# Using segmented linear regression as evidence for the limit of human lifespan

Nature published this year the following paper: Evidence for a limit to human lifespan1, in which the authors argue their "results strongly suggest that the maximum lifespan of humans is fixed and subject to natural constraints."

One of this paper's statistical analysis has been panned at some sites already, including Nature article is wrong about 115 year limit on human lifespan and Evidence for a limit to effective peer review, since it turned up in some popular media.

The study is based, among several things, on data from databases detailing the yearly maximum age of death. Among their analyses, the following figure is included:

Basically the authors argue there's a breakpoint, and so they performed a segmented regression before circa 1995 and after that point onward. The regression is used as evidence for the limit of human lifespan.

Does it make sense though? If not, what method could better be employed to study these data?

[1] Dong, Xiao, Brandon Milholland, and Jan Vijg. "Evidence for a limit to human lifespan." Nature 538.7624 (2016): 257-259.

• Linear regression for extrema seems weird ... and, they evidently used a discontinuous segmented regression, which is unusual ... – kjetil b halvorsen Dec 19 '16 at 13:02
• @kjetilbhalvorsen agreed. Extrema are well known examples of data violating normal assumptions quite wildly. I wonder how a maximum likelihood routine for Gumbel data would have performed... using the aptly named technique of survival analysis. – AdamO Feb 10 '17 at 13:57

First of all, let's manually extract the values from their original Figure 2 and plot the data without any colors or regression lines biasing our first visual inspection of the raw data.

year <- c(1968, 1970, 1973, 1975, 1978, 1979, 1980, 1981, 1982,
1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991,
1992, 1994, 1993, 1995, 1996, 1998, 1997, 1999, 2000,
2001, 2002, 2003, 2004, 2005, 2006)
age <- c(111, 111, 112, 111, 111, 110, 111, 113, 113, 113, 111,
114, 113, 114, 114, 112, 112, 112, 114, 115, 117, 112,
114, 115, 121, 119, 114, 115, 115, 114, 113, 114, 112)

plot(year,age,xlab="Year",
ylab="Yearly maximum reported age at death (years)",
pch=20,cex=2,ylim=c(108,124),xlim=c(1960,2010))


We obtain:

And, let's do the same for the data in Figure 6 (as presented in the question above):

age <- c(113, 109, 109, 110, 113, 109, 110, 111, 111, 111,
112, 112, 113, 111, 111, 113, 113, 113, 114, 115,
113, 114, 122, 119, 117, 114, 115, 115, 114, 114,
115, 116, 115, 115, 114, 114, 116, 116, 117)
year <- c(1954, 1957, 1958, 1958, 1963, 1964, 1965, 1967,
1968, 1970, 1975, 1972, 1976, 1976, 1977, 1980,
1981, 1982, 1984, 1985, 1986, 1987, 1997, 1998,
1998, 1999, 2001, 2001, 2002, 2003, 2006, 2006,
2008, 2007, 2010, 2011, 2011, 2012, 2015)

plot(year,age,xlab="Year",
pch=20,cex=2,ylim=c(108,124),xlim=c(1950,2020))


It seems that a simple linear regression model would be the natural candidate challenging the less parsimonious change-point model the authors proposed. Indeed, Philipp Berens and Tom Wallis have done so and published their re-analysis on github: https://github.com/philippberens/lifespan

• You seem to have made a mistake in taking the values from the figure - data is missing for some years. – Scortchi - Reinstate Monica Feb 10 '17 at 14:12
• Hmm ... According to Berens & Wallis, the authors explained that "the “missing” is due to the fact that the MRAD persons were younger than Jeanne Calment who was holding the record for the world’s oldest person at the time". So data on other people, each of whom was the eldest to die in the year of his death, is omitted owing to the continuing survival of someone elder. Sounds like a recipe for a breakpoint! – Scortchi - Reinstate Monica Feb 10 '17 at 14:37
• In the first version of the post, I had included just their Figure 2. I added data from Figure 6, in which we can see the discussed gap. – Brandmaier Feb 10 '17 at 15:18
• Sorry! I was assuming it was the same figure as in the question. – Scortchi - Reinstate Monica Feb 10 '17 at 15:27

I think the nature of the conclusions are totally bunk. We see between 1950 and 2015 an increasing trend followed by a decreasing trend. It is a classic fallacy of applying data which are suggestive of a hypothesis different than the one tested and presenting them as such. With these data, a segmented regression can interpolate and predict that in 1995 a local maxima of lifespan was about 115 years $\pm$ whatever error they estimate from segmented regression. This does not preclude 2020 or 2030 trends superseding that value.

1. The concept of natural lifespan conflicts with the preponderance of research in aging, genetics, and telomeres.
2. An experimental design to address natural human lifespan is needed using "body on a chip" technology.
3. 50 years is utterly trivial in the course of human history. There have been many points in the past where an upward trend in lifespan was followed by a downward one.
4. Data such as those presented could have been simulated from a non-linear model having discontinuities and/or asymptotes which are unmeasurable.
5. Since the model's goal is prediction, distributional assumptions, and mean-model correctness are needed, and neither (it seems) were these checked nor are they met.