to zero lead to a slower decay—for 

example, a λ of -0.05, will place greater weight on distant counties than a λ of, say, -0.2. In selecting the 

value of λ, there is a tradeoff between faster decay (averaging over counties that are located closer to the 

county with the suppressed value) and using more counties (leading to more precise estimates). This 

approach significantly reduces the number of unreportable area-cause death rates while maximizing local 

influence on the augmented rate. 

We conducted a grid search for the optimal λ using the following approach. First, we randomly chose 

counties in the Appalachian Region to be labeled as suppressed. We then calculated smoothed rates using 

the above methods for a variety of potential λ. We repeated this exercise 1,000 times using a different λ

each time. After each iteration, we calculated the mean squared error, or the average squared difference 

between the smoothed rate and the actual rate (the randomly chosen counties labeled as suppressed in this 

exercise had actual rates and served as the basis for comparison). This method allowed us to identify the λ

with the smallest mean squared error. The λ satisfying this condition was -0.125. We specified the same λ

for all mortality rates. 

With λ now in hand, the approach was as follows. For each suppressed county, we calculated the distance

(MILES) between that county centroid and the county centroid of all other counties. We then calculated 

the weight associated with each county using the weighting function noted above.

Any county with a weight of less than 0.01 was dropped from the analysis. This approach has little 

practical effect on the augmented rate and eases any rounding issues (e.g., a populous county that is very 

distant may still have more weight than a nearby county of moderate size). We aggregated the deaths and 

population (numerator and denominator) across nearby counties—incorporating their weights—to create 

an augmented numerator and denominator for the suppressed county. This augmentation includes any 

deaths and population reported for the suppressed county, as well. At this point, the suppressed county 

has a “smoothed” number of deaths and population, with closer counties contributing more to the value. 

The mortality rate can then be calculated directly from these numbers. 

For age-adjusted mortality rates (everything except infant mortality), the augmentation occurs prior to 

age-adjusting. Table 74 illustrates a simple example in which only two ages are considered: children and 

adults. Five counties are displayed, along with the number of deaths and population for both age groups. 

Distance from County A’s centroid determines the weight for each county. The final four columns 

calculate the weighted deaths and population. Note that County E, with a weight of less than 0.01, does 

not contribute to the aggregation. 
CREATING A CULTURE OF 

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377

Table 74: Sample County Illustration of Augmentation for Suppressed Data

County Deaths Population Age Group

Distance

in 

Miles

Weight

Children Adults

Wtd 

deaths Wtd pop Wtd deaths Wtd pop

A 2 1,000 Children 0 1.000 2.00 1000

A 18 10,000 Adults 0 1.000 18.00 10,000.0

B 2 1,200 Children 5 0.535 1.07 642.0

B 24 11,500 Adults 5 0.535 12.85 6,152.5

C 4 800 Children 10 0.287 1.15 229.6

C 37 7,900 Adults 10 0.287 10.60 2,267.3

D 3 1,500 Children 20 0.082 0.25 123.0

D 27 16,000 Adults 20 0.082 2.22 1,312.0

E 7 2,000 Children 40 0.007 weight < .01 => 0

E 91 18,500 Adults 40 0.007 weight < .01 => 0

TOTAL 4.47 1,994.6 43.7 19,731.8

After the aggregated deaths and population are calculated by age category, age-adjustment occurs using 

the approach outlined above (see Table 75). For purposes of this example, we specify weights of 0.1 

(children) and 0.9 (adults) and thus calculate an age-adjusted rate of 221.7. Note that the example rates 

here—like the mortality rates in the report—are standardized per 100,000 population.

Table 75: Age-Adjusted Step for Spatial Adjustment

Metric Children Adults

Mortality Rate 224.11 221.32

Age-adjusted weights (for example) 0.10 0.90

Weighted rate 22.41 199.32

AUGMENTED AGE-ADJUSTED RATE 221.73
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Reciprocal Measures

In order to report health professional supply measures consistently, we calculated the reciprocal of values 

pulled directly from County Health Rankings. For example, 2016 County Health Rankings Data for Bibb 

County, Alabama shows a Primary Care Physician Ratio of 2,814:1 (persons per physician). We use the 

reciprocal (1/2,814), converted to primary care physicians per 100,000 people. The calculation is as 

follows:

1/2,814 * 100,000 = .000355 * 100,000 = 35.5

Similarly, the dentist ratio of 5,627:1 becomes 17.8 dentists per 100,000. The only health professional 

supply measure that was not calculated in this manner was specialist physicians per 100,000, as County 

Health Rankings does not report this measure. Instead, the data for this measure come from the HRSA 

Area Health Resources File (AHRF).

Rurality in Appalachia 

ARC, in coordination with staff at USDA’s Economic Research Service (ERS), has developed a 

simplified version of the 2013 Urban Influence Codes (UIC) for their research and analytical work. To 

create the UICs, the USDA starts with the official listing of metropolitan Core Based Statistical Areas 

(CBSAs/MSAs) published by the Office of Management and Budget (OMB). The USDA then 

distinguishes metropolitan counties by the population size of their metro areas, and nonmetropolitan 

counties by (i) the size of their largest city or town and (ii) proximity to metro areas. ARC simplified the 

USDA’s original 12-part county classification into the five levels described below. 

