Cigs and Figs

A mathematician's guide to the news.
June 15 2001 3:00 AM

Cigs and Figs

How do you count dead smokers?

Recent TV ad: Three teen-agers bungee out of an airplane while chugging their favorite soda. Two of the boys positively beam with satisfaction. The other boy's head explodes. Tobacco, the ad concludes, is the only product that kills one in three people who use it.

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It's the best of the tobacco-settlement-funded spots to occupy the airwaves because it recognizes an essential fact about turning a number into a brand name: The smaller, the more graspable the number, the more powerful the brand. You know three smokers. You don't know 157,400 people, the number the American Cancer Society predicts will die of lung cancer this year.

But what does "one in three" mean? It could mean:

  • Of people who were smokers, one-third died of illnesses directly traceable to their smoking.
  • Of people who were smokers, one-third would have died of illnesses directly traceable to their smoking had they not died first of something else.
  • Of people who were smokers, one-third died of illnesses related to smoking that they would not have died from had they not smoked.
  • If you start smoking today, you have a 1-in-3 chance of dying from an illness directly traceable to your smoking.
  • If you start smoking today, and you don't die of something else before you're 60, you have a 1-in-3 chance of dying from an illness directly traceable to your smoking.
  • If you start smoking today, you have a 1-in-3 chance of dying from an illness related to smoking that you would not have died from had you not smoked.

One could easily go on; just to start, the word "people" could be replaced by "Americans," "teen-agers," "men," or the name of any other group on whom the statistic might be based.

The assertions above all speak to different questions—questions that may, in fact, have drastically different answers.Gerber used to advertise that four out of five pediatricians recommended Gerber baby food. "Four out of five," it turns out, was the answer to the question:

"Of doctors who recommend a specific brand of baby food, how many recommended Gerber?"

The answer to the question:

"Of doctors who recommend that babies eat baby food, how many specifically recommend eating Gerber?" was just 16 percent, as the Federal Trade Commission pointed out in a 1997 complaint. Gerber pulled the ads.

So, what question has the answer "one in three?" To find out, we trace the statistic back to its source, the Nov. 9, 1996, issue of a Centers for Disease Control publication agreeably titled Morbidity and Mortality Weekly Report. (This week's issue features "Responding to Fecal Accidents in Disinfected Swimming Venues.")

We learn from the CDC report that "one in three" means the following:

"Of young American adults who smoke, we project that 55 percent will become lifetime smokers, and there is a 50 percent chance that they will suffer a smoking-attributable death. The other 45 percent, who will quit sometime in their adult life, have a 10 percent chance of suffering a smoking-attributable death."

So, 50 percent of 55 percent plus 10 percent of 45 percent comes out to 32 percent, or—more or less—one in three.

So, what's a "smoking-attributable death"? It's a death from a smoking-related illness that wouldn't have occurred had the patient not smoked. How do we know what would have happened? We can only guess—but the majesty of statistics is that it can turn a sufficiently large aggregate of guesses into a number we can hope to trust. The estimates here are taken from Mortality From Smoking in Developed Countries, 1950-2000 (R. Peto, et al.), and they work like this: Suppose that the data from a large-scale study tell us that, in any given year, male lifelong smokers are about two and a half times as likely as male non-smokers to die of heart disease. Suppose that, this year, 100,000 male lifelong smokers die of heart disease. We then guess that if all these men were non-smokers, only 40,000 would have died of heart disease this year. There you are—60,000 smoking-attributable deaths. (The Peto study, in order to err on the low side, cuts these numbers in half right from the start.)

And now we have our answer:

"Of young American adults who smoke, one in three will die of smoking-attributable diseases, assuming current patterns of smoking and smoking-related death do not change."

Which is to say:

"One in three will die unless we convince more people to quit than do now, in which case fewer might die. Or unless increased seatbelt use allows more of them to survive long enough to die of lung cancer, in which case more might die. Or unless they're socioeconomically skewed so differently from the current crop of smokers that the data's unusable, in which case who knows? Or ..."

It's a lot like figuring out whether the budget will be balanced in 10 years, except that the uncertainty arises from the aggregated actions of millions of dumb teen-agers instead of hundreds of hungry politicians. You can decide for yourself which projection inspires more confidence.

Then, too, you might ask whether the question whose answer is "one in three" is the right question to ask. The death from lung cancer of a 35-year-old smoker is not the same thing as the congestive heart failure of a 72-year-old smoker. But the number in the TV ad counts both the same. And shouldn't the 72-year-old's accumulated decades of emphysemic wheezing and hacking count for something? Taking some of these issues into account, the CDC estimates that today's youth will pay a smoking penalty of 64 million years of lifespan. "64 million" is a big, impressive number. That's precisely why it's not as good as "one in three."

None of which should obscure the undeniable fact that smoking has a decent chance of killing you. But how good a chance? Maybe "a decent chance" is the most accurate answer. It's not clear that the question can be sensibly answered with a single number, or that such an answer would be good for much besides advertising and litigating. Simple questions rarely have simple answers—but there's one exception. That's the question that young smokers—and most advertisements—would rather leave unmentioned, and the question that the anti-smoking campaigns, to their credit, are attempting to keep in focus. The question is, "If you are a teen-ager today, what's the chance that you will die?" And the answer is the smallest, most powerful, and most precise of all numbers: one in one.

Jordan Ellenberg is a professor of mathematics at the University of Wisconsin and the author of How Not to Be Wrong. He blogs at Quomodocumque.

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