Worst Regression in American Health Care

According to Adrianna McIntyre at Vox.com, the following chart "is the most depressing graph in American health care." The Daily Kos clearly agrees.

The chart is from the OECD's "Health at a Glance 2013" report.

There appears to be a complete lack of critical statistical analysis at Vox and the Daily Kos. This graph contains one of -- if not the absolute worst -- regression in American health care. Look at the trendline (with its claimed R2=0.51, a measure of the quality of fit) and then look at the data.

Does it look like there is a positive relationship between "life expectancy in years" and "health spending per capita (USD PPP)" at health spending rates greater than $2,200 per capita? No way. There is absolutely no benefit in terms of higher life expectancy by spending more than $2,200 per capita on health care.

You can download the OECD's raw data behind their graph here. And when you do, and you plot it, it is clear the correct relationship between "life expectancy in years" and "health spending per capita (USD PPP)" should be as shown in the plot below. Namely, an approximately linear relationship between $0 and $2,200 per capita, and then a flat line at spending levels above $2,200.

Conducting linear regression on the countries that spend more than $2,200 per capita on health care -- and leaving out the United States -- yields a slope of zero (aka, no relationship between the variables).

While this may seem like arguing over statistical trivialities, it most certainly is not. First off, the OECD's regression is terrible. Even those with basic statistical training would know that the type of exponential association the OECD tried to fit to the data was highly inappropriate. I have long been unimpressed by many of the OECD's analyses -- especially given the deference this organization is generally accorded in the mainstream media -- and fundamental problems such as this make me wonder about the rest of their data analyses.

Second, the OECD's graph suggests that the USA is deriving far fewer benefits from its higher levels of health care spending than it actually is. Life expectancy is also an imperfect indicator of health system performance, since it integrates many lifestyle choices and health risks outside the scope of traditional health system expenditures, and entirely fails to include a measure for quality of life. Would you rather live 79 years and enjoy your life, or 81 years and despise it?

If we do accept the premise that life expectancy is somehow a useful indicator for the efficiency of health care expenditures, the data indicates unequivocally that each and every nation spending more than $2,200 per capita is wasting their money. The OECD's trend line indicates that ever-increasing health expenditures lead to ever-increasing life expectancies, but a rigorous analysis of their own data suggests this is just not true. Spending anything greater than $2,200 per capita has no influence on life expectancy whatsoever.

Hopefully in the future the OECD can practice solid statistical analyses that more accurately reflect the real trends in their datasets, and that left-wing websites will start to more critically discuss the OECD's analyses.