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.
In beta. This lesson was written for Hone and has not yet been checked by a physician. Practice material, not professional advice. What that means.
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 0.20Events over the size of that group.
Intervention group: 12 events in 100 people, a rate of 0.12The 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 peopleAlways rounded up, because you cannot count a fraction of a person.
Relative risk = 0.12 / 0.20 = 0.60, a ratio with no unitSixty 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
Solve one, graded on the server
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.