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Living Forever is Hard, or, The Gompertz Curve

44 Post author: gwern 17 May 2011 09:08PM

I recently recalled, apropos of the intermittent fasting/caloric restriction discussion, a very good blog post on mortality curves and models of aging:

For me, a 25-year-old American, the probability of dying during the next year is a fairly miniscule 0.03% — about 1 in 3,000.  When I’m 33 it will be about 1 in 1,500, when I’m 42 it will be about 1 in 750, and so on.  By the time I reach age 100 (and I do plan on it) the probability of living to 101 will only be about 50%.  This is seriously fast growth — my mortality rate is increasing exponentially with age.

...This data fits the Gompertz law almost perfectly, with death rates doubling every 8 years.  The graph on the right also agrees with the Gompertz law, and you can see the precipitous fall in survival rates starting at age 80 or so.  That decline is no joke; the sharp fall in survival rates can be expressed mathematically as an exponential within an exponential:

P(t) \approx e^{-0.003 e^{(t-25)/10}}

Exponential decay is sharp, but an exponential within an exponential is so sharp that I can say with 99.999999% certainty that no human will ever live to the age of 130.  (Ignoring, of course, the upward shift in the lifetime distribution that will result from future medical advances)

...There is one important lesson, however, to be learned from Benjamin Gompertz’s mysterious observation.  By looking at theories of human mortality that are clearly wrong, we can deduce that our fast-rising mortality is not the result of a dangerous environment, but of a body that has a built-in expiration date.

gravityandlevity then discusses some simple models of aging and the statistical characters they have which do not match Gompertz's law:

  1. 'lightning' model: risk of mortality each period is constant; Poisson distribution:

    What a crazy world!  The average lifespan would be the same, but out of every 100 people 31 would die before age 30 and 2 of them would live to be more than 300 years old.  Clearly we do not live in a world where mortality is governed by “lightning bolts”.

  2. 'accumulated lightning'; like in a video game, one has a healthbar which may take a hit each period; similar to above:

    Shown above are the results from a simulated world where “lightning bolts” of misfortune hit people on average every 16 years, and death occurs at the fifth hit.  This world also has an average lifespan of 80 years (16*5 = 80), and its distribution is a little less ridiculous than the previous case.  Still, it’s no Gompertz Law: look at all those 160-year-olds!  You can try playing around with different “lightning strike rates” and different number of hits required for death, but nothing will reproduce the Gompertz Law.  No explanation based on careless gods, no matter how plentiful or how strong their blows are, will reproduce the strong upper limit to human lifespan that we actually observe.

What models do yield a Gompertz curve? gravityandlevity describes a simple 'cops and robbers' model (which I like to think of as 'antibodies and cancers'):

...in general, the cops are winning.  They patrol randomly through your body, and when they happen to come across a criminal he is promptly removed.  The cops can always defeat a criminal they come across, unless the criminal has been allowed to sit in the same spot for a long time.  A criminal that remains in one place for long enough (say, one day) can build a “fortress” which is too strong to be assailed by the police.  If this happens, you die.

Lucky for you, the cops are plentiful, and on average they pass by every spot 14 times a day.  The likelihood of them missing a particular spot for an entire day is given (as you’ve learned by now) by the Poisson distribution: it is a mere e^{-14} \approx 8 \times 10^{-7}.

But what happens if your internal police force starts to dwindle?  Suppose that as you age the police force suffers a slight reduction, so that they can only cover every spot 12 times a day.  Then the probability of them missing a criminal for an entire day decreases to e^{-12} \approx 6 \times 10^{-6}.  The difference between 14 and 12 doesn’t seem like a big deal, but the result was that your chance of dying during a given day jumped by more than 10 times.  And if the strength of your police force drops linearly in time, your mortality rate will rise exponentially.

... The language of “cops and criminals” lends itself very easily to a discussion of the immune system fighting infection and random mutation.  Particularly heartening is the fact that rates of cancer incidence also follow the Gompertz law, doubling every 8 years or so.  Maybe something in the immune system is degrading over time, becoming worse at finding and destroying mutated and potentially dangerous cells.

...Who are the criminals and who are the cops that kill them?  What is the “incubation time” for a criminal, and why does it give “him” enough strength to fight off the immune response?  Why is the police force dwindling over time?  For that matter, what kind of “clock” does your body have that measures time at all? There have been attempts to describe DNA degradation (through the shortening of your telomeres or through methylation) as an increase in “criminals” that slowly overwhelm the body’s DNA-repair mechanisms, but nothing has come of it so far.

This offers food for thought about various anti-aging strategies. For example, given the superexponential growth in mortality, if we had a magic medical treatment that could cut your mortality risk in half but didn't affect the growth of said risk, then that would buy you very little late in life, but might extend life by decades if administered at a very young age.

Comments (85)

Comment author: jsalvatier 17 May 2011 09:38:47PM *  1 point [-]

This is wonderful.

Although it doesn't fit, for some reason this reminds me of Robin Hanson's cognitive tactic of collecting a set of stylized facts (this certainly seems like a useful one) about a field and then trying to come up with simple models which fit those stylized facts.

Perhaps what these have in common is that they both focus on eliminating lots of wrong models from a big pool rather than trying to choose the best model between a small pool (which is what most statistical techniques focus on).

Edit: I think their similarity has more to do with that they both use high level facts to eliminate and suggest classes of models.

Comment author: Vaniver 17 May 2011 09:50:18PM 0 points [-]

This offers food for thought about various anti-aging strategies. For example, given the superexponential growth in mortality, if we had a magic medical treatment that could cut your mortality risk in half but didn't affect the growth of said risk, then that would buy you very little late in life, but might extend life by decades if administered at a very young age.

Wait, what? What do you mean by halving your risk and not halving your risk growth, since your risk is determined entirely by your risk growth? I'm hoping you don't mean capping the risk of death at .5. If you mean halving the rate but keeping it as a Gompertz curve, then that makes sense.

I'm playing around with a bunch of numbers; they will appear in a comment shortly.

Comment author: Vaniver 17 May 2011 10:17:48PM *  5 points [-]

TL;DR? Scroll down to the bottom.

When I integrate the curve in the post from 25 to 300, I get 52.34. (When you integrate a cdf, you get an expected value- that's how many years I have left, on average.)

There are two parameters I can halve- the .003, and the 10. (I can also play with the age offset, 25).

Let's start off playing with the growth rate (in this curve, that's the 10). If I halve it (replace it with 20), my expected remaining years is now 104.7, which is an awesome boost- it doubles it. (This is no surprise, since all I've done is change the scaling on the x axis, and halving your experience of time doubles your lifespan.)

Now let's go back and see what my remaining life would look like at 65, rather than 25. With an age offset of 25 and a divisor of 10, I get 16.4 years years; with an age offset of 25 and a divisor of 20, I get 66.5 years; with an age offset of -15 and a divisor of 20, I get the expected 32.7 years.

That shows us a few things- first, living the extra 40 years from 25 to 65 only earned me 4.1 years. Computing the function, I get an 85% chance that I live to see 65. How we model changing your death rate matters as well- if we assume that we use this magical medical treatment on you at 65 and it halves the rate you age at, you are essentially turned into a 45 year old living half-time, and you still get several decades left. If you turn you into a 130-year old instead, living in half-time, then you're identical to the 65-year old living in normal time, and you get the normal doubling.

Now, let's look at the x displacement (the .003). That's what I think gwern means by halving your risk without halving the growth. As an added bonus, we don't have to muck around with the age offset. If you do it at 25 years, you can expect to live for 59.3 more years; if you do it at 65, you can expect to live for 21.8 more years. There's still some benefit to starting young: I get 7 extra years instead of 5.4 extra years- but the benefit is measured in months, not decades.

