Last week, Goran Bjelakovic and company made a splash with a meta-analysis review in JAMA, "Mortality in randomized trials of antioxidant supplements for primary and secondary prevention: Systematic review and meta-analysis" (Journal American Medical Association, Feb. 28 2007). If you can't read the original article, you can see a commentary on it here. They claim that beta-carotene and vitamins A and E are positively correlated with death - the more you take, the more likely you are to die. Therefore, vitamins kill.

This isn't the first time Bjelakovic et al. have accused vitamins of killing people. They published 2 very similar articles, using the same methodology:

Bjelakovic et al. 2006, "Meta-analysis: Antioxidant supplements for primary and secondary prevention of colorectal adenoma", Alimentary Pharmacology & Therapeutics 24, 281-291.

Bjelakovic et al. 2004, "Antioxidant supplements for prevention of gastrointestinal cancers: A systematic review and meta-analysis," The Lancet 364, Oct. 2 2004.

What all of these articles do, in excruciating detail, is to run a multiple linear regression on a lot of data from studies of patients taking vitamins. A multiple linear regression takes a set of data, where each datapoint looks like this:

     Y = a₁X₁ + a₂X₂ + ... a_nX_n

where Y and all the X_i's are known. It finds the values for a₁, ... a_n that best fit the data. In this case, Y is a 1 for someone who died and a 0 for someone who didn't, and each X_i is the amount of some vitamin taken.

The proper technique to use in a linear regression analysis would be a mutiple linear logistic regression in this case. I don't know what analysis they performed, since they didn't report what type of analysis they did; they only reported the computer program (STATA) and the command ("metareg"), without stating what that command actually does. It's clear from the way they reported the results, however, that it was a linear analysis.

The key word here is linear. A linear analysis assumes that the way vitamins act is, If 10 milligrams is good for you, then 100 milligrams is ten times as good for you, and 1000 milligrams is one-hundred times as good for you.

This is not how vitamins work. We already know this. We already know that vitamin A is toxic in doses over 15,000 IU/day, and vitamin E is toxic in doses over 400 IU/day (Miller et al. 2004, "Meta-Analysis: High-Dosage Vitamin E Supplementation May Increase All-Cause Mortality", Randomized Trial of Vitamin A and Vitamin E Supplementation for Retinitis Pigmentosa). The RDA for vitamin A is 2500 IU/day for adults. Good dosage levels for vitamin A appear to be under 10,000 IU/day, and for E, less than 300 IU/day. (Sadly, studies rarely discriminate in their conclusions between dosage levels for men and women.)

Quoting from last week's JAMA article:

The dose and regimen of the antioxidant supplements were: beta carotene 1.2 to 50.0 mg (mean, 17.8 mg) , vitamin A 1333 to 200 000 IU (mean, 20 219 IU), vitamin C 60 to 2000 mg (mean, 488 mg), vitamin E 10 to 5000 IU (mean, 569 IU), and selenium 20 to 200 μg (mean 99 μg) daily or on alternate days for 28 days to 12 years (mean 2.7 years).

Did you get that? The mean values used in the study of both A and E are in ranges already known to be toxic. The maximum values used were ten times the known toxic levels, and about 20 times the beneficial levels.

17.8 mg of beta-carotene translates to about 30,000 IUs of vitamin A, if it were converted to vitamin A. This is also a toxic value. It is surprising that beta-carotene showed toxicity, though, since the common wisdom among vitamin-takers is that beta-carotene is converted to vitamin A only as needed. This study shows that isn't true. That is its one true important result.

Vitamins, like any medicine, have an inverted-J-shaped response curve. If you graph their health effects, with dosage on the horizontal access, and some measure of their effects - say, change to average lifespan - on the vertical axis, you would get an upside-down J. (If you graph the death rate on the vertical axis, as this study should have, you would get a rightside-up J.) That is, taking a moderate amount has some good effect; taking a huge a mount has a large bad effect.

If you then try to draw a straight line through the J that best-matches the J, you get a line showing detrimental effects increasing gradually with dosage. That's what these studies all do. The results are exactly what we expect. The error is their conclusion, that "Treatment with beta carotene, vitamin A, and vitamin E may increase mortality." Treatment with anything may increase mortality, if you take ten times the toxic dose.

For a headache, some people take 4 200mg tablets of aspirin. 10 tablets of aspirin might be toxic. If you made a study averaging in people who took doses ranging from 1 to 100 tablets of aspirin for a headache, you would find that "aspirin increases mortality". That is exactly what this study does.

Anyone reading the study should have been alerted to this by the fact that all of the water-soluble vitamins in the study showed no harmful effects, while all of the fat-soluble vitamins "showed" harmful effects. Fat-soluble vitamins are stored in the fat, so they build up to toxic levels when people take too much for a long time.

If the paper had been rejected, I would say it was the fault of the authors for doing an elaborate study using a methodology that a grad student would get a failing grade for using. If the paper had been accepted at one publication, I would say it showed a problem with their peer review system.

But these people have published three such articles, in the most-highly-respected journals in medicine, using this totally incorrect methodology. Something is very wrong here.