• First read this, adapted from a paper by Cook and Sackett:

Example 1: Relative to a control group, for patients with mild hypertension, the therapy reduced the absolute risk of stroke over the next five years by 0.006. For patients with moderate hypertension, the therapy reduced it by 0.08. [Assume “mild” and “moderate” hypertension are appropriately defined elsewhere.]

Next, what’s your knee-jerk response to, “How well does this therapy work?” If you’re anything like me, you’re immediately trying to convert the numbers above into something more intuitive. For example, it’s fairly clear that for moderate hypertensive, the therapy would spare 8 out of 100 patients a stroke in the next five years (because 0.08 = 8%). For mild hypertensives, my quick mental calculation would be that the therapy did so for about 1 out of 200 patients (since 0.006 is close to 0.5%).

Now we’re getting somewhere. I have a decent, intuitive feel for what 8 out of 100 and 1 out of 200 mean as numbers. But we can do a bit better. Instead of reporting the absolute risk reduction, we could report the number needed to treat (or NNT). Try this:

Example 2: Relative to a control group, the number needed to treat (NNT) to spare one mild hypertensive patient a stroke over the next five years is 167. The NNT for moderate hypertensives is 13.

The NNTs 167 and 13 are just the (rounded) reciprocals of the absolute risk reduction 0.006 and 0.08 from the first example above. What they’re telling you is that one individual with mild hypertension out of 167 treated will benefit; one out of 13 moderate hypertensives will. Aren’t they easier to interpret? I think so.

Put yourself in the place of the patient here. Are you the one who will benefit or not? If you’re a mild hypertensive and you’re the one who benefits, then 166 of your fellow patients are the unlucky ones who don’t. That’s a lot of therapy doing nothing! If you’re a moderate hypertensive and you benefit, 12 of your fellow patients don’t. The odds are much better in this case and less therapy is wasted.

What I haven’t told you is that the numbers above are from studies that show that the relative risk reduction provided by therapy is the same for both groups, 40%. What absolute risk reduction (Example 1) makes clear, and the NNT (Example 2) does even better, is that the absolute benefit of therapy is very different for the two populations, even though the relative benefit is the same. It’s the absolute benefit that matters.

If you’re surprised by the NNTs in the example above—perhaps thinking they’re not typical—this is an important moment for you. Though single digit NNTs exist, NNTs in the tens to hundreds (or greater) are very typical in medicine. A ton of stuff gets done without any benefit because we have a hard time focusing treatment on precisely those for whom it will definitely help. I bet you think every time you pop a pill or get a procedure you’re benefiting. Guess what? The chances you’re not are very, very high. Are you the lucky one or not?

I plan to say more about NNTs later in the summer. For now, just let the idea, and their typical size, sink in. Here are some more resources:

• Apparently, this is the seminal paper on NNTs
• Here’s a website all about NNTs with values for tons of tests and treatments

@afrakt

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