TL;DR If you can halve your experience of time, you double your time alive. No surprise. If you can reduce your age to the 25-45 region, that age reduction is added almost exactly to your lifespan (98% chance to make it to 45 from 25). If you can just change the .003 number, you only get a few years, and it's very similar at all ages- 7 years if you start at 25, 5.4 years if you start at 65, 3 years if you start at 85.

Comment author: Vaniver 17 May 2011 10:56:58PM 5 points [-]

Why does Vaniver care?

So, I recently turned 23. I am on schedule to have my anti-aging regimen fully in place by 25, and beginning tonight am again attempting the uberman sleep schedule (which, if it works, will increase my subjective experience of time by 40-50%).

My logic for the 25 date was to give myself enough time to fully research the issue, and if I have to pick a time to freeze myself at, 25 seems a heck of a lot better than 45 or 65! But looking at models like this is interesting because you can see the difference between various kinds of freezes. If living healthily just drops the .003, then it's not where big gains are. If I managed to drop it by a factor of 10, then I'd get an extra 23 years out of doing so. But I'm still projected to die at 100, after a 10x reduction in risk! That's the same gain as increasing my time experience by 40% / decreasing my risk growth rate by 30%.

With changing that number, I also don't see much benefit to doing it early. Reducing my risk by 10x is reducing my risk by 10x, but if my chance of dying by the time I hit 45 is really low anyway, and I still get 22.2 extra years if I start living healthily at 45 (21 years if you take into account the chance of not hitting 45), then is it really worth it to live healthily for 20 years to get 2 more years at the end of my life?

So, really, all of the hope of life extension hinges on the slowdown (I can make the 10 into a 20), the freeze (I can make the 10 infinity, and only have to deal with accidents), or the reverse (I can lower my t, essentially giving everyone access to the freeze). It seems likely to me that some components of living healthily (the calorie restriction stuff, for example) does actually work by slowdown, but then you need to ask if the effects are cumulative (since I've been growing my mitochondria for 40 years at 65, they can knock cancer out of the park, compared to if I had only been growing them 20 years) or fixed (there's no reason to go on an anti-cancer diet until you get cancer).

Comment author: [deleted] 26 April 2013 10:47:40PM 2 points [-]

So, I recently turned 23. I am on schedule to have my anti-aging regimen fully in place by 25, and beginning tonight am again attempting the uberman sleep schedule (which, if it works, will increase my subjective experience of time by 40-50%).

So, two years later... How did it go? Are you still doing that?

Comment author: Vaniver 26 April 2013 11:20:53PM *  2 points [-]

Both that and a previous attempt at Uberman failed. I never got to the point where I felt more rested after a nap than I did before a nap (though I did seem more rested outside in the sunlight- I'm not sure if that actually reduced my level of fatigue, or just suppressed my awareness of it. I could look for a daily cycle in my psychomotor vigilance task data to check, but I never analyzed it). If I succeed in hacking the process of falling asleep (I have sleep onset insomnia and am getting tired of it), I'll attempt it again, but I see no point in reattempting Uberman without doing that.

I'm doing much better with my anti-aging regimen, but I don't think I'd call it "fully in place." I've been on intermittent fasting for over a year, which is comparable to caloric restriction. I've got a project in the works to significantly improve the nutritional content of my diet which will happen over this summer (basically, Soylent, except I don't quite trust his methodology / ingredient choices and so am planning on doing it myself. He's missed at least two essential nutrients that made it onto my list- iron and sulfur- and I don't think his judgment on non-essential nutrients is very good either).

I do regular strength exercises, though the regularity could stand to improve, and I'm beginning routine swimming exercise. About that time, I was starting the cat stretch which I stopped doing after a few months, because of a combination of low reward and not having a good spot for it in my morning ritual. I'm not sure what priority I should place on doing that exercise (which is primarily about maintaining your current level of control and flexibility) compared to learning skills and doing exercises that increase my level of control and flexibility.

Comment author: gwern 27 April 2013 03:08:31AM 3 points [-]

He's missed at least two essential nutrients that made it onto my list- iron and sulfur- and I don't think his judgment on non-essential nutrients is very good either

He says he's added sulfur: http://robrhinehart.com/?p=570

After three months I should be finding deficiencies, and I did. I started having joint pain and found I fit the symptoms of a sulfur deficiency. This makes perfect sense as I consume almost none, and sulfur is a component of every living cell. Sulfur is hard to miss in a typical diet so the FDA would have little reason to recommend it. A typical male physique has 140g of sulfur, making it the sixth most abundant element in the human body. Ten grams of sulfur from Methylsulfonylmethane cured me right away, and I now consume 2g/day...I have not experienced any other deficiency symptoms and am quite confident I am now getting everything I need, but I will keep testing.

Comment author: Vaniver 27 April 2013 06:15:19PM 2 points [-]

He says he's added sulfur

Right, that was how I noticed he had missed it, as with the iron deficiency that he discussed in his first post. When I made my list of nutrients, I checked to make sure everything on his list was on my list, but didn't think to do the reverse.

Comment author: Risto_Saarelma 18 May 2011 09:15:42AM 4 points [-]

beginning tonight am again attempting the uberman sleep schedule (which, if it works, will increase my subjective experience of time by 40-50%).

One of the possible uses for deep sleep is having a phase where the body heals itself more effectively. Some people have reported that the cuts they get heal noticeably slower than usual when they are on uberman. What if extreme polyphasic sleep does inhibit effective healing, and this also affects the anti-cancer component in the model for the Gompertz curve?

Comment author: Vaniver 18 May 2011 10:29:25AM 1 point [-]

What if extreme polyphasic sleep does inhibit effective healing, and this also affects the anti-cancer component in the model for the Gompertz curve?

That's a tough call, and depends on the numbers and how I value hours. Do I prefer daytime hours to nighttime hours? The reverse? Do I discount based on objective time, or subjective time? (i.e. should I seem less patient to others while on Uberman, because to me waiting 3 days for something represents being aware of waiting for 40% longer?) Do I try to weight the future more heavily, since the further future will probably be more awesome than the nearer future?

If I assume the simple goal of "maximize total number of hours awake," then I just need to know how uberman affects my risk growth rate. If it has no physiological effect except aging me at my subjective time (i.e. 16 years pass on the calendar, but I've been awake as much as most people are in 22 years, and my body is 22 years older rather than 16) then it doesn't matter whether I'm on it or not. If it ages me more slowly than that (my body ages 20 years in those 16, but I'm awake for 22) then I'm better off on it. If it ages me more quickly than that (my body ages 30 years in those 16), then I'm better off not doing it.

What seems likely as a middle road, though, is staying on uberman until my body hits 45 years old and cancer starts becoming an issue, and then switching to normal sleep, presuming that uberman does inhibit my cancer response but doesn't increase my chance of death due to accident.

I am regretting not getting a blood test done, though, as it would be nice to compare white blood cell counts before and after.

Comment author: jimrandomh 18 May 2011 02:38:31PM 12 points [-]

If it has no physiological effect except aging me at my subjective time (i.e. 16 years pass on the calendar, but I've been awake as much as most people are in 22 years, and my body is 22 years older rather than 16) then it doesn't matter whether I'm on it or not.

Incorrect, because you've only gotten the benefit of 16 years of medical advancement, rather than 22 years of medical advancement. This alone may overwhelm all other differences.

Comment author: gwern 05 July 2011 04:20:55PM 2 points [-]

And then there are other time-dependent things, like compounding interest/returns.

Comment author: STL 18 May 2011 06:50:13AM 36 points [-]

This offers food for thought about various anti-aging strategies. For example, given the superexponential growth in mortality, if we had a magic medical treatment that could cut your mortality risk in half but didn't affect the growth of said risk, then that would buy you very little late in life, but might extend life by decades if administered at a very young age.

