Besides state and higher-level health care expenditures, county level HCE are useful, integral really. For example, to promote the Triple Aim (the best care for the whole population at the lowest cost) you need per capita HCE. And knowing those costs at the county level would help a lot. However, county estimates generally don’t exist. They didn’t in Washington State until a client needed cost estimates for our 39 counties. To supply those estimates I used a regression approach resulting in this model:
percaphce = +0.1*percapinc + 247*pctage65 + 0.71*percapmedaid + 10.5*pctrural – 1349
Washington State Context
Before discussing model rationale and county HCE estimation, here’s some context about Washington State and its counties. You might view Washington as a microcosm of the nation. It has mountains, forests, deserts, rivers and lakes, vast rural areas, major cities, diverse populations and industries, and a varied climate. It is distinguished by active volcanoes and a coastal border. There is a wide range of political, social and economic clusters. In 2010 King County, where Seattle is located, median annual household income was about $67 thousand (the U.S. median was roughly $50 thousand) yet there are state counties where one in three children live in poverty. The total population is approximately 7 million with half of those people living in just three of the 39 counties.1 At the other end about a third of the counties have populations of 30 thousand or less.
An Aside about Seattle Weather
You may have been told that it rains all the time in Seattle. I live in Seattle and can tell you that’s a myth. Seattle’s average annual rainfall is less than New York City’s. However, during a good part of the non-summer months Seattle, and Puget Sound generally, is grey and cloudy. I once heard a story about the original settlers who landed in November, 1851, at Alki near present-day Seattle. The story is they were there for months before the weather finally cleared and they saw Mt. Rainier for the first time. I don’t know if that story is historically true, but as a Seattleite it’s believable. Regardless, Seattle is a summer paradise. Seattle summers, like most of Puget Sound, are characterized by pleasant sunny days, cool nights and no mosquitoes.
Background for the County HCE Estimates
Last year Empire Health Foundation of Spokane, Washington, asked me to estimate HCE for the 39 counties in the state. The purpose was for an upcoming meeting of policy types such as county commissioners, members of various health organizations, and other stake holders. A theme would be Donald Berwick’s Triple Aim, so cost estimates were wanted for benchmarks and context. The CMS2 Office of the Actuary had recently developed state HCE.3 If I could build a reasonable regression model on state-level data to predict state HCE, and there were similar variables at the county level, I could use the state model to estimate county HCE. That’s the approach I took. A caveat is my understanding was that acceptance—believability and reasonableness of the estimates to a lay audience—were as important as accuracy.
I explored various variables for a model and asked knowledgeable people and likely stake-holders what variables they thought should be included. In the end I settled on four 2010 predictor variables: per capita personal income, proportion of seniors (age 65 and older), per capita Medicaid expenditures, and percentage of the population living in rural areas. The response variable at the state level was the 2009 CMS health care expenditure estimates. These were all the most recent data.
At least for the U.S., income is a well known determinant of HCE: the more you make, within limits, the more you spend on health care. Estimates of personal income at state and county levels were readily available.
The percentage of people age 65-plus is an important variable in that close to half of total lifetime HCE occur during the senior years. And data are available at the state and county level. (An alternative might be local Medicare expenditures but I didn’t try that. It seemed that percentage of seniors was conceptually simple and straightforward so I went with it.)
I included Medicaid expenditures because, 1. I wanted to metaphorically anchor the model and, 2. account for government expenditures for the disadvantaged. Conceptually, the problem I had with this variable was the variability between states regarding eligibility of adults and that the number of cases versus expenditures are much different between adults and children (on average children account for the majority of the cases while adults can make up the bulk of expenditures). Nevertheless, Medicaid seems to have worked as a variable in the model. However, getting the county data was an unexpected problem in that I was told by the state agency involved that they could get me the data but when it came down to rug cutting they couldn’t. I was able to piece together sufficient data but that glitch pushed me up against the deadline. The state Medicaid data used was about 95 percent complete.
The fourth variable, percentage rural, is interesting. Just about everyone I discussed variable selection with told me I had to include a measure of how rural a county was. So just in terms of believability I felt I had to include rural. Percentage rural at both the state and county level was available from the decennial census, so that’s what I used. My initial understanding, with about a week to go, was that percentage rural from the 2000 census was all that was published; the 2010 estimates wouldn’t be out for many months. A week later I submitted my work to Empire Health Foundation. The very next day the Census Bureau released the 2010 estimates. OK. I updated the results and resubmitted. Regardless, it turns out that percentage rural (2000 or 2010), at least as measured by the Census Bureau, is not an important predictor for HCE. More on that later.
