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Living Forever is Hard, or, The Gompertz Curve

by gwern5 min read17th May 201187 comments

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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.

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[-][anonymous]11y 46

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, ... (read more)

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[-]Scott Alexander11y 30

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.

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1LukeStebbing10yCan you provide your reference for this? I looked at the meta-analysis [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736%2810%2962110-1/abstract] and what I assume is the 20-year follow-up [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736%2810%2961543-7/abstract] 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 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).
0LukeStebbing10yTheir 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."
[-]gwern10y 11

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/

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0jsalvatier10yThank you, very interesting.
0[anonymous]10yFrom the abstract at: http://archinte.ama-assn.org/cgi/content/abstract/archinternmed.2011.628v1 [http://archinte.ama-assn.org/cgi/content/abstract/archinternmed.2011.628v1] 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.
0gwern10yI'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.
0[anonymous]10yDo 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.)
6gwern10yI'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?
4LukeStebbing10yNo 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 [http://donner.ps.toyaku.ac.jp/d1c_st/d1c/sdarticle.pdf] 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.
1gwern10yIt doesn't have to, since they are not trials involving the same populations.
0[anonymous]10yPerhaps I'm misunderstanding the numbers ("OR, 0.93"), but the new study observed a 7% decrease in cancer mortality, which they called "not significant". 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.
1gwern10yNo, 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.) And you misunderstood the point about carriers defeating eradication attempts.
4Fly11y"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.
1loqi11yVitamin D is really important. There is an established causal link between vitamin D and immune function [http://www.scientificamerican.com/blog/post.cfm?id=another-reason-vitamin-d-is-importa-2010-03-07] . 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 [http://www.scientificamerican.com/blog/post.cfm?id=vitamin-d-deficiency-linked-to-more-2009-02-23] .
1[anonymous]11yI haven't seen thoroughly convincing studies, but it's quite possible that I missed them (among the blizzard of junk studies). 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. 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. 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.) 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).
3Fly11y"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 inflammatio
2[anonymous]11yYes. 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." Hope is not a plan.
0gwillen10yI 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."
0PhilGoetz10yFirst I heard this phrase was a book by the Army chief of staff: Hope is not a method [http://www.amazon.com/Hope-Not-Method-Gordon-Sullivan/dp/076790060X].
0Baughn10yHm? No, that's about as official as we have.
4jsalvatier11yYou've convinced me to look into this. Do you have a link to the metastudy? Have you considered a top level post about this?
9satt11yI got curious too and found an online copy [http://donner.ps.toyaku.ac.jp/d1c_st/d1c/sdarticle.pdf]. 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.
2[anonymous]11yFascinating - I learned several things from the full text. Have an upvote!
0TimFreeman11yBased 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.
3satt11yI 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: p. 36: p. 39: and 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.
3[anonymous]11yCool. 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. The NYT linked to its abstract [http://www.thelancet.com/journals/lancet/article/PIIS0140-6736%2810%2962110-1/abstract] at The Lancet's website. The full text is behind a paywall. 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 [http://en.wikipedia.org/wiki/Aspirin] 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.
5LukeStebbing11yI didn't actually do much research; I just went through several pages of hits for aspirin alcohol [http://www.google.com/search?q=aspirin+alcohol] and low-dose aspirin moderate alcohol [http://www.google.com/search?q=low-dose+aspirin+moderate+alcohol]. I saw consistent enough information to convince me: * never to take them at the same time, sample [http://www.highbeam.com/doc/1P2-1045321.html]: * that the nasty interactions only seemed to happen at 21+ drinks per week, sample [http://www.australianprescriber.com/magazine/28/1/18/9/]: That, in conjunction with the 2010 Dietary Guidelines for Americans [http://www.cnpp.usda.gov/dgas2010-dgacreport.htm], was enough to convince me to combine 81mg of aspirin in the morning with 0-3 US standard drinks [http://www.cdc.gov/alcohol/faqs.htm#standDrink] 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.
0Alicorn11yI would consider this significant reason to not take aspirin regularly. Ibuprofen decisively zaps my (frequent) headaches in a way that other analgesics do not.
2[anonymous]11y1. 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 [http://en.wikipedia.org/wiki/Migrane#Medication]: "There is some evidence that low-dose asprin has benefit for reducing the occurrence of migraines in susceptible individuals.[67][68][69][70]"
4Alicorn11yI 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?"
2[anonymous]11yFair enough - if I were in your shoes I would probably make the same decision as you.
0Alicorn11yAll that said: is taking aspirin regularly and an ibuprofen once a week inferior to not taking aspirin regularly and an ibuprofen once a week?
0[anonymous]11yI don't know. Wikipedia says [http://en.wikipedia.org/wiki/Ibuprofen#Interaction_with_aspirin]: 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.
1jimrandomh11yBased 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?
0Alicorn11yI 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.
1jimrandomh11yThere'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.
3Alicorn11yI'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?
4jimrandomh11yThat sounds like a worthwhile experiment. I would also suggest keeping a headache log and a food log (there are cell phone apps to make it easy; you photograph things instead of writing them down) and analyzing them after a month or two.
1Alicorn11yI'll restart the headache log and combine the food diary. (Is it worth including times of eating various things?) A cell phone app will not help, since I don't have a cell phone.
0wedrifid11yWow. That's a rather significant divergence from culture! Tim Ferris would be impressed.
5AdeleneDawner11yOr maybe just one that people don't talk about much. I only own a cell phone because I needed a way to have contact with the rest of the world while my internet access was down when I moved a few months ago. I don't think it's actually useable at this point - I haven't added minutes to it for quite a while.
4Alicorn11yI had a cellphone once for about a week, but then I gave it back.
0LukeStebbing11yThere'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 [http://en.wikipedia.org/wiki/Paracetamol] 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.
0Alicorn11yTylenol 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.
3gwern10yI 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 [http://chronopause.com/index.php/2011/08/12/interventive-gerontology-101-01-the-basics/#comment-3263] on aspirin;
-6aelephant10y
2Alicorn11yIs 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?
[-][anonymous]11y 10