This isn't an anti-aging strategy, but it is an anti-death strategy: low-dose aspirin. As explained in this New York Times article on December 6, 2010, "researchers examined the cancer death rates of 25,570 patients who had participated in eight different randomized controlled trials of aspirin that ended up to 20 years earlier".

Eight. Different. Randomized. Controlled. Trials. Twenty-five thousand people.

They found (read the article) that low-dose aspirin dramatically decreased the risk of death from solid tumor cancers. Again, this ("risk of death") is the gold standard - many studies measure outcomes indirectly (e.g. tumor size, cholesterol level, etc.) which leads to unpleasant surprises (X shrinks tumors but doesn't keep people alive, Y lowers cholesterol levels but doesn't keep people alive, etc.). Best of all is this behavior: "the participants in the longest lasting trials had the most drastic reductions in cancer death years later."

Not mentioned in the article is the fact that aspirin is an ancient drug, in use for over a century with side effects that, while they certainly exist, are very well understood. This isn't like the people taking "life-extension regimens" or "nootropic stacks", who are, as far as I'm concerned, finding innovative ways to poison themselves.

Yet the article went on to say this:

But even as some experts hailed the new study as a breakthrough, others urged caution, warning people not to start a regimen of aspirin without first consulting a doctor about the potential risks, including gastrointestinal bleeding and bleeding in the brain (hemorrhagic strokes).

“Many people may wonder if they should start taking daily aspirin, but it would be premature to recommend people starting taking aspirin specifically to prevent cancer,” said Eric J. Jacobs, an epidemiologist with the American Cancer Society.

I'm a programmer, not a doctor - but after looking around, I concluded that the risks of GI bleeding were not guaranteed fatal, and the risks of hemorrhagic strokes were low in absolute terms. Also, aspirin is famously effective against ischemic strokes. According to Wikipedia: "Although aspirin also raises the risk of hemorrhagic stroke and other major bleeds by about twofold, these events are rare, and the balance of aspirin's effects is positive. Thus, in secondary prevention trials, aspirin reduced the overall mortality by about a tenth."

So unless aspirin's risks are far more grave than I've currently been led to believe, as far as I'm concerned, people saying "hey, even if you're not subject to aspirin's well-known contraindications, you shouldn't start low-dose aspirin just yet" are literally statistically killing people. Cancer is pretty lethal and we're not really good at fixing it yet, so when we find something that can really reduce the risk (and there aren't many - the only other ones I can think of are the magical substances known as not-smoking and avoiding-massive-doses-of-ionizing radiation), we should be all over that like cats on yarn.

I make damn sure to take my low-dose aspirin every day. I started it before reading this article on the advice of my doctor who thought my cholesterol was a little high - I'm almost 28, so it'll have many years in which to work its currently poorly understood magic.

That said, this reduces the risk of one common cause of death (two or three if you throw in heart attacks and ischemic strokes). There are lots of others out there. Even if you could avoid all of them (including the scariest one, Alzheimer's - it's insanely common, we have no fucking clue what causes it or how to stop it, and it annihilates your very self - even if cryonics is ultimately successful, advanced Alzheimer's is probably the true death), humans pretty clearly wear out with an upper bound of 120 years. Maybe caloric restriction can adjust that somewhat. But I think I'll sign up for cryonics sooner rather than later - I'm in favor of upgrading probability from "definitely boned" to "probably boned but maybe not".

Comment author: gwern 17 January 2012 12:17:03AM *  6 points [-]

And I think I have my answer:

Last week, researchers in London reported that they had analyzed nine randomized studies of aspirin use in the United States, Europe and Japan that included more than 100,000 participants. The study subjects had never had a heart attack or stroke; all regularly took aspirin or a placebo to determine whether aspirin benefits people who have no established heart disease.

In the combined analysis, the researchers found that regular aspirin users were 10 percent less likely than the others to have any type of heart event, and 20 percent less likely to have a nonfatal heart attack. While that sounds like good news, the study showed that the risks of regular aspirin outweighed the benefits.

Aspirin users were about 30 percent more likely to have a serious gastrointestinal bleeding event, a side effect of frequent aspirin use. The overall risk of dying during the study was the same among the aspirin users and the others. And though some previous studies suggested that regular aspirin use could prevent cancer, the new analysis showed no such benefit. Over all, for every 162 people who took aspirin, the drug prevented one nonfatal heart attack, but caused about two serious bleeding episodes.

http://well.blogs.nytimes.com/2012/01/16/daily-aspirin-is-not-for-everyone-study-suggests/

Comment author: jsalvatier 17 January 2012 04:27:46AM 0 points [-]

Thank you, very interesting.

Comment author: STL 17 January 2012 12:46:50AM 0 points [-]

From the abstract at:

http://archinte.ama-assn.org/cgi/content/abstract/archinternmed.2011.628v1

During a mean (SD) follow-up of 6.0 (2.1) years involving over 100 000 participants [...] There was no significant reduction in CVD death (OR, 0.99; 95% CI, 0.85-1.15) or cancer mortality (OR, 0.93; 95% CI, 0.84-1.03)

I am suspicious of the 6-year followup. In the original paper linked elsewhere in this comment tree, the observed reduction in cancer mortality grew over time.

I would be more willing to believe this new study if it followed patients for a longer period of time, observed the reduction in cancer mortality, and still concluded that the risks outweighed the benefits.

Comment author: gwern 17 January 2012 01:04:15AM 0 points [-]

I'd like to point out that this pooled analysis of healthy people covered more than 4 times as many healthy people as your original citation covered sick people.

Comment author: STL 17 January 2012 02:07:29AM 0 points [-]

Do you think that the "sick people" were somehow susceptible to cancer in an aspirin-prevention-friendly manner, while the "healthy people" weren't?

(I am considering cancer separately from cardiovascular disease and bleeding risks, as they can be analyzed separately before overall risk-benefit is determined. I would not be surprised to learn that aspirin is very effective at reducing cardiovascular disease among those at risk, while not being worth it for cardiovascular disease among the general population.)

Comment author: gwern 17 January 2012 02:28:21AM 3 points [-]

I'll try again: your original cite said the cancer benefit was detectable at 5 years, and later. I've presented you with a 4 times larger study, in the relevant subpopulation, at 6 years which found no cancer benefit - and you are still asking rhetorical questions and coming up with excuses.

Do you think that if you had seen the evidence the other way around that you would be asking the same questions?

Comment author: LukeStebbing 17 January 2012 05:32:57AM *  3 points [-]

No matter which study I saw first, the other would be surprising. A 100k trial doesn't explain away evidence from eight trials totaling 25k. Given that all of these studies are quite large, I'm more concerned about methodological flaws than size.

I have very slightly increased my estimate that aspirin reduces cancer mortality (since the new study showed 7% reduction, and that certainly isn't evidence against mortality reduction). I have slightly decreased my estimate that the mortality reduction is as strong as concluded by the meta-analysis. I have decreased my estimate that the risk tradeoff will be worth it later in life. I have very slightly increased my estimate that sick people are generally more likely to develop cancer and aspirin is especially good at preventing that kind of cancer, but I mention that only because it's an amusingly weird explanation.

If this new study is continued with similar results, or even if its data doesn't show increased reduction when sliced by quartile (4.6, 6.0, 7.4 years), I would significantly lower my estimate of the mortality reduction.

I'll continue to take low-dose aspirin since my present risk of bleeding death is very low, and if the graphs of cumulative cancer mortality reduction on p34 of the meta-analysis reflect reality, I'll be banking resistance to cancer toward a time when I'm much more likely to need it. I can't decide to take low-dose aspirin retroactively.

