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:
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:
- '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”.
- '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
.
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
. 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.
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)
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.
And I think I have my answer:
http://well.blogs.nytimes.com/2012/01/16/daily-aspirin-is-not-for-everyone-study-suggests/
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)
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.
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.
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)
Related: the Hayflick Limit
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)
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.
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)
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.