The model presented for the meeting had different coefficients than the one given here, and originally I didn’t include the constant term, which was essentially zero. The results for the meeting made sense: counties you’d expect to have high per capita expenditures were high and conversely, the adjusted R-squared was a decent 0.71, and when I averaged the 39 county estimates the result was very close to the overall state average from the Office of the Actuary estimates.
For all that, a subsequent second look showed the model was biased. It was biased because of Alaska which had by far the lowest percentage of seniors, and the second highest HCE in the nation, i.e. Alaska was an outlier with respect to age and HCE. This was readily seen in a plot of pctage65 v. residuals.
Recall that I had built the model based on the 50 states and then imported it to Washington’s counties by substituting county data. Redoing the state-level regression without Alaska, using 49 states, corrected the bias4 and increased the adjusted R-square to an excellent 0.8, the regression diagnostics were clean, and averaging county estimates gave satisfactory results. The county-level estimates with the updated model were again reasonable but with more extreme tails, i.e., originally high HCE counties were now even higher, and conversely low ones were lower. For example, San Juan County had the highest HCE county with many wealthy retired people while Whitman County, the home of Washington State University, had the lowest with a quarter of the population being age 25 or younger and in the bottom quartile in per capita income. The updated model, coefficients rounded, is the model given above and repeated here (variables listed in order of importance). The coefficients themselves are interesting.
percaphce = +0.1*percapinc + 247*pctage65 + 0.71*percapmedaid + 10.5*pctrural – 1349,
The model says that: for every additional $10 someone earns, a dollar goes to health care; a one percent increase in the percentage of seniors increases per capita HCE by almost $250; that a $1 increase in per capita Medicaid increases total per capita expenditures by 71 cents; each percentage increase in rural designation increases per capita HCE by $10.50; and after doing the multiplications and adding, subtract off $1,350 for a final per capita HCE estimate.
For those who would like access to the details, the county estimates along with the inputs are available in the first workbook of an Excel file, retrieved by clicking here. The state-level data used to build the model and the summary regression statistics are in the second workbook.
More on the Rural Variable
Based on this model and data, percentage rural is not an important predictor for HCE. The Census Bureau measure used, urban v. rural population clusters, was barely significant at 0.05 and when left out of the model had minimal affect on the adjusted R-squared (0.78 compared with 0.80 when rural is included). Perhaps there’s some other measure of rural at the county as well as state level?
In terms of averages, rural residents have less income, generally worse social determinants of health, and so have more morbidities than urban populations. Furthermore they often have health care access constraints. But just as increasing income is related to increasing HCE, so is decreasing income associated with lower expenditures. We know low income is associated with poorer health, so rural populations have greater health care needs—thus the common perception that rural would be an important variable. But it’s not for predicting HCE. However, families living in rural areas do spend proportionally more of their income on health care, though in absolute terms their HCE are similar to urban families.5 So expenditures relative to income, were it available, would likely be a better metric in analyzing rural HCE.
The analysis used 2009 HCE data. The Office of the Actuary won’t have new estimates before 2016. In the meantime to use the existing per capita HCE estimates there’s little to be done except adjust for health care inflation. Inflation estimates are available from the October 2013 Health Affairs.6 That article, authored by nine analysts from the Office of the Actuary, gives the inflation factor for 2010-2012 as 3.9%; 3.8% for 2013; 6.1% for 2014; and 5.8% for 2015. Note that if you were to convert from per capita to total county expenditures, you’d also want to adjust for expected county population growth (which in Washington State should be available from the Office of Financial Management).
The state level estimates don’t include costs of insurance program administration, research or construction expenses. I don’t know how these might vary by state or by county so I ignored them. However, national estimates of those three components are in the July 2012 Health Affairs.7 For 2010 the three were estimated to be $495 out of $8,402, or almost 6% of per capita national health care expenditures.
Frank de Libero is an independent statistical consultant oriented toward policy and strategy. He blogs regularly at Letting the Data Speak, where this post originally appeared.
- The three highest population counties are King, Pierce and Snohomish. Summary county demographic and geographic information is at: http://en.wikipedia.or/wiki/List_of_counties_in_Washington. ↩
- CMS: Centers for Medicare & Medicaid Services ↩
- Data links are supplied in the Excel file noted in the last paragraph of the Resultssection. ↩
- This could also have been corrected by including a squared term for age (i.e., seniors) but I opted for keeping the model simple by just excluding Alaska. ↩
- See, e.g., http://www.bls.gov/opub/btn/volume-2/expenditures-of-urban-and-rural-households-in-2011.htm ↩
- Found at http://content.healthaffairs.org/content/early/2013/09/13/hlthaff.2013.0721.full.html.↩
- See Exhibit 1 in http://content.healthaffairs.org/content/early/2012/06/11/hlthaff.2012.0404.full.html.↩