Comment author: gwern 17 January 2012 03:56:32PM 1 point [-]

A 100k trial doesn't explain away evidence from eight trials totaling 25k.

It doesn't have to, since they are not trials involving the same populations.

Comment author: STL 17 January 2012 02:43:43AM 0 points [-]

Perhaps I'm misunderstanding the numbers ("OR, 0.93"), but the new study observed a 7% decrease in cancer mortality, which they called "not significant".

Do you think that if you had seen the evidence the other way around that you would be asking the same questions?

I would be unhappy with the other study's population, but very happy with its followup period. (The fact that the observed benefit grew with the length of time taking aspirin was especially convincing, as I mentioned earlier. That is a property that is very unlike "maybe we're seeing it, maybe we're not" noise at the threshold of detection.)

Last year, I told you that polio had no natural reservoirs, and you continued to believe otherwise, so I am not especially inclined to argue further.

Comment author: gwern 17 January 2012 02:52:47AM 1 point [-]

Perhaps I'm misunderstanding the numbers ("OR, 0.93"), but the new study observed a 7% decrease in cancer mortality, which they called "not significant".

No, that's correct. If you want to use stuff that doesn't reach significance, I can't stop you. (You didn't reply to Yvain's points, incidentally.)

Last year, I told you that polio had no natural reservoirs, and you continued to believe otherwise, so I am not especially inclined to argue further.

And you misunderstood the point about carriers defeating eradication attempts.

Comment author: gwern 13 August 2011 11:56:26PM 3 points [-]

I wonder how the aspirin trials would look in regular people (I haven't checked, are any of your randomized trials in normal people?). Mike Darwin on aspirin;

"...My point was that other NSAID drugs wreak more death and mayhem than Vioxx did every year, and yet thy are sold OTC and no one gives the truly incredibly morbidity and mortality a second thought. Any GP or ED doc will regurgitate countless stories of serious GI bleeding due to NSAIDS (and especially aspirin) on cue. Of course, they don’t mention all the hemorrhagic strokes caused by aspirin’s anti-platelet activity because they have no way to distinguish those from “regular strokes” and with so much of the population on aspirin that wouldn’t be easy.

Aspirin causes a truly gruesome and often fatal condition in children called Reye’s syndrome, and if it were any other drug than aspirin, it WOULD have been pulled from the market, Instead, a massive educational campaign was launched to teach parents not to give sick children aspirin – the rational thing to do! However, meanwhile (until the population was educated), children continued to be neurologically maimed and killed by Reye’s. I’ve dialyzed youngsters with multi-system organ failure from Reye’s and it is a wretched and heartbreaking illness with a poor outcome."

Comment author: Yvain 19 May 2011 12:56:25PM *  22 points [-]

The meta-analysis you cite is moderately convincing, but only moderately. They had enough different analyses such that some would come out significant by pure chance. Aspirin was found to have an effect on 15-year-mortality significant only at the .05 level, and aspirin was found not to have a significant effect 20-year-mortality, so take it with a grain of salt. There was also some discussion in the literature about how it's meta-analyzing studies performed on people with cardiac risk factors but not bleed risk factors, and so the subjects may have been better candidates for aspirin than the general population.

The Wikipedia quote you give is referring to secondary prevention, which means "prevention of a disease happening again in someone who's already had the disease". Everyone agrees aspirin is useful for secondary prevention, but there are a lot of cases where something useful for secondary prevention isn't as good for primary. In primary prevention, aspirin doesn't get anywhere near a tenth reduction in mortality (although it does seem to have a lesser effect).

I would say right now there's enough evidence that people who enjoy self-experimentation are justified in trying low-dose aspirin and probably won't actively hurt themselves (assuming they check whether they're at special risk of bleeds first), but not enough evidence that doctors should be demonized for not telling everyone to do it.

Comment author: LukeStebbing 17 January 2012 03:12:12AM *  1 point [-]

Aspirin was found to have an effect on 15-year-mortality significant only at the .05 level, and aspirin was found not to have a significant effect 20-year-mortality, so take it with a grain of salt.

Can you provide your reference for this? I looked at the meta-analysis and what I assume is the 20-year follow-up of five RCTs (the citations seem to be paywalled), and both mention 20-year reduction in mortality without mentioning 15-year reductions or lack thereof.

Edit: Never mind, I found it, followed immediately by

the effect on post-trial deaths was diluted by a transient increase in risk of vascular death in the aspirin groups during the first year after completion of the trials (75 observed vs 46 expected, OR 1·69, 1·08–2·62, p=0·02), presumably due to withdrawal of trial aspirin.

I'd like to see 20-year numbers for people who maintained the trial (and am baffled that they didn't randomly select such a subgroup).

Comment author: LukeStebbing 17 January 2012 05:32:09AM 0 points [-]

The meta-analysis you cite is moderately convincing, but only moderately. They had enough different analyses such that some would come out significant by pure chance.

Their selection methodology on p32 appears neutral, so I don't think they ended up with cherry-picked trials. Once they had their trials, it looks like they drew all conclusions from pooled data, e.g. they did not say "X happened in T1, Y happened in T2, Z happened in T3, therefore X, Y, and Z are true."

Comment author: Fly 18 May 2011 11:21:05PM 4 points [-]

"Cancer is pretty lethal and we're not really good at fixing it yet, so when we find something that can really reduce the risk (and there aren't many - the only other ones I can think of are the magical substances known as not-smoking and avoiding-massive-doses-of-ionizing radiation), we should be all over that like cats on yarn."

Maintaining moderately high blood levels of vitamin D may reduce over all cancer rates by up to 30%. There is also evidence for green tea significantly reducing cancer rates.

Aspirin is an anti-coagulant so wounds take longer to stop bleeding. A surgeon will require that you stop taking aspirin long enough for the blood clotting factors to recover. (Surgeons hate it when they can't stop the bleeding.) If I were under 30 I wouldn't take a daily aspirin as I doubt it provides any benefit and does increase risk slightly. By the time you are 40 your body tissues are in a state of mild, chronic inflammation. That may be good for fighting off infections but isn't so good for the cardiovascular system, lungs, and brain. I recommend baby aspirin for anyone over 40.

Moderate alcohol use is correlated with a significant reduction in cardiovascular events. As with aspirin I would only recommend it for older people and then only if the likelihood of abuse is small.

Comment author: STL 19 May 2011 05:51:41AM 1 point [-]

Maintaining moderately high blood levels of vitamin D may reduce over all cancer rates by up to 30%. There is also evidence for green tea significantly reducing cancer rates.

I haven't seen thoroughly convincing studies, but it's quite possible that I missed them (among the blizzard of junk studies).

Aspirin is an anti-coagulant so wounds take longer to stop bleeding.

This is true, although I've noticed no significant effects. (When the air is cold and dry, I'm sometimes prone to nosebleeds, but they didn't get worse after I started low-dose aspirin).

It's also a bug and a feature. Heart attacks and ischemic strokes are no fun at all.

A surgeon will require that you stop taking aspirin long enough for the blood clotting factors to recover. (Surgeons hate it when they can't stop the bleeding.)

Not a problem for elective surgery (just stop taking it). If you need immediate surgery (e.g. because of an accident), then low-dose aspirin may be a slight risk - but it doesn't transform you into an instant hemophiliac.

If I were under 30 I wouldn't take a daily aspirin as I doubt it provides any benefit

Eight different randomized controlled trials suggest you're wrong. I'm unsure as to whether they studied relatively young adults like me - the problem is that it'd take even more decades to notice an effect. I consider aspirin's effects in older men to be persuasive evidence that it has the same effects for women and younger men like me. (In fact, as I mentioned, my doctor saw my slightly elevated cholesterol and told me to start fish oil and low-dose aspirin when I was 25 - it was only later that I saw the article about cancer.)

