Open Thread, April 27-May 4, 2014

NancyLebovitz

You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

And, while this is an accidental exception, future open threads should start on Mondays until further notice.

You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

And, while this is an accidental exception, future open threads should start on Mondays until further notice.

60-yo men die all the time; anytime someone who writes on diet dies, someone is going to say 'I wonder if this proves/disproves his diet claims', no matter what the claims were or their truth. They don't, of course, since even if you had 1000 Seth Roberts, you wouldn't have a particularly strong piece of evidence on correlation of 'being Roberts' and all-cause mortality, and his diet choices were not randomized, so you don't even get causal inference. More importantly, if Roberts had died at any time before his actuarial life expectancy (in the low 80s, I'd eyeball it, given his education, ethnicity, and having survived so long already), people would make this claim.

OK, so let's be a little more precise and play with some numbers.

Roberts published The Shangri-la Diet in 2006. If he's 60 now in 2014 (8 years later), then he was 52 then. Let's say people would only consider his death negatively if he died before his actuarial life expectancy, and I'm going to handwave that as 80; then he has 28 years to survive before his death stops looking bad.

What's his risk of dying if his diet makes zero difference to his health one way or another? Looking at http://www.ssa.gov/OACT/STATS/table4c6.html from 52-80, the per-year risk of death goes from 0.006337 to 0.061620. What's the cumulative risk? We can, I think, calculate it as (1 - 0.06337) ... (1 - 0.061620). A little copy-paste, a little Haskell, and:

> foldr1 (*) $ map (1-) [0.006337,0.006837,0.007347,0.007905,0.008508,0.009116,0.009723,
                         0.010354,0.011046,0.011835,0.012728,0.013743,0.014885,0.016182,
                         0.017612,0.019138,0.020752,0.022497,0.024488,0.026747,0.029212,
                         0.031885,0.034832,0.038217,0.042059,0.046261,0.050826,0.055865,
                         0.061620]
0.5065374918662645

So roughly speaking, Roberts had maybe a 50% chance of surviving from publishing his diet book to a ripe old age. (Suppose Roberts's ideas had halved his risk of death in each time period, which we can implement with a call to map (/2). It's not quite as simple as dividing 50% by 2, but when you rerun the probability, then he'd have a 71% chance of survival, or more relevantly, he still has a 29% chance of dying in that timespan.)

In summary: Life sucks, and diet gurus can be expected to die all the time no matter whether their ideas are great or horrible, so their deaths tell us so little that discussing it at all is probably biasing our beliefs through an anchoring or salience effect.

So roughly speaking, Roberts had maybe a 50% chance of surviving from publishing his diet book to a ripe old age.

If his actuarial life expectancy was 80 and he had died at 79 it wouldn't have looked particularly suspicious. But according to your data, his probability of dying between 52 and 60 was only about 7.5%, which is not terribly low, but still enough to warrant reasonable doubt, especially considering the circumstances of his death.

5brazil8412y

Agreed. [...] Not sure about that, for example if he had died at the age of 81 in a car accident. Although I appreciate your effort, I am not sure that you have the reference class of events correct. The evidence suggest that Roberts died (1) suddenly; (2) due to failure of some bodily system; (3) at an age which is well under his life expectancy. The prior probability of this happening has got to be far less than the prior probability of him simply dying from any cause before his actuarial life expectancy. At the same time, he was apparently consuming large amounts of butter, omega fatty acids from flax seeds, and other esoteric things. Of course it's difficult to even being estimating the risk inherent in doing such things. Ironically, Seth Roberts was a big believer in "n=1 experiments." Do you have an estimate of the probability that Robert's death is related to his supplement regime?