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 m... (read more)

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[-]JoshuaZ11y 20

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.

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3Sergej_Shegurin6yIf we can 3D-print or grow up organs than the problem mentioned by you gets effectively solved for anything but our brains. That's why I like organ engineering approach much better than other approaches. As for brain, CRISPR/Cas9 engineering is a really great approach. It gives us potentially so many degrees of freedom.
[-]gwern10y 12

"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 he

... (read more)
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3gwern8y"The World’s Oldest Person Is getting Younger" [http://www.thetimes.co.uk/tto/opinion/columnists/article3872913.ece]: To get an idea of just how extraordinary an outlier Calment was, see my graphing of the GRG oldest-person dataset [http://math.stackexchange.com/a/388131].
[-]CronoDAS11y 10

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.

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[-]PhilGoetz11y 8

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... (read more)

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2timtyler11yA more conventional explanation [http://en.wikipedia.org/wiki/Reliability_theory_of_aging_and_longevity]:
1gwern10yOr... it really is just data collection problems. Via FightAging [http://www.fightaging.org/archives/2012/01/a-counterpoint-to-the-concept-of-the-late-life-mortality-plateau.php] , "Mortality measurement at advanced ages: A study of the Social Security Administration Death Master File" [http://longevity-science.org/pdf/Mortality-NAAJ-2011.pdf] (emphasis added):
2timtyler10yNo, since late life mortality deceleration and mortality plateaus are observed in numerous organisms - including Drosophila melanogaster [http://darwin.bio.uci.edu/~mueller/pdf/evolution_02.pdf] - e.g. see the details in Why organisms show late-life mortality plateaus: a null model for comparing patterns of mortality [http://www.uky.edu/~cfox/Pubs/Papers/2003.EvolutionaryEcologyResearch.Mortality%20plateaus.pdf] .
0gwern10yIt's the humans that matter for us...
0timtyler10yFor 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.
2Eugine_Nier11yWell the wikipedia article on the topic [http://en.wikipedia.org/wiki/Gompertz%E2%80%93Makeham_law_of_mortality] 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.
[-]Fly11y 1

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 coul... (read more)

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0wedrifid11yNot Telomeres?
3Fly11yConsider 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 initia
[-]jsalvatier11y 1

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.