I recommend baby aspirin for anyone over 40.

Citation needed. Do you really think that, in your 20s and 30s, your cells aren't accumulating damage that eventually leads to cancer, so that low-dose aspirin has nothing to prevent? Really? It's possible that the cumulative damage hypothesis, for lack of a better name, is false, but I consider it overwhelmingly likely to be true.

Obviously, in making this decision, my own health is at stake - and I am very careful. In my judgment, trying to be as rational as possible, I believe that the risks of starting low-dose aspirin in my 20s are very small, and outweighed by the cumulative benefit, when I'm older, of having taken it for so long (the time-dependent nature of the benefit is important).

Comment author: Fly 19 May 2011 07:29:47AM 2 points [-]

"Eight different randomized controlled trials suggest you're wrong."

If the studies were done 20 years ago my guess is that the original trials were performed to see if aspirin reduced the risk of heart attacks. (At least that is what I recollect from that time period.) I doubt there were many people under 30 in those trials. I saw no indication in the linked article that ages were broken out so that one could determine whether people in their 20s who took aspirin for several years had less cancer 20 years later. Since few young people would be expected to get cancer I doubt the studies show that people in their 20s developed significantly fewer cancers from taking aspirin. My guess is that most of the people in the studies were men in their 40s, 50s, and 60s, i.e., those most at risk of heart attack.

"Do you really think that, in your 20s and 30s, your cells aren't accumulating damage that eventually leads to cancer, so that low-dose aspirin has nothing to prevent?"

My opinion is that the typical young person under 30 who doesn't abuse their body by smoking or excessive drinking has sufficient mechanisms to repair molecular damage so that aspirin will provide no additional benefit. Metabolism causes damage but it only becomes a problem when the body systems have deteriorated to the point where the body no longer keeps up with the damage done.

I believe that the cancer and Alzheimer prevention benefits from aspirin are due to reducing inflammation. I doubt people in their 20s typically experience mild chronic inflammation so I doubt aspirin will be beneficial. (I don't have specific papers to cite. This is just my impression from reading about cancer, Alzheimer's Disease, and inflammation for decades. I suspect you could find papers that discuss increasing inflammation levels with age and other papers that discuss the connection between inflammation and cancer and AD and other papers that discuss aspirin and inflammation reduction.) By their 40s such inflammation is common. For people in their 30s I viewed it as a toss-up.

I doubt most people in their 20s or 30s will be troubled by cancer or Alzheimer's Disease. There should be effective cures and preventative measures long before they are at significant risk.

Comment author: STL 19 May 2011 12:14:19PM 3 points [-]

If the studies were done 20 years ago my guess is that the original trials were performed to see if aspirin reduced the risk of heart attacks.

Yes. The study's full text said: "We therefore determined the effect of aspirin on risk of fatal cancer by analysis of individual patient data for deaths due to cancer during randomised trials of daily aspirin versus control (done originally for primary or secondary prevention of vascular events) in which the median duration of scheduled trial treatment was at least 4 years."

There should be effective cures and preventative measures long before they are at significant risk.

Hope is not a plan.

Comment author: gwillen 09 June 2011 10:09:29PM 1 point [-]

Hope is not a plan.

I don't know if this is original, but it reminds me of the unofficial motto of Google's Site Reliability Engineering organization: "Hope is not a strategy."

Comment author: PhilGoetz 23 December 2011 04:46:20AM 1 point [-]

First I heard this phrase was a book by the Army chief of staff: Hope is not a method.

Comment author: Baughn 22 October 2011 01:25:24PM 0 points [-]

Hm? No, that's about as official as we have.

Comment author: loqi 19 May 2011 05:48:46PM 1 point [-]

Vitamin D is really important. There is an established causal link between vitamin D and immune function. It doesn't just enhance your immune response - it's a prerequisite for an immune response.

Anecdote: Prior to vitamin D supplementation, I caught something like 4 colds per year on average. I'm pretty sure I never did better than 2. I started taking daily D supplements about a year and half ago, and caught my first cold a few days ago. It's worth taking purely as a preventative cold medicine.

Comment author: jsalvatier 18 May 2011 03:31:57PM 3 points [-]

You've convinced me to look into this. Do you have a link to the metastudy? Have you considered a top level post about this?

Comment author: STL 19 May 2011 05:17:28AM 2 points [-]

You've convinced me to look into this.

Cool. I also convinced LukeStebbing, my best friend, to begin taking low-dose aspirin. He researched (i.e. looked up on the Internet) its interaction with moderate alcohol consumption, which I currently don't consume (although if he's right about its health benefits, I should - the problem is that there aren't any massive RCTs demonstrating a clear effect). I'm harassing him now to add a comment about what he learned.

Do you have a link to the metastudy?

The NYT linked to its abstract at The Lancet's website. The full text is behind a paywall.

Have you considered a top level post about this?

If post-ifying long comments is kosher, I could do that - but I really have nothing more to add, except one more thing I remembered. Aspirin and its NSAID relatives share similar-but-different mechanisms of action - aspirin is special because it has irreversible effects, see Wikipedia's article for more info. In particular, this means that other NSAIDs can interfere with aspirin (not in a way that's likely to do nasty damage to you - there are plenty of those interactions - but in a way that blunts aspirin's special effects). As a result, while I used to occasionally take ibuprofen for headaches, when I began low-dose aspirin I stopped doing that. Now, when I have a rare headache, I'll take full-strength aspirin.

Comment author: Alicorn 19 May 2011 05:24:41AM *  0 points [-]

As a result, while I used to occasionally take ibuprofen for headaches, when I began low-dose aspirin I stopped doing that. Now, when I have a rare headache, I'll take full-strength aspirin.

I would consider this significant reason to not take aspirin regularly. Ibuprofen decisively zaps my (frequent) headaches in a way that other analgesics do not.

Comment author: STL 19 May 2011 06:16:02AM 2 points [-]
  1. Have you tried aspirin specifically for headaches?

  2. I'm not a doctor, so I can't diagnose anything, especially over the Internet (unless the patient is a C++ program), but it's possible for headaches to have a root cause that should be addressed, instead of the symptoms. In my case, getting a plastic nightguard from my dentist to prevent unconscious teeth grinding at night, also alleviated jaw clenching at night - so much so that when I make the effort to brush my teeth and wear my nightguard (which is unfortunately not all the time) I almost never wake up with a headache anymore.

  3. I can't think of a way to say this without sounding snarky (and I really liked Luminosity/Radiance, so I especially don't want to be rude), but I'm going to say it anyways:

Which do you dislike more: headaches, or cancer? Choose carefully.

Back to being non-snarky: I assume/hope that debilitating, world-shattering migranes aren't the issue - faced with them, "screw cancer reduction, I need to be able to function day-to-day" would be an entirely rational response. Interestingly, I just noticed this (and a typo) at Wikipedia: "There is some evidence that low-dose asprin has benefit for reducing the occurrence of migraines in susceptible individuals.[67][68][69][70]"

Comment author: Alicorn 19 May 2011 06:44:28AM *  4 points [-]

I do not have debilitating, world-shattering migraines. I just get headaches. More days than not. I have one right now. My mom once had a headache for an entire year. (This remains a medical mystery.) I have on occasion had headaches that lasted so long that I expected to imitate her, although so far I don't think I've actually broken a full week (with breaks provided by ibuprofen).

I actually don't usually medicate them. I do that when they are so bad that they wake me up in the middle of the night, or when they occur early in the day; otherwise I let sleep take care of them.

