Absolute risk reduction and number needed to treat

What it is

The number needed to treat (NNT) is defined as the number of people who would need to receive an intervention in order for one person to benefit. It is the inverse of the absolute risk reduction (ARR), and the ARR is the difference in risk for a disease without and with an intervention.

Both terms are built from a trial with a study arm and a control arm:

• EER, the experimental event rate, is the proportion of patients in the experimental treatment group who are observed to experience the outcome of interest.
• CER, the control event rate, is the proportion of patients in the control group who are observed to experience the outcome of interest.
• Relative risk is the ratio of risk in the study arm to the control arm: RR = EER/CER.
• Relative risk reduction is the proportional reduction in rates of bad outcomes between experimental and control participants in a trial: RRR = 1 - RR x100%, that is RRR = 1 - (EER/CER) x100%.
• Absolute risk reduction is the absolute difference in rates of bad outcomes between experimental and control participants in a trial, the risk difference: ARR = CER - EER.
• Number needed to treat is the number of patients who need to be treated with the specified intervention to prevent one bad outcome or produce one good outcome over the period of time specified in the study.

Both pages that carry the formula agree that NNT is the inverse of ARR, but they write it in two ways: one gives the correct formula for calculating NNT as 1/ARR, and the other gives NNT = (100/ARR) x100%.

Since the two are inverse, a given NNT fixes the ARR. The U.S. Preventive Services Task Force recommends screening all adults for obesity and offering intensive, multicomponent behavioral interventions to patients with a BMI >=30 kg/m2. That recommendation is based on trials that show that behavioral weight-loss interventions for overweight and obese patients with elevated plasma glucose levels reduce the incidence of diabetes mellitus by 30%-50% over 2-3 years and the number needed to treat is 7. The absolute risk reduction for developing diabetes in those trials is 1/7.

NNH are not a concept in therapeutic studies, but in context with exposure/non-exposure.

Held as an order of work, the relative risk reduction is got in three steps: RR = EER/CER first, then 1 - RR, then x100%. What comes out is the part of the control arm's risk that the treatment takes away, which is why RRR can read large while ARR, that is CER - EER, stays small in the same trial. The same two arms can be read straight off a table of four cells. In the study arm (Y), a is the positive outcome and b the negative outcome; in the control arm (X), c is the positive outcome and d the negative outcome. The risk of outcome is then Y = a/(a+b) in the study arm and X = c/(c+d) in the control arm, so RR = Y/X, RRR = (1 - Y/X) x 100%, and ARR = X - Y. Said in whole people, NNT is the number of patients you need to treat to prevent one additional bad outcome such as death or stroke: if a drug has an NNT of 5, it means you have to treat 5 people with the drug to prevent one additional bad outcome.