# Numbers needed to treat

Suppose you read about a new drug for treating headaches called Headeeze and you want to determine if the drug has any benefit. You find a randomised control trial that shows that; in a control group 90 out of 100 people still experienced a headache 2 hours after taking a placebo. This is known as the control event rate (CER) and is usually expressed as a percentage.

However, in a group treated with Headeeze the number who still experienced a headache at 2 hours fell to 70 out of 100. This is known as the experimental event rate (EER) and is again usually presented as a percentage. The difference between the experimental and control event rate is known as the absolute risk reduction (ARR).

The numbers needed to treat is the reciprocal (or inverse) of the absolute risk reduction. It is calculated by dividing 1 by the absolute risk reduction. As the absolute risk reduction is usually expressed as a percentage, we need to multiply the answer by 100.

In the example here this would give a value of 5, showing that 5 people would need to be treated with the drug in order for 1 to show a beneficial effect of the drug at 2 hours.