The one time I tried aspirin for pain relief, I don't remember what it was for, although a headache was likely. I do remember that it gave me a stomachache which was worse than whatever it was supposed to get rid of for me. I wouldn't expect a tiny dose to have this effect, especially if I took it with food or something, but if I were forced to rely on it as my only analgesic, I would be in something of a quandary.

The question is not, "Which do you dislike more: headaches, or cancer?" It's, "Which do you prefer: effective pain relief for your extended, commonplace pain, or a risk-reducing drug which has not actually been extensively tested in your gender or age group?"

Comment author: jimrandomh 19 May 2011 01:28:42PM 1 point [-]

I do not have debilitating, world-shattering migraines. I just get headaches. More days than not. I have one right now. My mom once had a headache for an entire year. (This remains a medical mystery.) I have on occasion had headaches that lasted so long that I expected to imitate her, although so far I don't think I've actually broken a full week (with breaks provided by ibuprofen).

Based solely on this description, this sounds like a pretty big deal. It also sounds like the sort of thing that might have a subtle but simple cause, which might be discovered by taking sufficiently detailed notes. I haven't tried it myself, but I recall seeing references to software for this purpose, which might suggest specific things to investigate as possible causes. Are your headaches by any chance related (positively or negatively) to eating choline? Would you be able to detect if there were other relations of that type?

Comment author: Alicorn 19 May 2011 06:38:21PM 0 points [-]

I tracked my headaches for about a month and a half once and then stopped, but I didn't correlate it with food (particularly not choline, which I don't even know what foods it comes in). I haven't noticed any decisive correlations between various foods and the headaches. I got one yesterday evening (a rare overnighter, which I'm waiting for the ibuprofen to chase away now) and that day I had leftover vegetable strata and juice and toast with hummus and some ice cream, none of which are or contain unusual foods for me.

Comment author: jimrandomh 19 May 2011 06:58:24PM 1 point [-]

There's lots of choline is in meat and eggs, and there're smaller qantities of it in various other things. I've heard of headaches from both too much choline (when taking choline supplements) and too little (especially when taking piracetam, which depletes choline. I take both piracetam and choline citrate). Being a vegetarian is listed as a risk factor for deficiency on the wikipedia page.

Comment author: Alicorn 19 May 2011 07:03:10PM 2 points [-]

I've been eating a lot of eggs lately. Should I try eating eggs every day for a week and then no eggs for a week and see what happens?

Comment author: STL 19 May 2011 06:57:14AM 2 points [-]

Fair enough - if I were in your shoes I would probably make the same decision as you.

Comment author: Alicorn 19 May 2011 07:13:21AM 0 points [-]

All that said: is taking aspirin regularly and an ibuprofen once a week inferior to not taking aspirin regularly and an ibuprofen once a week?

Comment author: STL 19 May 2011 12:09:30PM 0 points [-]

I don't know. Wikipedia says:

According to the U.S. Food and Drug Administration, "Ibuprofen can interfere with the antiplatelet effect of low-dose aspirin (81 mg per day), potentially rendering aspirin less effective when used for cardioprotection and stroke prevention." Allowing sufficient time between doses of ibuprofen and immediate release aspirin can avoid this problem. The recommended elapsed time between a 400 mg dose of ibuprofen and a dose of aspirin depends on which is taken first. It would be 30 minutes or more for ibuprofen taken after immediate release aspirin, and 8 hours or more for ibuprofen taken before immediate release aspirin. However, this timing cannot be recommended for enteric-coated aspirin. But, if ibuprofen is taken only occasionally without the recommended timing, the reduction of the cardioprotection and stroke prevention of a daily aspirin regimen is minimal.[19]

Which of course doesn't mention the cancer effects, but there you go.

My intuition suggests that regular low-dose aspirin and weekly ibuprofen still has benefits that outweigh the risks, as compared to weekly ibuprofen only. However, my intuition didn't expect the effect, mentioned in the study's full text, where alternate-day low-dose aspirin appeared to have no effect on cancer.

Comment author: LukeStebbing 19 May 2011 04:39:07PM *  0 points [-]

There's also paracetamol (secret identity: acetaminophen (secret secret identity: tylenol)), which is not an NSAID, but I would guess you've tried it too. Fun snacks and/or facts:

http://en.wikipedia.org/wiki/Paracetamol

Until 2010 paracetamol was believed to be safe in pregnancy (as it does not affect the closure of the fetal ductus arteriosus as other NSAIDs can.) However, in a study published in October 2010 it has been linked to infertility in the posterior adult life of the unborn.

recent research show some evidence that paracetamol can ease psychological pain

ETA: I just remembered two important contraindications: Don't take more than 2g/day if you drink alcohol, and consider not taking more than 650mg at a time, since that's the FDA's revised recommendation after the old max dosage was shown to alter liver function in some healthy adults.

Comment author: Alicorn 19 May 2011 06:29:09PM 0 points [-]

Tylenol works about as well as other non-ibuprofen analgesics, which is to say it makes the headaches fade rather than go the hell away.

I don't drink alcohol ever, so that's not an issue.

Comment author: LukeStebbing 19 May 2011 05:52:10AM *  5 points [-]

I didn't actually do much research; I just went through several pages of hits for aspirin alcohol and low-dose aspirin moderate alcohol. I saw consistent enough information to convince me:

  • never to take them at the same time, sample:

    In a paper published in the Journal of the American Medical Association, researchers at the Veterans Administration Medical Center in the Bronx found that taking aspirin one hour before drinking significantly increases the concentration of alcohol in the blood.

  • that the nasty interactions only seemed to happen at 21+ drinks per week, sample:

    There is no proof that mild to moderate alcohol use significantly increases the risk of upper gastrointestinal bleeding in patients taking aspirin, especially if the aspirin is taken only as needed. However, people who consumed at least 3-5 drinks daily and who regularly took more than 325 mg of aspirin did have a high risk of bleeding.

That, in conjunction with the 2010 Dietary Guidelines for Americans, was enough to convince me to combine 81mg of aspirin in the morning with 0-3 US standard drinks in the evening at an average of 1.0/day. I'd like more information, but I haven't had time to dig it up yet and combining them seemed like a lower-risk provisional decision than inaction.

I recommend you do your own research and talk to your doctor, but maybe someone will find that information to be a helpful starting point.

Comment author: satt 19 May 2011 04:58:24AM 8 points [-]

I got curious too and found an online copy. Reference: Rothwell et al. (2011), "Effect of daily aspirin on long-term risk of death due to cancer: analysis of individual patient data from randomised trials", The Lancet, vol. 377, pp. 31-41.

Comment author: STL 19 May 2011 06:32:57AM 1 point [-]

Fascinating - I learned several things from the full text. Have an upvote!

Comment author: TimFreeman 20 May 2011 10:35:30PM *  0 points [-]

Effect of daily aspirin on long-term risk of death due to cancer: analysis of individual patient data from randomised trials

Based just on the title, they seem to be looking at the wrong thing. You want to know the effect of daily aspirin on long-term risk of death, not on long-term risk of death from cancer. Your life isn't improved much if you trade death from cancer for death from (say) depression and suicide. (I have no reason to expect such a trade.)

I read the abstract too, and my concern was not changed. I have not read the whole paper.

Nevertheless, if that's the best available information, that's worth knowing. Thanks for posting it. Have an upvote.

