# How many people really benefit from various treatments

Pediatrician Aaron Carroll explains how to compute various measures of benefit for various health interventions, including drugs, diagnostic techniques, and diet. One of the most useful and easy-to-understand measures is the "Number Needed to Treat" (NNT), meaning the number of people you'd have to treat before you'd be reasonably confident of seeing one benefit (such as one life saved).

His explanation of NNT might be a little confusing, so let me give an alternative version without formulas:

Suppose every science fiction fan has a 10 percent chance of getting Twonk's disease (a legendary disease affecting fans). However, research shows that if you eat a hotdog every day for breakfast, the risk falls to just 3 percent.

So to put it another way, out of 100 people who don't eat hotdogs for breakfast, you'd expect on average that 10 of them will likely come down with Twonk's disease. But if you convince them all to eat hotdogs every morning, then (again, on average), only 3 of them would get it. So if 100 people change their diets, you'd expect 2 of them to benefit -- the ones who otherwise would have contracted the disease.

So since treating 100 people on average benefits 2, treating 50 would presumably benefit 1. So the average "Number Needed to Treat" in order to benefit a single individual person is 50.

Now consider a drug that cuts the risk of some disease by 80 percent. That sounds really good! But suppose the risk in question is just 1 in a million to start with. So basically if you treated 100 million people, you'd prevent about 80 of them from getting the disease who otherwise would have. The NNT to benefit one person would be 100 million divided by 80, or about 1 1/4 million. It's not at all obvious that it's worth the trouble to take the drug, especially if it costs a lot of has serious side effects.

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