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V_V comments on Open Thread, April 27-May 4, 2014 - Less Wrong Discussion
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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:
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.
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.
I think the more interesting question is the probability of a man in his age range (who is not obese; not a smoker; and has no serious self-reported history of health problems) suddenly collapsing and dying. I don't know the answer to this question, but it's a pretty unusual event.
By the way, here is a video of Seth Roberts speaking about his butter experiment a few years ago. Seth Roberts mentions that he eats a half a stick of butter a day on top of his Omega-3 regimen. (And probably this is on top of daily consumption of raw olive oil).
http://vimeo.com/14281896
At around 11:00, an apparent cardiologist concedes that the butter regimen may very well improve brain function but he warns Roberts that he is risking clogging up the arteries in his brain and points out that Roberts brain function won't be so great if he has a stroke. Roberts is pretty dismissive of the comment and points out that there is reason to believe the role of fat consumption in atherosclerosis over-emphasized or mistaken.
Still, if someone suddenly collapses and dies, from what I understand it's usually a cardiovascular problem -- a blood clot; stroke; aneurism; heart attack, internal bleeding, etc. And Roberts was consuming copious amounts of foods which are widely believed to have a big impact on the cardiovascular system.
It's silly to ignore this information when assessing probabilities. Here's an analogy: Suppose that Prince William has a newborn son and you are going to place a bet on what the child's name will be. You might reason that the most common male given name in the world is "Mohamed" and therefore the smart money is on "Mohamed." Of course you would lose your money.
The flaw in this type of reasoning is that when assessing probabilities, there is a requirement that you use all available information.
I imagine Gwern would respond that he is merely setting an upper bound. But that's silly and pointless too. If 90% of male children in Saudi Arabia are named "Mohamed," we can infer that the probability the Royal Baby will be named "Mohamed" does not exceed 90%. But so what? That's trivial.
I disagree (reasonable doubt under what assumptions? in what model? can you translate this to p-values? would you take that p-value remotely seriously if you saw it in a study where n=1?), and I've already pointed out many systematic biases and problems with attempting to infer anything from Roberts's death.
Isn't the p-value simply 100%-7.5%?
I'm not saying we can scientifically infer from his premature death that his diet was unhealthy.
I'm saying that his premature death is informal evidence that his diet at best didn't have a significant positive impact on life expectancy, and at worst was actively harmful. I can't quantify how much, but you were the one who attempted a quantitative argument and I've just criticized your argument, namely your strawman definition of "suspicious death", using your own data and assumptions, hence it seems odd that you now ask me for assumptions and p-values.