Comment author: satt 21 May 2011 05:17:36AM 3 points [-]

I haven't read the whole paper, but I also wanted to see what aspirin's effect on all causes of death was. (I wondered whether the higher risk of bleeding would offset the lower risk of cancer; it didn't.) The magic keywords to Ctrl-F for are "all-cause".

p. 34:

The reduction in cancer deaths on aspirin during the trials resulted in lowered in-trial all-cause mortality (10.2% vs 11.1%, OR 0.92, 0.85–1.00, p=0.047, webappendix p 4), even though other deaths were not reduced (0.98, 0.89–1.07, p=0.63).

p. 36:

In patients with scheduled duration of trial treatment of 5 years or longer, all-cause mortality was reduced at 15 years’ follow-up (HR 0·92, 0·86–0·99, p=0·03), due entirely to fewer cancer deaths, but this effect was no longer seen at 20 years (0·96, 0·90–1·02, p=0·37). However, the effect on post-trial deaths was diluted by a transient increase in risk of vascular death in the aspirin groups during the first year after completion of the trials (75 observed vs 46 expected, OR 1·69, 1·08–2·62, p=0·02), presumably due to withdrawal of trial aspirin.

p. 39:

Fourth, we were unable to determine the effect of long-term (eg, 20–30 years) continued aspirin use on cancer death or all-cause mortality because of the finite duration of the trials.

and

Our analyses show that taking aspirin daily for 5–10 years would reduce all-cause mortality (including any fatal bleeds) during that time by about 10% (relative risk reduction). Subsequently, there would be further delayed reductions in risk of cancer death, but no continuing excess risk of bleeding.

The big caveat I have in light of this is that the trial patients were in their 40s and older. I would guess the cost-benefit balance tilts the other way for sufficiently young people because younger people have a lower risk of cancer or CVD.

Comment author: Alicorn 18 May 2011 07:18:22AM 1 point [-]

Is a regular dose of low aspirin something that my doctor should be informed about in case she wants to prescribe contraindicative medications at some point in the future (are there any?) or is it so harmless that I don't even need to update her? What low dose is indicated?

Comment author: STL 18 May 2011 07:43:58AM 8 points [-]

I didn't mean to imply that "you should do this now without telling your doctor". You should certainly tell your doctor about all the medications you're taking! I would even say that "ask your doctor immediately whether this is a good idea" is a reasonable approach(1), in contrast to the inexplicably indifferent tone of the article - although I'm sure the writer and editors have processed a zillion "observational study on a limited number of people for a limited amount of time indicates that X may have some influence on Y which ultimately leads to Z" articles, where the correct action in response really is to say "yes, that's nice, tell me when you know more".

The most significant caveat mentioned in the article was: "While Dr. Jacobs said the study design was valid, relatively few women were included in the trials, making it difficult to generalize the results to women." I'm male, so that one didn't apply to me. But look down a few paragraphs in the article: "who did an observational study several years ago reporting that women who had taken aspirin regularly had a lower risk of ovarian cancer". Even if I were female (it must be frustrating to have studies commonly ignore the half of the population that you're a member of(2)), I'd take the sum of this evidence as arguing in favor of starting low-dose aspirin.

What low dose is indicated?

"The specific dose of aspirin taken did not seem to matter — most trials gave out low doses of 75 to 100 milligrams"

As I recall from looking around the Internet, full-strength aspirin sizes vary around the world - in the US, Bayer sells 325mg pills, while I remember seeing that 300mg was common elsewhere. The low-dose aspirins also seem to vary as a consequence: 325/4 = 81.25, 300/4=75.

  1. Although I would say that if you explain the study to your doctor, and they tell you that you shouldn't do it, and they can't explain why other than vague and unspecified risks, in the face of damn solid evidence - that you should get a new doctor.

  2. On the other hand, it must be nice to have 5.2 additional years of life expectancy at birth. On the third hand, wow, I had forgotten that the difference was that large. On the fourth hand, some of that is due to men more commonly doing stupid things (like smoking) that I don't do.

Comment author: gwern 19 July 2011 05:17:31PM 8 points [-]

"Last month, a 114-year-old former schoolteacher from Georgia named Besse Cooper became the world's oldest living person. Her predecessor, Brazil's Maria Gomes Valentim, was 114 when she died. So was the oldest living person before her, and the one before her. In fact, eight of the last nine "world's oldest" titleholders were 114 when they achieved the distinction. Here's the morbid part: All but two were still 114 when they passed it on. Those two? They died at 115.

The celebration surrounding Cooper when she assumed the title, then, might as well have been accompanied by condolences. If historical trends hold, she will likely be dead within a year.

It's no surprise that it's hard to stay the "world's oldest" for very long. These people are, after all, really old. What's surprising is just how consistent the numbers have been. Just seven people whose ages could be fully verified by the Gerontology Research Group have ever made it past 115. Only two of those seven lived to see the 21st century. The longest-living person ever, a French woman named Jeanne Calment, died at age 122 in August 1997; no one since 2000 has come within five years of matching her longevity.

...In the past few years, the global count of supercentenarians—people 110 and older—has leveled off at about 80. And the maximum age hasn't budged. Robert Young, senior gerontology consultant for the Guinness Book of World Records, says, "The more people are turning 110, the more people are dying at 110."

Young calls this the "rectangularization of the mortality curve." To illustrate it, he points to Japan, which in 1990 had 3,000 people aged 100 and over, with the oldest being 114. Twenty years later, Japan has an estimated 44,000 people over the age of 100—and the oldest is still 114. For reasons that aren't entirely clear, Young says, the odds of a person dying in any given year between the ages of 110 and 113 appear to be about one in two. But by age 114, the chances jump to more like two in three."

--Slate, "The World's Deadliest Distinction: Why aren't the oldest living people getting any older?"

Comment author: gwern 19 September 2013 03:35:11PM 1 point [-]

"The World’s Oldest Person Is getting Younger":

The two oldest men in the world died recently. Jiroemon Kimura, a 116-year-old, died in June in Japan after becoming the oldest man yet recorded. His successor Salustiano Sanchez, aged 112 and born in Spain, died last week in New York State. That leaves just two men in the world known to be over 110, compared with 58 women (19 of whom are Japanese, 20 American). By contrast there are now half a million people over 100, and the number is growing at 7 percent a year.

For all the continuing improvements in average life expectancy, the maximum age of human beings seems to be stuck. It’s still very difficult even for women to get to 110 and the number of people who reach 115 seems if anything to be falling. According to Professor Stephen Coles, of the Gerontology Research Group at University of California, Los Angeles, your probability of dying each year shoots up to 50 percent once you reach 110 and 70 percent at 115.

Female “supercentenarians” — as 110-plus people are called — are a long way off breaking the record for long life. The record, 122, was set by Jeanne-Louise Calment in 1997, and the oldest living person in the world, Misao Okawa, 115 years and 199 days as of today, would have to live another seven years to overtake that: meaning Ms Calment’s record will stand for at least 23 years. Ms Okawa is the only person over 115 alive today, whereas in 1997 there were four.

... The lack of any increase in people living past 110 is surprising. Demographers are so used to rising average longevity all that they might expect to see more of us pushing the boundaries of extreme old age as well. Instead there is an enormous increase in 100-year-olds and not much change in 110-year-olds.

... All those people who eat wheat germ or special yoghurt or vitamin supplements in the hope of living forever are probably wasting their time. So too are those who practice “caloric restriction” on the grounds that mice live much longer if nearly starved. Such gaunt folk might get to 100 instead of 90, but they are not going to get to 120 by such means.

To get an idea of just how extraordinary an outlier Calment was, see my graphing of the GRG oldest-person dataset.

Comment author: CronoDAS 18 May 2011 11:56:45PM 6 points [-]

I once read that the human body has the reliability profile of a massively redundant system that starts out riddled with defects. (I think it was in a textbook on fault-tolerant hardware design.)

See also.

Comment author: Fly 18 May 2011 06:04:44AM 1 point [-]

Scientists have already demonstrated interventions that significantly extend maximum lifespan in several species. I see no reason to believe humans will be different.