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[-]Vaniver11y 0

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 d... (read more)

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7Vaniver11yTL;DR? Scroll down to the bottom. When I integrate the curve in the post from 25 to 300 [http://www.wolframalpha.com/input/?i=integrate+exp[-.003*exp[%28t-25%29%2F10]]+dt+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 [http://www.wolframalpha.com/input/?i=integrate+exp[-.003*exp[%28t-25%29%2F20]]+dt+from+25+to+300] , 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 [http://www.wolframalpha.com/input/?i=integrate+exp[.003*exp[%2865-25%29%2F10]]*exp[-.003*exp[%28t-25%29%2F10]]+dt+from+65+to+300] years; with an age offset of 25 and a divisor of 20, I get 66.5 years [http://www.wolframalpha.com/input/?i=integrate++exp[.003*exp[%2865-25%29%2F20]]*exp[-.003*exp[%28t-25%29%2F20]]+dt+from+65+to+300] ; with an age offset of -15 and a divisor of 20, I get the expected 32.7 years [http://www.wolframalpha.com/input/?i=integrate++exp[.003*exp[%2865%2B15%29%2F20]]*exp[-.003*exp[%28t%2B15%29%2F20]]+dt+from+65+to+300] . 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 [http://www.wolframalpha.com/input/?i=exp[-.003*exp[%2865-25%29%2F10]]] 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 livin
7Vaniver11yWhy 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 [http://www.wolframalpha.com/input/?i=integrate+exp[-.0003*exp[%28t-25%29%2F10]]-exp[-.003*exp[%28t-25%29%2F10]]+dt+from+25+to+300] 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 [http://www.wolframalpha.com/input/?i=integrate+exp[.0003*%28exp[%2845-25%29%2F10]-exp[%28t-25%29%2F10]%29]-exp[.003*%28exp[%2845-25%29%2F10]-exp[%28t-25%29%2F10]%29]+dt+from+45+to+300] if I start living healthily at 45 (21 years [http://www.wolframalpha.com/input/?i=integrate+exp[-.003*exp[%2845-25%29%2F10]]*exp[.0003*%28exp[%2845-25%29%2F10]-exp[%28t-25%29%2F10]%29]-exp[.003*%28exp[%2845-25%29%2F10]-exp[%28t-25%29%2F10]%29]+dt+from+45+to+300] 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 mak
5Risto_Saarelma11yOne of the possible uses for deep sleep is having a phase where the body heals itself [http://en.wikipedia.org/wiki/Sleep#Restoration] 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?
2Vaniver11yThat'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.
[-]jimrandomh11y 17

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.

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4gwern10yAnd then there are other time-dependent things, like compounding interest/returns.
4[anonymous]9ySo, two years later... How did it go? Are you still doing that?
4Vaniver9yBoth 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 [http://www.youtube.com/watch?v=bcYppAs6ZdI] ), 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 [http://www.soylent.me/], 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 [http://daysomatics.comeze.com/catstretch.html] 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.
6gwern9yHe says he's added sulfur: http://robrhinehart.com/?p=570 [http://robrhinehart.com/?p=570]
3Vaniver9yRight, 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.
0[anonymous]11yPlease correct me if I'm wrong, but it appears that the curve [http://www.wolframalpha.com/input/?i=exp%5B-.003*exp%5B%28t-25%29%2F10%5D%5D] in question cannot be a cdf [http://en.wikipedia.org/wiki/Cumulative_distribution_function] because it is clearly not nondecreasing.