Content of review 1, reviewed on October 19, 2016

Dear Brandon Milholland,

Thank you for your interesting comments on your paper "Evidence for a limit to human life span", Dong et al., Nature 2016.

May I ask some questions regarding your Figure 1d, which presents the relationship between calendar year and the age that experiences the most rapid gains in survival:

How do you measure the gains in survival in this particular case: as a difference between the numbers of survivors over time, or as a difference between the LOGARITHMS of the numbers of survivors over time? Or something else?

What time intervals do you use, when you measure the gains in survival over time: just one year time interval (data for two close calendar years, say years 1981 and 1982, for example)? Or do you use longer time intervals?

Please advise. Thank you!

P.S.: By the way, you may enjoy our related published study, which explains why the chances for longevity records are much smaller than they were assumed earlier: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4342683/

Source

    © 2016 the Reviewer (CC BY 4.0).

Comments   (Guidelines)

Brandon Milholland

12:49 a.m., 20 Oct 16 (UTC) | Link

The gain in survival is measured as the slope of the linear regression of the log-transformed number of survivors per 100,000.

In Figure 1d, the data used is for the 100 year interval preceding the date (e.g., if the x-coordinate is 1940, then the regressions were performed on the data from 1840-1940; then the age with the highest gain was used to determine the y-coordinate of the point).

Leonid Gavrilov

3:25 p.m., 20 Oct 16 (UTC) | Link

Dear Brandon Milholland,

Many thanks for your helpful reply! What is the evidence that the dependence of log-transformed data for survivors is indeed a strictly linear function of time over the entire century?

Figure 1b and the Extended Data Figure 2 contain no data points (just graphic lines only) to prove that this relationship is indeed linear. Have you tried a segmented regression to check for possible breakpoints in the linear regression for this particular case?

Did you observe any curvature for these trajectories, and in what direction: were they concave up or concave down?

Please advise. Thank you!

Brandon Milholland

5:35 p.m., 26 Oct 16 (UTC) | Link

They were linear, without any sign of curvature or breakpoints. This was confirmed by the goodness-of-fit statistics (R>.85), (p<2.2e-16).

Ilya Kashnitsky

8:17 a.m., 27 Oct 16 (UTC) | Link

Dear Brandon,

Goodness-of-fit statistics is not enough to conclude that there is no curvature in the data.

Please, consider the following example.

R code:

library(ggplot2)
library(dplyr)

# generate data with curvature
df <- data.frame(x = 1:100) %>% mutate(y = sqrt(x))

# plot
ggplot(df, aes(x,y)) + 
        geom_point() + 
        stat_smooth(method = 'lm', color = 'red') +
        theme_minimal()

summary(lm(df, formula = y~x))

Plot produced

plot

Summary statistics of the liner model fitted to the evidently curved data

Call:
lm(formula = y ~ x, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.7984 -0.2555  0.1324  0.3597  0.4406 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 2.719268   0.090610   30.01   <2e-16 ***
x           0.079116   0.001558   50.79   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4497 on 98 degrees of freedom
Multiple R-squared:  0.9634,    Adjusted R-squared:  0.963 
F-statistic:  2580 on 1 and 98 DF,  p-value: < 2.2e-16

Conclusion

The goodness-of-fit statistics of a liner trend fitted to the data generated by y = sqrt(x) is 0.96 (compared to your 0.85).


Please, provide a better proof of no curvature in the data.

Ilya Kashnitsky

8:35 a.m., 27 Oct 16 (UTC) | Link

Sorry, markdown is parsed poorly.

Please, see the same comment properly parsed here http://txti.es/161027-comment-to-bm/images

Leonid Gavrilov

6:59 p.m., 7 Nov 16 (UTC) | Link

Dear Brandon Milholland,

Thank you for your brief reply to my earlier question (what is the evidence that the dependence of log-transformed data for survivors is indeed a strictly linear function of time over the entire century):

--"They were linear, without any sign of curvature or breakpoints. This was confirmed by the goodness-of-fit statistics (R>.85), (p<2.2e-16)."

What particular country, sex (male or female?), age group and time interval did you analyze by the goodness-of-fit statistics to get this R>.85, (p<2.2e-16)?

Also taking into account a prior valid comment by Ilya Kashnitsky here (see above), have you tried a more powerful segmented regression to check for possible breakpoints in the linear regression?

If the number of survivors to a particular age is indeed increasing strictly exponentially over time for the entire century with absolutely no deviation, as you suggest, that would be a major demographic discovery and a revolution in population forecasting. Hence some more details and proof are needed to justify this statement.

Please advise. Thank you, and looking forward to hear from you.

Edouard Debonneuil

8:20 p.m., 18 Nov 16 (UTC) | Link

It would be interesting to do a mascarade article with nematodes: "Evidence for a limit to nematode lifespan": similar biased statistics would support the adult lifespan of lab c elegans to converge towards 20 days, whereas in practice some people like Hugo Aguilaniu make those animals live 300 days.

Leonid Gavrilov

6:35 p.m., 20 Nov 16 (UTC) | Link

Correction to the Nature article "Evidence for a limit to human lifespan"

The following sentence in the legend for Extended Data Figure 4 needs to be corrected:

"The rate of change is the slope of the line calculated by an EXPONENTIAL regression, that is, b in the equation y = a + bx, where x is AGE and y is the logarithm of the number of survivors to that age per 100,000."

Two corrections are needed:

EXPONENTIAL --> LINEAR AGE --> TIME

The corrected sentence should be:

"The rate of change is the slope of the line calculated by LINEAR regression, that is, b in the equation y = a + bx, where x is TIME and y is the logarithm of the number of survivors to that age per 100,000."

I have discussed these corrections with one of the authors of the Nature article, @Brandon Milholland, who agreed with them:

https://www.facebook.com/brandon.milholland/posts/10207660175934999?comment_id=10207669460367104&comment_tracking=%7B%22tn%22%3A%22R2%22%7D

https://www.facebook.com/brandon.milholland/posts/10207660175934999

Martin J Sallberg

7:55 p.m., 17 Dec 16 (UTC) | Link

Any good post mortem must contain an investigation of what went wrong. In this case, it is obvious that it is the extreme fragmentation of the most respected journals that prevents relevant empirical data from being used to falsify bunkum. This phenomenon is, on a general level, explained with ideas on how to solve it at http://scientific-method.wikia.com/wiki/Scientific_Method_Wiki

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