First, there is value to data-driven (as opposed to hypothesis-driven) research3. We are surprised by the opposition towards the visual inspection of data. We thought that the field of statistics had decades ago dispensed with the notion that ‘actually looking at the data is cheating’ and acknowledged that graphs are not only useful but also essential for choosing one’s model4. Cubic smoothing splines of data from the International Database on Longevity (figure 2b of ref. 2) suggested a trend break around the mid-1990s, which could be parsimoniously modelled with a segmented regression. But even within the framework of hypothesis proposal and testing, our work is valid because it relies on multiple datasets. Data from the Human Mortality Database (HMD; http://www.mortality.org/) indicate that there have been limited gains in survival to very old age (see figure 1 and extended data figures 1–5 of ref. 2), suggesting that there might be a limit to human lifespan. This limit was confirmed by a segmented regression, using the breakpoint suggested by smoothing splines, on the maximum reported age at death (MRAD; figure 2 of ref. 2); the stagnation in MRAD since the 1990s found by this model is corroborated with data from the Gerontology Research Group (GRG; extended data figure 6 of ref. 2).
Regarding sample size, in the figure 2 legend of our paper2, we wrote 534 as the number of supercentenarians for figure 2c. Brown et al.1 misinterpret the 534 as applying to figure 2a. We apologize if the legend was ambiguous. Next, Brown et al.1 claim that it is not possible to draw any firm conclusions from the 33 observations over 40 years (1968–2006) because of this limited sample size, but no statistical justification was provided to support this claim; although more data would increase the strength of our conclusions, we were still able to arrive at a fairly narrow 95% confidence interval for the level at which the MRAD has plateaued. In addition, they suggest using extreme value theory (EVT)1. Additional investigation of the data using EVT may indeed prove insightful, but this does not undermine the value of the analyses presented in our Letter. Brown et al.1 do not seem to provide any statistical justification to demonstrate why EVT is suitable and our analyses are not, and they do not apply EVT in their subsequent analyses. Recently, another group applied EVT to mortality at old ages and found evidence for a finite ‘ultimate age’, arriving at results that they say are ‘very close’ to ours5.
To demonstrate that a single linear model is a better fit for the data, Brown et al.1 first examine the average age at death of supercentenarians, performing a comparison of alternatives to our spline model from figure 2c of ref. 2. However, their analyses are undermined by several issues. First, the spline model to which they compare their models is not the one from our figure 2c. We modelled the yearly average age at death of supercentenarians, but they did not perform the averaging when constructing their model. Also, their linear model has R2 = 0.03. This suggests that there is no linear correlation between calendar year and age at death of supercentenarians, a result that supports our claim.
Finally, Brown et al.1 claim that our results are due to the outlier data point of Jeanne Calment, and claim to show this by finding a steady increase in lifespan after they relocate Jeanne Calment’s data point. We agree that Jeanne Calment’s death is an influential point, but our findings, far from being “entirely dependent” on this data point, as they assert, do not require its presence at all: a regression split at 1995 would still find a plateau if Jeanne Calment were omitted entirely. The alternative models suggested by Brown et al.1 consist of changing Jeanne Calment’s age and dates of birth and death without any biological or statistical justification. With this data manipulation, Brown et al.1 seem to have altered the data to fit their model, rather than vice versa. Even after these changes, the alternative model still supports our claim that there is no significant increase in the maximum age at death after 1995 (figure 1 of ref. 1, bottom panel, R2 = 0.032, P = 0.579), indicating the robustness of our result. Brown et al.1 note that it is “curious” that Jeanne Calment is a critical part of our argument for a limit to human lifespan; however, our evidence for a limit to lifespan is not dependent on Jeanne Calment. Our findings are unchanged by the omission of this one data point, which is completely inessential to our conclusions. By contrast, their results seem to require not only its presence but also its relocation.
Brown, N. J. L., Albers, C. J. & Ritchie, S. J. Contesting the evidence for limited human lifespan. Nature 546, http://dx.doi.org/10.1038/nature22784 (2017)
Dong, X., Milholland, B. & Vijg, J. Evidence for a limit to human lifespan. Nature 538, 257–259 (2016)
van Helden, P. Data-driven hypotheses. EMBO Rep. 14, 104 (2013)
Anscombe, F. J. Graphs in statistical analysis. Am. Stat. 27, 17–21 (1973)
Gbari, S., Poulan, M., Dal, L. & Denuit, M. Extreme value theory analysis of mortality at the oldest ages: a case study based on individual ages at death. Society of Actuaries International Symposium Presentation https://livingto100.soa.org/pdf/2017-living-100-sym-session-2b.pdf (2017)
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Dong, X., Milholland, B. & Vijg, J. Dong et al. reply. Nature 546, E7 (2017). https://doi.org/10.1038/nature22785