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 p_{A} and p_{B} of this endpoint under treatments A and B, respectively, are known, then the absolute risk reduction is computed as p_{B}-p_{A}.
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
- ↑ 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