1. Large Metros: Metropolitan counties in large metro areas of more than 1 million residents

2. Small Metros: Metropolitan counties in small metro areas of less than 1 million residents

3. Non-metro, Adjacent to Large Metros: Nonmetropolitan counties adjacent to a large metro 

area

4. Non-metro, Adjacent to Small Metros: Nonmetropolitan counties adjacent to a small metro 

area

5. Rural (non-metro, not adj. to a metro): Nonmetropolitan counties not adjacent to a metro area

Table 76 illustrates the USDA twelve county classification system and the crosswalk from the USDA 

categories to the simplified five-class scheme. 
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Table 76: USDA Twelve County Classification System

ARC 

Crosswalk 

Category

UIC Code Description

Metropolitan counties: 

1 1 In large metro area of 1+ million residents 

2 2 In small metro area of less than 1 million residents 

Nonmetropolitan counties:

3 3 Micropolitan area adjacent to large metro area 

3 4 Noncore adjacent to large metro area 

4 5 Micropolitan area adjacent to small metro area 

4 6 Noncore adjacent to small metro area and contains a town of at least 

2,500 residents 

4 7 Noncore adjacent to small metro area and does not contain a town of at 

least 2,500 residents 

5 8 Micropolitan area not adjacent to a metro area 

5 9 Noncore adjacent to micro area and contains a town of at least 2,500 

residents 

5 10 Noncore adjacent to micro area and does not contain a town of at least 

2,500 residents 

5 11 Noncore not adjacent to metro or micro area and contains a town of at 

least 2,500 residents 

5 12 Noncore not adjacent to metro or micro area and does not contain a 

town of at least 2,500 residents 

Population-weighted Averages for Large Geographies

To create measures for geographic units larger than the county, we used population-weighted averages.

We used the same method of calculating these averages for all large geographies, including the United 

States, the Appalachian Region, the five Appalachian subregions, and then also the Appalachian, nonAppalachian, and total values for each state. The groupings of counties based on rurality and economic 

status also used this same methodology. These calculations are necessary because our data sources do not 

contain values for many of the report’s key geographies, such as the Appalachian Region or the 

Appalachian subregions. We thus needed a methodology to apply to all geographic groups in order to 

have a valid comparison. The population-weighted average approach provides a valid, consistent method.

The specific calculation used to generate population-weighted values is described here. Consider i

counties that are members of an area A. Area A could be a state, a specific economic status (e.g. 

distressed), or any other geography or grouping described in the report. The population-weighted average 

for variable x is calculated as the sum of the product of x and the population of each county, divided by 

the sum of the 2014 ACS populations of the counties in the area.
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AAAAAAAAAAAAAAAA = � 1

∑ii∈AA PPPPPPii

��[PPPPPPii ∙ xxii]

ii∈AA

As a result of the population weighting, values in this report for even commonly reported geographies—

such as the United States as a whole—may differ slightly from published sources. However, using this 

population-weighted approach across all geographies ensures an accurate, consistent comparison.

Time Periods of Mortality Measures

For the mortality measures examined in this report, the values for each represent performance over a span 

of years: 2008–2014. This has the effect of reducing suppressed values in low population counties, as well 

as helping smooth single year spikes in mortality. These seven-year periods represent the original time 

period of the data as they are found in the CDC’s Compressed Mortality File.

State-level effects of BRFSS Data

Many of the variables derived from the CDC’s Behavioral Risk Factor Surveillance System (BRFSS)

survey data show sharp state-level border effects. Because the survey is conducted at the state level, 

statistical modeling is utilized by County Health Rankings to develop these county-level values. Due to 

low numbers of responses in many counties, even with these statistical techniques, robust estimates for 

each county are not always possible. As such, county-level numbers oftentimes show little variation in 

any particular state. For more detailed information, please visit the County Health Rankings website.

Box Plots

A box plot is a type of graph that shows the distribution of data. Comparing box plots among different 

groups shows how the median of each group compares to the other groups, how much variation exists 

within each group, and how the variation compares between the groups.

Figure 190: Components of a Box Plot
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The edges of the whiskers and the black line represent specific statistics calculated from the data. For 

example, the black line denotes the median (half of values are greater than this value, half are less than 

this value). The lower and upper edges of the box represent the 25th and 75th percentiles, respectively. 

The 25th percentile is the value for which 25 percent of county values are less, and the remainder (75 

percent) are greater. The 75th percentile is defined similarly. The caps of the whiskers are defined as 

“adjacent values” (Tukey, 1977). The upper adjacent value (“top whisker”) is the largest observed value 

that is less than or equal to the 75th percentile plus 3/2 of the difference between the 75th and 25th 

percentile. The lower adjacent value is defined similarly. Outside values —the dots described as 

“unusually high or low values”—are those values that lie outside the adjacent values.
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