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Lessons · Medicine foundations · absolute risk, relative risk and number needed to treat

Absolute risk, relative risk, and how many people

The absolute risk reduction is one group's event rate minus the other's; the number needed to treat is one divided by that difference; the relative risk is one rate divided by the other.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

A journal club paper leads with a relative risk because it is the biggest-sounding number in the study. The absolute difference and the number of people it takes to see one of them is what a reader needs, and both come from the same two rates in two lines of arithmetic.

How to think about it

Turn each group into a rate first: events divided by people in that group. Subtract for the absolute difference. One over that difference is the number needed, and it is rounded up to a whole person, because two thirds of a person is not a count. Divide one rate by the other for the relative risk, which has no unit at all.

Worked example

Control group: 20 events in 100 people, a rate of 0.20
Events over the size of that group.
Intervention group: 12 events in 100 people, a rate of 0.12
The same arithmetic on the other group.
Absolute risk reduction = 0.20 − 0.12 = 0.08, which is 8 %
A difference between two rates, so it is a rate itself.
Number needed to treat = 1 / 0.08 = 12.5, rounded up to 13 people
Always rounded up, because you cannot count a fraction of a person.
Relative risk = 0.12 / 0.20 = 0.60, a ratio with no unit
Sixty percent of the control rate, which is the same study reported to sound larger.

Your turn

A problem gives an absolute risk reduction of 0.05. Write the line that gives the number needed to treat.

NNT = 1 / 0.05 =  people

The trap

Quoting the relative risk as though it were the size of the benefit. A relative risk of 0.60 sounds like forty percent of something; if the rates were 0.005 and 0.003 it is four people in a thousand, and the absolute difference is the only one of the two that says which.

Practise absolute risk, relative risk and number needed to treat on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.