Science Puzzle
The Drug That Halves Your Risk
A newspaper headline announces that a new drug halves your risk of a rare illness. The trial behind it was large and fair, and the result is real. Over five years, 2 in every 1,000 people who didn't take the drug got the illness, compared with 1 in every 1,000 people who did.
If you took the drug for five years, how much would it really change your own chance of getting the illness?
The Answer
Your chance falls from 0.2% to 0.1%. The headline is true, and so is this: they're two ways of describing the same result.
Going from 2 cases to 1 is a halving, so the drug cuts the risk by 50%. That's the relative risk reduction, which compares the two groups with each other. But it says nothing about how big the risk was to begin with. The absolute risk reduction looks at the actual chances: 2 in 1,000 is 0.2%, 1 in 1,000 is 0.1%, so the drug lowers your chance by 0.1 percentage points.
Another way to see it: 1,000 people would need to take the drug for five years to prevent a single case. Doctors call this the number needed to treat. Of those 1,000 people, 998 would never have got the illness anyway and one gets it despite the drug. Only one person in the whole group actually benefits.
That doesn't make the drug useless. For someone at high risk, or for an illness that's very serious, it could be well worth taking. But it does change the decision. Suppose 1 person in 100 had a bad side effect from the drug: then for every 1,000 people treated, 10 would be harmed to save 1. Headlines and adverts prefer the relative figure because "halves your risk" sounds far more impressive than "0.1 percentage points". The question to ask is always: half of what?
The principle: Relative versus absolute risk. A relative change such as "halves your risk" says nothing about how large the risk was to begin with, so the absolute change, and the number of people who must be treated to help one, show what a result really means for you.