Extreme aging and statistical outliers revisited
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A little more than three years ago, I wrote about how a Russian mathematician, Nikolay Zak, had raised questions about whether Jeanne Calment — a French woman who was the oldest person whose age had ever been verified by good documentary evidence — had actually lived to be 122. His argument was that she had died many decades earlier than her purported death in 1997, and that the woman who died then was actually her daughter, who had perpetrated some sort of elaborate insurance fraud.
His arguments were taken seriously enough that for a few months at least the Wikipedia article on the world’s oldest people characterized Calment’s age as “disputed.” Since then, it seems Zak’s argument has been pretty thoroughly debunked, and Mme. Calment’s ultimate lifetime achievement award has been returned to its previously undisturbed status.
Looking back at my post on the subject, I did make a couple of good points — specifically that one of the other “official” five oldest people of all time, Lucy Hannah, involved some pretty clearly dubious evidence (it’s since been shown that she was in fact claiming to be far older than she really was), and that some of Zak’s arguments seemed shaky — but the statistical core of my argument was in retrospect a bad one.
That argument was that Calment’s age was such a massive statistical outlier that Zak’s basic hypothesis that it was fraudulent should be given a lot of credence as a matter of Bayesian probabilities. At the time, Andrew Gelman pointed out that the strong clustering of the ages achieved by the oldest people ever at around 117 was probably just random, and that, if you assumed that annual mortality rates pretty much flatten out at somewhere around 50% once people reach 110 — there’s a good deal of evidence for this — then one person reaching the age of 122 wasn’t wildly unlikely, given the number of people who have reached 110 years of age in recent decades, although of course it was still a big outlier.
Three-plus years later, it’s clear Gelman was right and I was wrong (Gelman is a professional statistician and I’m a guy on a blog on the internet, so statistically speaking this isn’t a shocking outcome or anything).
The reason this is so clear now is that as of today three of the five oldest people of all time are people who weren’t in that category when I wrote that post just three years ago. In other words, the strong clustering around the age of 117 was, as Gelman suggested, merely a random statistical phenomenon: the number of people who have reached the age of 118 has doubled since then, while a third person has now reached the age of 119. These developments by themselves make Calment quite a bit less of an outlier statistically than she was just three years ago, although as Gelman pointed out at the time, she wasn’t as radical an outlier then as I was assuming she was.
On the broader question of extreme human longevity, I find it interesting that there wasn’t a single verified case of a person reaching the age of 114 prior to the mid-1980s, when in the less than four decades since then no less than 57 people around the world have had a verified — or “verified;” as Gelman noted, from a Bayesian perspective all claims of really extreme old age should be viewed at least initially with caution — 115th birthday, while probably close to a couple of hundred have turned 114.