# Absolute risk reduction

Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]

## Overview

The absolute risk reduction is the decrease in risk of a given activity or treatment in relation to a control activity or treatment. It is the inverse of the number needed to treat.[1]

In general, absolute risk reduction is usually computed with respect to two treatments A and B, with A typically a drug and B a placebo (in our example above, A is a 5-year treatment with the hypothetical drug, and B is treatment with placebo, i.e. no treatment). A defined endpoint has to be specified (in our example: the appearance of colon cancer in the 5 year period). If the probabilities pA and pB of this endpoint under treatments A and B, respectively, are known, then the absolute risk reduction is computed as pB-pA.

The inverse of the absolute risk reduction, NNT, is an important measure in pharmacoeconomics. If a clinical endpoint is devastating enough (e.g. death, heart attack), drugs with a low absolute risk reduction may still be indicated in particular situations. If the endpoint is minor, health insurers may decline to reimburse drugs with a low absolute risk reduction.

## Worked example

For example, consider a hypothetical drug which reduces the risk of colon cancer by 50%. Even without the drug, colon cancer is fairly rare, maybe 1 in 3,000 in every 5 year period. The absolute risk reduction for a 5-year treatment with the drug is therefore 1/6,000, as by treating 6,000 people with the drug, one can expect to reduce the number of colon cancer cases from 2 to 1.

 Abbreviation Variable Equation Value - subjects in control group - 250 - subjects in experimental group - 150 - events in control group - 100 - events in experimental group - 15 CER control event rate = events / subjects in control group 0.4, or 40% EER experimental event rate = events / subjects in experimental group 0.1, or 10% ARR absolute risk reduction (or increase) = CER - EER 0.3, or 30% RRR relative risk reduction (or increase) = (CER - EER) / CER 0.75 NNT number needed to treat/number needed to harm = 1 / ARR 3.33 OR, RR odds ratio, relative risk (not really identical, but similar -- see articles for details) = CER / EER 4

## References

1. Laupacis A, Sackett DL, Roberts RS (1988) An assessment of clinically useful measures of the consequences of treatment. N Engl J Med 318 (26):1728-33. DOI:10.1056/NEJM198806303182605 PMID: 3374545