X-Message-Number: 10854 Date: Mon, 30 Nov 1998 08:00:13 -0500 From: Thomas Donaldson <> Subject: CryoNet #10852 - #10853 Hi everyone! This will bring up a subject again which I discussed some time before. One major distinction between calorie restriction and other (drug) treatments of aging is the idea that calorie restriction, even when begun AFTER puberty, will cause a lifespan increase, AND that the evidence for this lifespan increase, especially its ability to increase maximal lifespan, is far better than any such evidence for drugs. It happens that a number of different antiaging drugs do show lifespan curves in which some animals taking the drug live longer than those which do not --- ie. they live longer than ALL of those not taking the drug, not just the majority of them. In terms of statistics, this is a difference between a small number of animals, much smaller than the original. It's not so easy to work out the statistics for a small subset of surviving animals. (This is not a criticism of the main point of the experiments, either with calorie restriction or these drugs; it is a discussion of how strong the evidence is that EITHER calorie restriction after puberty, OR the drugs would increase MAXIMUM lifespan). One of the problems is that a lifespan curve may very well not be well approximated either by a normal distribution or a lognormal one. However a few calculations with simple probability give as an idea of what would be needed to DISPROVE the claim that a drug increases maximum lifespan. We simply do this: suppose that the upper 5% of a lifespan curve lies above the lifespans of any control. We can then work out the number of animals needed to show that survival at these lifespans is purely accidental. I'll restate that to make it clearer: if we want to do an experiment to prove that maximum lifespan on a particular drug will not be increased, then we need a certain number of animals (Nmax) which is usually significantly greater than those we need merely to show that the drug increases mean (average) lifespans. All you have to do to find out the required number of animals is to take the accuracy you want (say 95%) and raise it to a power large enough that (.95)^^N < .05. Here is what happens with CoQ10: the log of 0.95 is ~~-0.051293294. The log of 0.05 is ~~-2.995732274 (I am using the numbers from my calculator, and ultimately will round them off for an approximate result. The higher order numbers are unlikely to mean anything). When we find the value of Nmax required, we get: Nmax = 2.9957 / .0512932 == roughly 58 test animals and 58 controls. There is an experiment which uses 30 animals and did not find that these animals had a MAXIMUM lifespan greater than that of controls. On these figures, this result could have easily happened simply by chance. What's happening here is this: we want to have a number of animals such that the probability that some lived to the high lifespans of a few treated animals, simply by chance, becomes less than 5%. The opposite of this probability is the probability that ALL animals live to less than the 95% span; this is (0.95) raised to the power N (where N is the number of animals required). We then do the algebra. Of course, the failure of an experiment to DISPROVE an increase in maximum longevity does not mean that the animals actually do have an increase in their maximum longevity. Of the various drugs I mentioned before, using only the experiments in my book, melatonin looks the weakest here statistically: there were only 15 animals used, though some of these animals did live longer than the maximum for controls. I will add, though, that Pierpaoli has not done just the experiments I give in my book. I may come out with an update on this issue, though. I would also emphasize that nothing that I say here argues against the value of these experiments in showing an increase in AVERAGE lifespans. Best and long long life to all, Thomas Donaldson Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=10854