The limit to human lifespan, or not?

Back in October, an article was published in the journal Nature by Xiao Dong, Brandon Milholland, and Jan Vijg (all Albert Einstein College of Medicine in New York), entitled "Evidence for a limit to human lifespan". Dong et al. demonstrate what they suggest is evidence that natural human lifespan reached a peak in the mid-1990s, at about 114.9 years. Here is their key graph, which shows the maximum reported age at death for each year in their dataset (from the International Database on Longevity):

You can clearly see that, prior to 1995, the trend-line is upward sloping, and after 1995, the trend-line is downward sloping. This result was widely reported in the media (see for example here, and here, and here).

However, these results were also rubbished (see for example this piece by Hester van Santen). Van Santen makes the obvious point that the authors chose 1995 as their potential break point in the data:

An important bit of information: Vijg assumed this break in the trend in advance, he told NRC on the phone – in Dutch, as the biologist was born in Rotterdam. Vijg then had the computer calculate two underlying ‘trends’, one for the period before 1995 and one for after. These are the lines seen on the graph.

That’s not how these things are supposed to be done.

“No,” confirms statistician Van der Heijden. “You need to have solid theoretical substantiation before you start. When you infer that kind of turnaround using only the data, there’s a good chance that what you’re seeing is mere coincidence.”

The key point is that there wasn't anything special about 1995 in particular that makes it the best theoretical choice. If they had chosen some other year to break their data, the result might disappear (which van Santen suggests, but doesn't actually demonstrate for us).

I have another gripe with the Nature paper however. The data points used to construct their regressions are annual maximum recorded age at death from the dataset. So, there is only one data point for each year. So, the orange regression line (1995 onwards) is based on only twelve data points. No regression line is valid based on only twelve observations, and it's statistically illiterate to think otherwise.

Van Santen concludes (emphasis theirs):

Statistical evidence to support the assertion that the oldest living people haven’t gotten any older since 1995 is weak, according to two professors. We find the idea that the maximum human lifespan is 115 years to be unfounded.

However, it's important not to overstate this conclusion. Just because one of Dong et al.'s results is suspect, that is not enough to suggest that there is no maximum human lifespan, only that Dong et al. haven't provided enough evidence to support it. I really like this post by Matt Ridley from a few years ago, which makes some good points:

For all the continuing improvements in average life expectancy, the maximum age of human beings seems to be stuck. It’s still very difficult even for women to get to 110 and the number of people who reach 115 seems if anything to be falling. According to Professor Stephen Coles, of the Gerontology Research Group at University of California, Los Angeles, your probability of dying each year shoots up to 50 per cent once you reach 110 and 70 per cent at 115...

The lack of any increase in people living past 110 is surprising. Demographers are so used to rising average longevity all that they might expect to see more of us pushing the boundaries of extreme old age as well. Instead there is an enormous increase in 100-year-olds and not much change in 110-year-olds...

Next time you hear some techno-optimist say that the first person to live to 250, or even 1,000, may already have been born, remind them of these numbers. The only way to get a person past the “Calment limit” of (say) 125 will be some sort of genetic engineering.

I'd go a little bit further. The size of the cohorts reaching age 100 is increasing (because of improved health at younger ages, especially at very young ages), then we should also expect to see larger cohorts achieving age 110, age 115, and age 120. However, there isn't any evidence of these hyper-aged cohorts getting much bigger. [*] This suggests to me that the mortality rate for those aged 100 years and over might be increasing over time, thereby offsetting the effect of larger cohorts achieving age 100. If I get some spare time, this is a research question that deserves further attention.

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[*] Although an absence of evidence is not evidence of absence. There's probably an opportunity for an honours or Masters project to look at New Zealand longitudinal census data on those aged 100 years and over.