### The Linear Fallacy

(I had a pleasant holiday from you, dear readers, and, I trust, you from me as well. Now let’s get down to it boppers.)

Toxicologists say that the dose is the poison, and Americans could save themselves millions of dollars if they only understood what that means.

Everything on earth, from arsenic to mother’s milk, is toxic if ingested in sufficient quantity. If we graph the lifetime dose on the x-axis and the chance of resulting loathesomeness on the y (what’s with me and the graphs lately?), we wind up with the risk curve. For your quotidian poisons like cigarettes, red meat, and smog, the risk begins at zero and stays very close to it until a certain dose is reached, at which point the curve inflects and the risk begins to increase quite radically. Not all risk curves have this shape, of course. For highly toxic substances like sarin or finely-ground anthrax it inverts. The risk escalates very rapidly and then flattens at the top of the graph after a certain exposure, at which point you die.

The curve, however, is always a curve, never a straight line. Have you heard that every cigarette you smoke cuts five minutes, or eight, or ten, off your life? This is the linear fallacy in full flower. Smokers’ diseases like emphysema and lung cancer concentrate overwhelmingly in the heaviest, longest-term smokers. People who smoke for a few years have scarcely higher mortality than people who never smoke at all. (You kids bear this in mind when you’re thinking of lighting up.) The first cigarette you smoke probably does you no harm at all. The 150,000th — pack a day for twenty years — may, like W.C. Fields’ Fatal Glass of Beer, be the one that does you in. The dose is the poison.

It gets worse. An intense dose over a short period is generally far more toxic than the same dose spread out over a lifetime. Risk varies radically not only with the lifetime dose, but also with its rate, which renders extrapolation effectively impossible. Animal tests classically deal with this fact by ignoring it. Suppose you want to determine the long-term risks of swilling pistachio nuts and maraschino cherries, which contain Red Dye No. 3. Time’s a-wasting, and you don’t have 50 years to conduct your research. Instead you stuff a bunch of gerbils with a whole lot of Red Dye No. 3 over a few weeks or months and see what happens. If a few gerbils get cancer, you extrapolate, bury your reliance on the linear model in a couple of footnotes, and voilĂ ! a new carcinogen. Politicians and journalists thunder against the unacceptable risks to maraschino cherry addicts, the Delaney Clause is invoked, Red Dye No. 3 is banned, a new, slightly less attractive red dye replaces it, and the cycle begins anew.

Good-sized industries have sprung up to exploit the linear fallacy. The EPA tells gullible homeowners to shell out a couple grand to a radon-removal outfit if their radon level in their water is more than 4 pCi/I (picocuries per liter). Turns out that exposure at that level for 20 years increases the lifetime risk of cancer by less than 1%, unless you also smoke, which bumps it up to a ghastly 3% or so. Mind you, this is not increased mortality, but increased risk of cancer. Since the lifetime risk for cancer is in the 25% range, we’re discussing, in terms of overall mortality, something less than 0.3%. Save your money and try to stay out of automobiles instead.

The asbestos boys make the radon boys look positively public-spirited. Asbestos is dangerous if you spend your life working with it; non-smoking asbestos workers have cancer rates about five times the general non-smoking population. Asbestos is essentially harmless when it’s minding its own business insulating pipes. In 1985 the British epidemiologists Doll and Peto estimated the annual lung cancer risk from such exposure to be 1 in 1,000,000; other reputable estimates are similar. Yet the Asbestos Hazard Emergency Response Act, passed in 1987, mandated asbestos removal for 45,000 public schools, many with airborne asbestos concentrations no higher than the outdoors. When you remove asbestos improperly you stir it up and increase the exposure, and since removing asbestos properly is extremely expensive the incentive to do it improperly is immense. \$100 billion or so later, overall asbestos risk is probably higher than it ever was. Lead paint, Alar, DDT: the song remains the same.

So there’s good news and bad news. The bad news is you’re going to die of something. The good news is that it almost surely won’t be an exotic environmental poison.

Aaron Haspel | Posted October 4, 2003 @ 3:24 PM | Business,Heuristic

#### 6 Responses to “The Linear Fallacy”

1. 1 1. steve

Ah, but there’s money in it; there’s money in protecting us. And if a word like cigarette or asbestos or radon can be made to present an image…how was it ole Ez put it, a cluster of emotions in a moment of time, well then, the cash will really start pouring in.

2. 2 2. Bill Kaplan

The risk curves you speak of are very interesting indeed. For example, shepherds get very low doses of anthrax on a daily basis. This actually permits them, over time, to become immune from much larger doses. Phenylketonurics grow immune to phenylalanine as they age. Arsenic is clearly additive as are the heavy metals because bodily clearance mechanisms are poor.

I read somewhere that the risk of cancer from asbestos used in the building trades is negligible. The problem is that the asbestos used in shipbuilding, which for some reason came in large part from Brazil, was rather nasty stuff, and that the risks have been conflated.

I guess my point (if I have any) is that it is not the dose that is the poison, but the dose over time, that is.

3. 3 3. Tracy

I thought you could build up some immunity to arsenic by taking low doses regularly. I’ve read some mystery novels that turn on the murderer being able to share the poisoned food with the victim due to this.

Though I don’t know what those murderers were doing to their long-term survival likelihood.

4. 4 4. Bill Kaplan

Tracy:

My knowledge of arsenic poisoning comes nearly entirely from the experience someone I know had when he was poisoned by his Russian mail-order bride. He gave a colleague a sandwich prepared by his beloved and, when that colleague became terribly ill, the colleague was tested for arsenic poisoning. When the colleague tested positive, he too was tested and found to be have abnormally high blood levels of the stuff. Apparently, the sandwich was to be the coup-de-gras.

5. 5 5. Rich Rostrom

An excellent coverage of this issue; but one point is neglected. The comment on cigarette smokers doesn’t explicitly illustrate the non-linearity of toxic exposure. A, who smokes for one year, is at far less risk than B, who smokes for twenty years, even under the linear model, which would assign A 1/20th of the risk of B. The reality is that the risk to A is probably less than 1/100 of the risk to B. With many toxins, there is a threshold below which there is no risk at all. The linear-risk rule says that one-millionth of the lethal dose of cyanide will kill 1 out of 1 million exposed; but any chemist can prove that it cannot possibly harm anyone.

6. 6 6. Chris H

Smoking does shave minutes of your life, but your rather to catch lung cancer or another disease before getting something else. I just hope people that smoke know all of this….

Thanks,

Chris

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