My guess is that the primary cause of human aging is a combination of "depleted" stem cells combined with a gradual disruption of regulatory homeostasis. Part of the problem with "depleted" stem cells is an accumulation of silencing errors in the stem cell DNA. Another part is a gradual breakdown in local cell signaling that regulates cell fate. I believe both problems could be reversed by targeted "rebooting" of stem cell niches. I.e., inject new stem cells which have been engineered to stimulate tissue rejuvenation while also injecting growth factors and cell differentiation factors in the local tissue. (Most likely the would be done by injecting a fluid which forms a scaffolding which then releases the stem cells and factors over time. Such technology is currently being developed to repair cartilage.)

It may also be necessary to kill some existing cells so that they can be replaced by rejuvenated tissue. E.g., rebooting the immune system. This technology is currently being developed for bone marrow transplant, organ transplantation, and training the immune system to target cancers.

I expect such technologies will be common within the next two decades and should make Gompertz curves obsolete for humans.

Comment author: wedrifid 18 May 2011 06:27:32AM 0 points [-]

My guess is that the primary cause of human aging is a combination of "depleted" stem cells combined with a gradual disruption of regulatory homeostasis.

Not Telomeres?

Comment author: Fly 18 May 2011 08:19:58PM *  2 points [-]

Consider spermatogenesis as a model. There is a primary pool of slow dividing stem cells which are maintained in that state by local signaling from neighboring cells. In these stem cells, telomerase is sufficiently active that telomere length is preserved. The primary stem cell pool slowly replenishes a pool of fast dividing secondary stem cells in which telomerase is slightly less active. These are stem cells as the pool is largely self renewing. The secondary stem cell pool also generates progenitor cells which divide and differentiate to become sperm. Telomerase activity is much lower in these later cell generations so telomere length shortens with each division.

My speculation...

Bone marrow niches contain a common primary stem cell pool which has the potential to restore the primary stem pools in local tissues such as the testes. E.g., conditions in testes would cause release of signaling molecules into the blood. Those molecules would stimulate a special bone marrow stem cell causing differentiation into a primary sperm stem cell which is released into the blood. From the blood the stem cell enters the testes where it takes up residence in the local stem cell pool. In a similar manner wound healing recruits a variety of stem cell types from the bone marrow. (This would explain why fast cell turnover tissues don't acquire mutations or shorter telomeres at a significantly higher rate than slow turnover tissues.)

Average telomere length decreases when the primary stem cell pools become depleted. E.g., chronic inflammation or stress might deplete the primary stem cell pool so that the secondary stem cell pools aren't replenished, leading to decreased telomere length in the daughter cells. I.e., short telomeres are a sign of primary stem cell pool depletion, not a cause of aging. (Note that removing chronic stress may result in average telomere length increasing for white blood cells.)

Potential causes of stem cell depletion: 1) Stochastic differences in initial stem cell state. Due to molecular events such as DNA methylation, histone modifications, and differing signaling gradients from the local neighborhood some stem cells will divide faster and produce a higher percentage of differentiated daughter cells. Over time the stem cell pool will consist of cells whose initial internal settings favored slow division and a low percentage of daughter cells. This depleted stem cell pool becomes less and less able to meet the tissue regeneration needs of the body. 2) Gradual dis-regulation of the stem cell niche causes non-optimal functioning of stem cell renewal and differentiation. (With age red, blood cell producing, bone marrow gradually transforms into yellow, fat cell producing bone marrow.) 3) Environmental factors that alter stem cell epigenetic state causing poor functioning.

A strategy for rejuvenation would be to supply new stem cells engineered to be in an optimal epigenetic state for tissue renewal. By itself this would not suffice since mouse studies have shown that merely providing young stem cells won't cause old muscle to heal. Various grow factors and other signaling molecules must also be provided in the target tissue. Eventually the old cells would be replaced and the local tissue would return to a "young" signaling environment.

Comment author: PhilGoetz 18 May 2011 04:06:58AM *  6 points [-]

The literature I've seen - notably Finch, Senescence and the Genome - plot the Gompertz curve as a pure exponential that falls off at the end. It gives a really nice fit to the exponential almost up to the end. Then - sorry, this is the opposite of what is claimed in the post - it falls off! That is, if you live to be about 100, the chance of your dying stops increasing exponentially.

(As George Burns said, "The secret to living forever is to live to be 100. Very few people die after the age of 100.")

This suggests (doesn't prove, just suggests) that our mortality rate is adaptive. The Gompertz curve falls off at the high end because it doesn't get enough data points to evolve a proper fit there.

Comment author: timtyler 18 May 2011 10:35:33AM 1 point [-]

The Gompertz curve falls off at the high end because it doesn't get enough data points to evolve a proper fit there.

A more conventional explanation:

Redundancy exhaustion over the life course explains the observed 'compensation law of mortality' (mortality convergence at later life, when death rates are becoming relatively similar at advanced ages for different populations of the same biological species), as well as the observed late-life mortality deceleration, leveling-off, and mortality plateaus.

Comment author: gwern 21 January 2012 09:13:26PM *  1 point [-]

Or... it really is just data collection problems. Via FightAging, "Mortality measurement at advanced ages: A study of the Social Security Administration Death Master File" (emphasis added):

Accurate estimates of mortality at advanced ages are essential to improving forecasts of mortality and the population size of the oldest old age group. However, estimation of hazard rates at extremely old ages poses serious challenges to researchers: (1) The observed mortality deceleration may be at least partially an artifact of mixing different birth cohorts with different mortality (heterogeneity effect); (2) standard assumptions of hazard rate estimates may be invalid when risk of death is extremely high at old ages and (3) ages of very old people may be exaggerated.

...Study of several single-year extinct birth cohorts shows that mortality trajectory at advanced ages follows the Gompertz law up to the ages 102-105 years without a noticeable deceleration. Earlier reports of mortality deceleration (deviation of mortality from the Gompertz law) at ages below 100 appear to be artifacts of mixing together several birth cohorts with different mortality levels and using cross-sectional instead of cohort data. Age exaggeration and crude assumptions applied to mortality estimates at advanced ages may also contribute to mortality underestimation at very advanced ages.

Comment author: timtyler 21 January 2012 11:31:25PM *  1 point [-]

No, since late life mortality deceleration and mortality plateaus are observed in numerous organisms - including Drosophila melanogaster - e.g. see the details in Why organisms show late-life mortality plateaus: a null model for comparing patterns of mortality.

Comment author: gwern 21 January 2012 11:50:41PM 0 points [-]

It's the humans that matter for us...

Comment author: timtyler 22 January 2012 12:59:55AM 0 points [-]

For you maybe. Those interested in biological senescence need a general theory that accounts for late life mortality deceleration. Attributing it to "data collection problems" fails to capture the phenomenon.

Comment author: Eugine_Nier 18 May 2011 04:16:18AM 2 points [-]

Well the wikipedia article on the topic suggests that the probability of dying also includes an age-independent component, i.e., lightning strikes, which tends to small for humans in developed countries.

Comment author: JoshuaZ 18 May 2011 03:42:06AM *  17 points [-]

There's a related problem that often isn't appreciated. In general, in the natural environment if the average lifespan is around L, evolution will have no problem creating all sorts of tricks to maximize what it gets out of organs but causes them to fail just around or sometime after L. That means, that if evolution can get an advantage by making things fail late in the process, it will. This is consistent with the Gompertz curve, and it also suggests that optimists like Aubrey de Grey may be massively underestimating the difficulty in extending lifespan. As we get a larger population of very elderly, we're likely to run into diseases and problems we've never even seen before. To reach actuarial escape velocity, we will likely need to anticipate such diseases, and effective treatments, before we even ever encounter the diseases. That requires a degree of understanding of the human body that is well beyond our current level.

Comment author: Yvain 18 May 2011 12:48:45AM 4 points [-]