Gelman and Auerbach 2016a — Age-Aggregation Bias in Mortality Trends

Summary

A two-page methodological comment on Case and Deaton (2015), submitted to the Proceedings of the National Academy of Sciences (PNAS). Gelman and Auerbach show that Case and Deaton's headline finding — a steady increase in all-cause mortality for white non-Hispanic Americans aged 45–54 from 1999 to 2013 — is partly a statistical artifact. Because the baby boom cohort's passage through the 45–54 age band shifted the group's average age upward, the raw (unadjusted) mortality rate rose mechanically even if no individual's age-specific rate changed. After age-adjusting within the band, mortality rose 1999–2005 but has been flat since 2005. A further sex breakdown reveals that the increase is concentrated among women; men's 1999–2005 gain is nearly reversed by 2013.

Key Claims

• Case and Deaton calculated group mortality as total deaths / total population for ages 45–54, without adjusting for the internal age distribution shift as baby boomers moved through. This is age-aggregation bias.
• The baby boom's passage raised the average age inside the 45–54 band over 1999–2013, which alone predicts a rising group mortality rate even under constant individual age-specific rates.
• Age-composition change explains approximately half the raw mortality increase since 1999 and all the increase since 2005.
• Age-adjusted, the trend has two phases: (1) genuine increase 1999–2005; (2) flat/constant 2005–2013.
• After adjustment and stratification by sex: women show a genuine sustained increase through 2013; men's increase from 1999–2005 is nearly reversed by 2013. The paper's combined-sex headline obscures this asymmetry.
• Cross-country and cross-race comparisons in Case and Deaton survive age adjustment because the aggregation bias (5% in the 1999–2003 trend) is small relative to those group differences (20%).
• Regional pattern (age-adjusted): most notable increase in death rates among women in the South; both-sex declines in the Northeast.

Concepts Introduced or Extended

• Period Mortality — age-aggregation as a third form of within-group compositional bias
• Deaths of Despair — qualifies the absolute trend; sex asymmetry after adjustment

Entities Mentioned

• Andrew Gelman
• Jonathan Auerbach
• Anne Case
• Angus Deaton

Quotes

"Adjusting for age confirmed this suspicion. Contrary to Case and Deaton's figure, we find there is no longer a steady increase in mortality rates for this age group. Instead there is an increasing trend from 1999–2005 and a constant trend thereafter."

"The changing composition in age explains about half the change in the mortality rate of this group since 1999 and all the change since 2005."

"Stratifying age-adjusted mortality rates by sex shows a marked increase only for women and not men, contrary to the article's headline."

"We stress that this does not change a key finding of the Case and Deaton paper: the comparison of non-Hispanic U.S. middle-aged whites to other countries and other ethnic groups. These comparisons hold up after our age adjustment."

My Take

The age-adjustment critique is technically correct and the mechanism is clearly demonstrated. It narrows the Case and Deaton finding — the "steady increase through 2013 for both sexes" claim does not survive — but leaves the most important claims intact: U.S. exceptionalism, racial/ethnic asymmetry, and the morbidity deterioration (Table 2 of Case and Deaton is entirely unaffected). The sex stratification finding is the genuinely new contribution: a sustained increase for women, a partial reversal for men, is a more precise characterization than the combined trend. The paper is a methodological comment, not a refutation; the deaths of despair phenomenon is real, particularly for white women and particularly in the South.