Absolute risk reduction

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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



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