On Ending a Health Care Fallacy

Here it’s argued that we need to retire the health care fallacy, “We spend more on health care than other rich countries but have worse outcomes.” The fallacy implies U.S. health care is deficient in spite of being costly. Indeed our health care costs too much, but there is little evidence that our care is less effective than care in other countries. On the other hand, there’s plenty of evidence that our social determinants of health are worse.

The argument segues off a recent article by Victor Fuchs. The case is presented by using a simple linear model to explore how life expectancy might change when we substitute the numbers of other countries’ determinants of health for U.S. numbers. After making these substitutions and holding health care spending constant the model predicts U.S. life expectancy is right there with the other OECD countries, 81.6 years compared to their average 81.4 years. This what-if modelling makes clear what should be obvious but the fallacy hides, that health care is only one part of population health.

The Fuchs Essay
Victor Fuchs’s recent essay1 impressed me. He wrote of the lack of a positive relationship between life expectancy and health care expenditures (HCE) in OECD countries. A chart was included for empirical support. I liked the idea behind the chart which demonstrated his point using data from select countries and our 50 states. Professor Fuchs has written on this topic for years (e.g., in his 1974 book “Who Shall Live?”). I posted on the fallacy in March 2013 but was not as nuanced.2

Building a Model
In the JAMA essay Fuchs empirically demonstrates his point. Let’s extend his idea. We’ll keep a measure of HCE, use life expectancy as the outcome, restrict the modelling data to the United States, and represent two other dimensions, an environmental and a socioeconomic dimension. If this simple mathematical model reasonably predicts life expectancy, and it does, then we can substitute OECD values3 for the two dimensions to see how longevity might change while holding expenditures constant. In this way we’d observe the likely effects on longevity due only to epidemiological changes.

Percentage Rural as the Environmental Dimension
As a relevant aside, I was a medic in the army. I took my medical training, circa 1959, at Fort Sam Houston, Texas, before being sent to Germany. I was impressed, especially having been born and raised in New York City, by the size and spaciousness of Texas. While there I heard the following story. During World War II some German prisoners were sent stateside, some of these to Texas. Two or three of the Texas POWs escaped. They were recaptured three days later and were incredulous to learn that after three days on the run they were still in Texas.

Anyone who’s been to Europe surely has been struck by how many more people per unit area there are compared to our country. The numbers bear this out: in 2007 on average the U.S. had 84 persons per square mile, France 289, Germany 609, and the UK 650 persons per square mile.4 There are countries, such as Sweden and Ireland, which are less dense but on average the 24 OECD countries used by Fuchs and used here have more people per unit area than in the United States. And, unsurprisingly, average national density correlates with the percentage of people who live in rural areas.

Noting a Potential Problem
According to OECD estimates, the percentage of people in the U.S. living in primarily rural areas is 37.7%, while the median for the remaining 24 OECD countries is 20.8%.5 However, the U.S. Census Bureau and the OECD measure percentage rural differently which creates a challenge. The U.S. estimate, from the 2010 census, of percentage of persons living in rural areas is 19.3% compared to OECD’s 37.7%, a significant difference. More on this shortly.

Rural Matters
Earlier this year I posted on estimating county HCE.6 During the model’s variable selection phase I was told by everyone I spoke with “to be sure and include a measure of rural”. It’s widely recognized in the health community and literature that rural living is negatively associated with population health; that as the percentage of people who live in the rural environment increases, population health gets worse. For instance, on country roads there are more fatal accidents per capita, and if you don’t die right off you have less access to emergency facilities, and if you do make it to the ER alive, there may not be an attending physician with the expertise you need. Rural populations tend to be poorer, less educated, older, and generally have fewer opportunities.7 Reading some of their literature, other OECD countries have similar rural health issues as we do; it’s just they’re less rural as a percentage of the population, in itself suggesting their overall average life expectancy would be higher than ours.

