Earlier today I discussed a paper by Anne Case and Angus Deaton in which they noted an increase in mortality rates among non-Hispanic white Americans from 1989 to 2013, a pattern that stood in sharp contrast to a decrease in several other rich countries and among U.S. Hispanics as well:
Interpretation of this graph is tricky though, because the “45-54” age group was, on average, younger at the beginning of this time series than at the end, what with the big fat baby boomer generation passing through (see image at top of page). Average age increased from 49.1 in 1989 to 49.7 in 2013. Not a huge increase, but not trivial either given the steady increase in mortality rate as a function of age (approximately 8% per year) among the middle-aged.
I did a quick calculation to estimate what we might expect to happen to the mortality rate in the 45-54 age group, just from the changing age distribution, and here’s what I found:
Based on this analysis, the entire increase in mortality among non-Hispanic white Americans aged 55 in the Case-Deaton graph can be explained by changing age composition. Sociologist Philip Cohen sliced the data in a somewhat different way and estimated that the change in age composition could explain about half of the increase.
As I wrote in my earlier post, the Case-Deaton result is still interesting because of the comparison to other countries (and to Hispanics within the U.S.): these other groups show declines in mortality rates of around 30%, which is much more than could be explained by any age-aggregation artifacts.
I asked a colleague to point this post to Deaton, and he (Deaton) replied with the following data from the CDC showing deaths per 100,000 among white non-Hispanics in 1999 (not 1989, which was the beginning of the series shown above, but 1999; apparently the pre-1999 data are harder to grab) and 2013:
Age 1999 2013 Change 45 262.3 260.7 -1.6 46 292.9 289.8 -3.1 47 305.9 323.5 17.6 48 337.2 342.9 5.7 49 359.0 384.5 25.5 50 376.7 422.2 45.5 51 429.0 466.1 37.1 52 444.8 481.2 36.4 53 545.1 526.7 -18.4 54 555.3 572.7 17.4
Deaton pointed out that the mortality rate increased among most age groups. And, indeed, the average increase is about 4%.
Deaton also sent this analysis to the New York Times, where David Leonhardt reports:
Breaking down the 45-to-54 age group into single years of age, which should avoid Mr. Gelman’s concern, still shows the same pattern.
“If we want to be more precise about the age range involved, we could say that for all single years of age from 47 to 52, mortality rates are increasing,” wrote Mr. Deaton, the most recent winner of the Nobel Prize in economics. “So the overall increase in mortality is not due to failure to age adjust.” . . .
“We stick by our results,” he said.
According to the table above, mortality rates among non-Hispanic whites aged 45-54 increased by an average of about 4% after controlling for age. But if you go to Case and Deaton’s graph above, you’ll find an increase of about
12% 9% in the raw mortality rate for that group from 1999 (again, not 1989 for this comparison) and 2013.
So according to these calculations, if you correct for the age-composition bias, about
2/3 half of the observed change from 1999 to 2013 goes away. If you look at the top graph above, 1999 appears to be an unusual year so it might not be the best to use as a baseline.
Here, then, is a quick summary of our estimates of the bias from age composition in estimating the recent changes in death rate for non-Hispanic white Americans aged 45-54:
After controlling for age, there was a decline in the death rate from 1989 to 1999, then an increase from 1999 to 2005, then it’s been steady since then. See graphs here.
In my post, I estimated no change because I was considering the entire range, 1989-2013, as presented in the original Case and Deaton paper. In his reply Deaton estimated an increase because he was just looking from 1999-2013. Actually, though, all that increase occurred between 1999 and 2005.
So there appears to have been no aggregate increase in age-adjusted mortality in this group in the 1989-2013 period.
Is it then appropriate to say “We stick by our results”?
In this case I say yes, that Case and Deaton’s main results seem to stand up just fine.
As noted above (and in my earlier post), their key claim was that death rates among middle-aged non-Hispanic whites in the U.S. slightly increased, even while corresponding death rates in other countries declined by about 30%. Even after you apply a bias correction and find that death rates among middle-aged non-Hispanic whites in the U.S. were actually flat (or maybe even decreased slightly), the key comparison to other countries is barely affected. A bias of 5% is small compared to an observed difference of 30%.
And this is why I emphasized throughout that this statistical bias did not invalidate the Case and Deaton study. As a statistician, I am of course interested in such biases, and it wasn’t clear to me ahead of time how large the correction would be. It turned out that the bias explained the observed increase among 45-54-year-old non-Hispanic whites, and that’s interesting, but the cross-national comparison is still there, and that seems to be the most important thing.
P.S. Deaton also asked why I estimated the bias using the age distribution rather than single-year mortality rates. The answer to this question is that I just used the data I found. I have no great familiarity with demographic data and I did not know that the data by ethnicity and year of age were easily available. I agree that the natural thing to do would be to analyze death rates by year of age. If someone can point me to such a dataset, I’d be glad to fit a model to it, indeed this would be an excellent project.
P.P.S. The mortality rates by year of age from 1999 to 2003 are at CDC Wonder, so that’s a start. If anyone knows where the 1989-1998 data are, please let me know.
I agree with Case and Deaton on the main point, for sure: if indeed there was a decrease from 1989 to 1999, and an increase from 1999 to 2005, and no change after that, this is largely consistent with their story of there being a reversal, or at least a stalling of improvement, after decades of progress. And, in any case, the change compared to other countries and groups is huge. Which is a point that I emphasized in all my posts. The existence of a bias does not imply that there is no underlying effect. Indeed, that’s why I wanted to quantify the bias, to get a sense of how it changes one’s conclusions.
P.P.P.S. More graphs here, including this: