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

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