Correcting statistical biases in “Rising morbidity and mortality in midlife among white non-Hispanic Americans in the 21st century”: We need to adjust for the increase in average age of people in the 45-54 category | E-Axes
 

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Correcting statistical biases in “Rising morbidity and mortality in midlife among white non-Hispanic Americans in the 21st century”: We need to adjust for the increase in average age of people in the 45-54 category

Author(s): Andrew Gelman

From Statistical Modelling, Causal Inference and Social Science:

In a much-noticed paper, Anne Case and Angus Deaton write:

This paper documents a marked increase in the all-cause mortality of middle-aged white non-Hispanic men and women in the United States between 1999 and 2013. This change reversed decades of progress in mortality and was unique to the United States; no other rich country saw a similar turnaround.

 

Here’s the key figure:

Screen Shot 2015-11-05 at 7.53.11 PM

 

I have no idea why they label the lines with three-letter abbreviations when there’s room for the whole country names, but maybe that’s some econ street code thing I don’t know about.

Anyway, the graph is pretty stunning. And for obvious reasons I’m very interested in the mortality of white Americans in the 45-54 age range.

But could this pattern be an artifact of the coarseness of the age category? A commenter here raised this possibility a couple days ago, pointing out that, during the period shown in the above graph (1989 to the present), the 45-54 bin has been getting older as the baby boom has been moving through. So you’d expect an increasing death rate in this window, just from the increase in average age.

How large is this effect? We can make a quick calculation. A blog commenter pointed out this page from the Census Bureau, which contains a file with “Estimates of the Resident Population by Single Year of Age, Sex, Race, and Hispanic Origin for the United States: April 1, 2000 to July 1, 2010.” We can take the columns corresponding to white non-Hispanic men and women. For simplicity I just took the data from Apr 2000 and assumed (falsely, but I think an ok approximation for this quick analysis) that this age distribution translates by year. So, for example, if we want people in the 45-54 age range in 1990, we take the people who are 55-64 in 2000.

If you take these numbers, you can compute the average age of people in the 45-54 age group during the period covered by Case and Deaton, and this average age does creep up, starting at 49.1 in 1989 and ending up at 49.7 in 2013. So the increase has been about .6 years of age.

How does this translate into life expectancy? We can look up the life table at this Social Security website. At age 45, Pr(death) is .003244 for men and .002069 for women. At age 54, it’s .007222 for men and .004301 for women. So, in one year of age, Pr(death) is multiplied by approximately a factor of (.007222/.003244)^.1 = 1.08 for men and (.004301/.002069)^.1 = 1.08 for women—that is, an increase in Pr(death) of 8% per year of age.

The above calculations are only approximate because they’re using life tables for 2011, and for the correct analysis you’d want to use the life table for each year in the study. But I’m guessing it’s close enough.

To continue . . . in the period graphed by Case and Deaton, average age increases by about half a year, so we’d expect Pr(death) to increase by about .6*8%, or about 5%, in the 45-54 age group, just from the increase of average age within the cohort as the baby boom has passed through.

Doing the calculation a bit more carefully using year-by-year mortality rates, we get this estimate of how much we’d expect death rates in the 45-54 age range to increase, just based on the increase in average age as the baby boom passes through:

births

This is actually not so different from the “US Whites” line in the Case-Deaton graph shown above: a slight decrease followed by a steady increase, with a net increase in death rate of about 5% for this group. Not identical—the low point in the actual data occurs around 1998, whereas the low point is 1993 in my explain-it-all-by-changes-in-age-composition graph—but similar, both in the general pattern and in the size of the increase over time.

But Case and Deaton also see a dramatic drop in death rates for other countries (and for U.S. Hispanics), declines of about 30%. When compared to these 30% drops, a bias of 5% due to increasing average age in the cohort is pretty minor.

Summary

According to my quick calculations, the Case and Deaton estimates are biased because they don’t account for the increase in average age of the 45-54 bin during the period they study. After we correct for this bias, we no longer find an increase in mortality among whites in this category. Instead, the curve is flat.

So I don’t really buy the following statement by Case and Deaton:

This paper documents a marked increase flattening in the all-cause mortality of middle-aged white non-Hispanic men and women in the United States between 1999 and 2013. This change reversed ended decades of progress in mortality and was unique to the United States; no other rich country saw a similar turnaround stasis.

Still newsworthy.

P.S. Along similar lines, I’m not quite sure how to interpret Case and Deaton’s comparisons across education categories (no college; some college; college degree), partly because I’m not clear on why they used this particular binning but also because the composition of the categories have changed during the period under study. The group of 45-54-year-olds in 1999 with no college degree is different from the corresponding group in 2013, so it’s not exactly clear to me what is learned by comparing these groups. I’m not saying the comparison is meaningless, just that the interpretation is not so clear


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