Child Poverty as the Socioeconomic Dimension
Child poverty is obviously not directly related to life expectancy in the same year. However, the same milieu that permits child poverty may well also shorten life. I tend to use child poverty as a measure instead of general population poverty because children are obviously not responsible for their situation, and child poverty can more readily stand-in, conceptually, as a metric of societal health. The child poverty plot that follows distinctly shows its associated deleterious health effect, just as the rural environment has a negative effect. Also child poverty in the U.S. is about double what it is in the OECD, roughly 20% versus 10%, so it’s a good candidate for inclusion as a variable in the model.

What the Variables Look Like
The what-if model has life expectancy as the response variable and three explanatory variables: percentage of people living in rural areas as defined by the U.S. Census Bureau;8 Child poverty, again as defined by the Census Bureau;9 and Bureau of Economic Analysis’ per capita state GDP in conjunction with state-level HCE.10 The data points represent the states.

Just concentrating on the overall trends for the moment, both percentage rural and child poverty have highly significant negative linear trends relative to life expectancy. As the two variables rural and poverty increase, average life is shortened. Though not shown, there’s barely a significant correlation between child poverty and percentage rural. This lack of collinearity helps keep the model simple. Lastly, just as Fuchs demonstrated, there’s no important relationship between HCE and longevity.11

The Model
These three explanatory variables were used to construct a model to predict life expectancy. The initial construction was encouraging, the model was highly significant with an adjusted R² = 0.63.12 However, regression diagnostics (which included the above graph and Cook’s D, a measure of influence) showed there were two decidedly influential outlier states, VT and ME. They are obvious in the percentage rural plot, where both states have above average life expectancy yet are the highest in percentage rural. This is contrary to expectation; what’s going on? Well, according to at least one study VT was ranked number 1 in social capital and ME number 3.13 Talk about the importance of social determinants of health! (NH was number 2.) Furthermore, ME was an outlier on the expenditures dimension, which also makes sense: the states with the three oldest populations in order are ME, WV and lastly FL. Older populations mean higher HCE. While Mississippi is the poorest state in the nation, has the highest poverty rate, and the shortest longevity of all 50 states.

Having the highest Cook’s D values we take VT and ME out, so the final model is based on 48 states. The adjusted R² is 0.69 (i.e., the model explains about 69% of the variance in life expectancy), percentage rural and child poverty are both significant at p < 0.001 while the expenditure variable is not statistically significant. The signs of the coefficients make sense: as rural and poverty increase longevity decreases, and though not significant, HCE is positive, i.e., money spent on health care contributes some to longevity. It appears that we’ve been successful. With coefficients rounded to practical significance here’s the model used for prediction:

LifeEx = – 0.06PctRural – 0.2ChPov + 0.044HceGdp + 83.54.

Using the Model to What-If
Now we run into a measurement snag. The OECD measures poverty and rural differently than we do. The difference in poverty is not bad. We have traditionally carried forward a 1960’s breadbasket approach. It’s in the process of change but for now the official measure uses the old method, which gives the 2010 child poverty rate as 21.6%. On the other hand, the OECD estimates poverty as income below 50% of median family income. They estimate U.S. child poverty at 21.2% compared to our 21.6%. Assuming that small difference is representative for other OECD countries we ignore the discrepancy and simply accept the OECD median, 10.0%, at face value and substitute it into the model.14

On the other hand, there’s a much bigger difference between the respective estimates of percentage of people living in rural areas, the Census Bureau’s 19.3% compared to the OECD calculation of 37.7%. The Census Bureau estimates the percentage of persons living in urban areas and clusters and what’s left over is deemed percentage rural. The OECD defines rural differently, and furthermore they have recently revised their methodology.15 To move past this difference, we proportionally adjust the OECD (other than U.S.) median of percentage rural, 20.8%. Specifically, we let 19.3/37.7 = x/20.8, giving the OECD median rural value of 10.5% as though it were determined by the Census Bureau. This is what we’ll use for substitution.

The Result
Finally the model can give us an idea how U.S. life expectancy might be if we had a similar environment and social milieu. Substituting the OECD median values, 10.5% (rural) and 10.0% (poverty), and the U.S. unweighted average HCE as a percentage of state GDP, into the model:

Life expectancy = – 0.06*10.5 – 0.2*10.0 + 0.044*15.6 + 83.54
= 81.6, which is similar to the OECD average of 81.4 years.

There’s essentially no difference which suggests that our average life expectancy would be comparable to like countries through environmental and socioeconomic changes. This underscores the lack of substance in the health care fallacy.16

Variables Not Included
We picked just two of possible variables and so the model has room for improvement. Another candidate for inclusion, a variable in common with but different in average value between the U.S. and the remaining OECD, is our incarceration rate which is much greater than OECD’s. Spending 4-5 or more years in prison surely is not health inducing. Just consider increased prevalence of HIV and TB.

For example, from his paper, “Incarceration and Population Health in Wealthy Democracies,” Christopher Wildeman writes (from the abstract)17

…point estimates from these models suggest that life expectancy at birth in 2005 in the United States would have been 1.4 years longer had the U.S. incarceration rate remained at the 1981 level.

To make complex information understandable means, among other things, rejecting incoherent accounts of that information. Our overly expensive health care calls for remedy so that we can better invest in America.18 Likewise, improving our population health would reduce unnecessary suffering, early death, and our international health disadvantage. Considering the need for clarity and improvement, carelessly repeating misleading statements about our health care is not helpful. It’s time to put this fallacy to rest.

The expenditure data used for both HCE and GDP were “per capita.” I failed to state that in the above text. Thanks to commenter Greg L for pointing that out.


  1. Victor R. Fuchs, “Critiquing US Health Care,” JAMA, 312 No.20 (November 26, 2014): 2095-2096. Gated access.
  2. http://www.lettingthedataspeak.com/?p=213
  3. The U.S. is part of the OECD, the original 20 in fact. But for this essay it’s sometimes rhetorically easier to refer to the “OECD” as shorthand for “OECD countries other than rhe U.S.”.
  4. http://www.infoplease.com/ipa/A0934666.html
  5. OECD data taken from “OECD Regions At a Glance 2013”, Table A.4: http://dx.doi.org/10.1787/888932915964
  6. http://www.lettingthedataspeak.com/?p=259
  7. See, e.g., http://www.ruralhealthweb.org/go/left/about-rural-health
  8. http://www.census.gov/geo/reference/ua/urban-rural-2010.html
  9. US child poverty: http://www.census.gov/prod/2011pubs/acsbr10-05.pdf
  10. GDP at http://www.bea.gov, while HCE estimates are at http://www.statehealthfacts.org/comparemaptable.jsp?ind=596&cat=5
  11. The data are available as Excel spreadsheets: https://drive.google.com/file/d/0B8XSmAJ_rKgNOFBQVm9XdGVRUkk/view?usp=sharing and https://drive.google.com/file/d/0B8XSmAJ_rKgNSmpiLWFwRVN2OVE/view?usp=sharing
  12. R² ranges between 0 and 1, 1 indicating a perfect fit. Adjusted R² controls for the number of cases and variables giving a more reasonable measure of fit. R² in conjunction with other statistics and views of the data (like the above graph) is useful but used alone is potentially misleading.
  13. Daniel Hawes & Rene Rocha, “Social Capital in the Fifty States: Measuring State-Level Social Capital 1986-2004”, 2010. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1643243
  14. The median was used to partially compensate for averages not being weighted by population size.
  15. The OECD has a wealth of information available, e.g., http://www.oecd.org/regional/how-s-life-in-your-region-9789264217416-en.htm
  16. Environmental changes would include better access to care, socioeconomic would include reducing the sources of child poverty. The fallacy is an instance of the fallacy of equivocation.
  17. http://www.yale.edu/ciqle/CIQLEPAPERS/Wildeman(Crossnational).pdf
  18. Professor Fuchs wrote a New York Times Op-Ed on what we might do with a $1T savings in HC, e.g., increase expenditures on infra-structure by 50 percent; increase annual salaries of K-12 teachers by an average of $25,000. Each with annual costs of $100 billion: http://economix.blogs.nytimes.com/2014/03/14/how-to-shave-1-trillion-out-of-health-care/

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