How many people do you need to treat to help one person? Increasingly, statisticians have been asking this question, because it puts all of health care in perspective.

Consider the prostate drug whose wider use was debated in yesterday’s New York Times. One expert says that with finasteride, or Proscar, “as many as 100,000 cases of prostate cancer a year could be prevented.” Is 100,000 a lot or a little?

Another specialist explains, “While 10 percent of men 55 and older find out they have prostate cancer, the cancer is lethal in no more than 25 percent of them. So if finasteride reduced the prostate cancer’s incidence by 30 percent, about 7 percent of men would get a cancer diagnosis and approximately 1.8 percent instead of 2.5 percent would have a lethal cancer.”

One way to boil down this sort of data is a measure called “number needed to treat,” or NNT. The concept is reasonably simple. Imagine that with a particular intervention, 30 per cent of subjects, or three in ten, get a good result or avoid a bad one. Let’s also say that given a placebo, two subjects in ten do well. That is, when you provide the treatment to ten people, three will get better — but two would have gotten better anyway. You need to treat ten people in order truly to benefit one. In this example, ten is the NNT, the number needed to treat in order to help one additional person.

The mathematically inclined will see that the formula for NNT is 1/(probability of responding to intervention – probability of responding to placebo), in this case 1/(.30 - .20) = 10. (The probability is the percentage of responders expressed as a decimal, so that 30% becomes .30.) This measure makes medical care look unimpressive. In our example, a drug company might tout a 33% reduction in harm, when the NNT would reveal that if you treat ten people, only one will actually be helped by medication.

Using the estimates in the Times article, and assuming that no one would respond to placebo, we can conclude that you would need to treat 33 men [1/(.93 - .90)] to prevent one cancer, and 143 men to prevent one cancer death. These numbers are high, for a preventive public health intervention, but they are not outrageous. A ballpark estimate of the benefits of statins in the prevention of heart attacks puts the NNT at 50. Of course, you can do much better if instead of prescribing medication for, say, all men over 55, you give it to people known to be at high risk.

Where do mental health treatments fit in this calculus? It’s hard to say. We don’t do much in the way of targeted prevention.

If you look at the kind of study that is common in the mental health literature, you tend to find that, say, 55 per cent of patients respond to a given medication or psychotherapy, as opposed to 35 per cent of subjects on placebo. This outcome gives a NNT of 5. That is to say, one person benefits, while four are exposed to treatment to little effect. This NNT is usually for 12 weeks of treatment, while the public health measures we are discussing involve years or decades of medication-taking. In general, for brief treatments of active disease, researchers like to see NNTs below ten.

What about death as an outcome? Here, we are entering into a realm of wild speculation, but if you accept the sort of back-of-the-envelope guesses discussed in the Times article on finasteride, you might say that if 4 or 5 per cent of untreated mentally ill patients eventually commit suicide, then for an intervention whose NNT is five (to block the underlying illness), the NNT to prevent suicide would be in the 110 range. This figure does not take into account lives lost to cardiac disease and stroke. In practice, we do not treat mental illness merely to prevent premature death.

The NNT statistic helps explain why editors get excited about certain research studies. In 2000, the New England Journal of Medicine published a paper by Dr. Martin Keller (here at Brown) and others that found an extraordinarily favorable outcome in a hard-to treat population. Looking at patients with chronic major depression, 85 per cent responded to a combination of psychotherapy and antidepressant. The researchers estimated that 12 per cent of comparable patients would respond to placebo. Using these figures, the NTT would be an astonishing 1.4. Even with a placebo response rate of 35 per cent, the NNT would be two. We are actually pleased in medicine when half of patients benefit from our treatments in some well-defined way.

The NEJM paper is an exception. Mostly the “number to treat” is a humbling statistic. A psychiatrist who is aware of NNT estimates knows that he or she must be working with a good number of people who would fare just as well on their own. The same is true for all doctors, in all specialties.

Note: For those interested in more details about NNT, the evidence-based medicine site out of Oxford University, Bandolier, has useful summaries here and here. The Evidence Based Emergency Medicine site has an on-line calculator that allows you to throw in data to produce an NNT. Readers may want to fiddle with a comparable statistic for side effects, the number needed to harm, or NNH.

Further note: I followed up this posting with a further submission here.