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Absolute risk

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In epidemiology, the absolute risk reduction or risk difference is the decrease in risk of a given activity or treatment in relation to a control activity or treatment.[1] It is the inverse of the number needed to treat.[2]

For example, consider a hypothetical drug which reduces the relative risk of colon cancer by 50% over five years. Even without the drug, colon cancer is fairly rare, maybe 1 in 3,000 in every five-year period. The rate of colon cancer for a five-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.

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.

Presenting resultsEdit

The raw calculation of absolute risk reduction is a probability (0.003 fewer cases per person, using the colon cancer example above). Authors such as Ben Goldacre believe that this information is best presented as a natural number in the context of the baseline risk ("reduces 2 cases of colon cancer to 1 case if you treat 6,000 people for five years").[3] Natural numbers, which are used in the number needed to treat approach, are easily understood by non-experts.

Worked exampleEdit

  Example 1: risk reduction Example 2: risk increase
Experimental group (E) Control group (C) Total (E) (C) Total
Events (E) EE = 15 CE = 100 115 EE = 75 CE = 100 175
Non-events (N) EN = 135 CN = 150 285 EN = 75 CN = 150 225
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400 ES = 150 CS = 250 400
Event rate (ER) EER = EE / ES = 0.1, or 10% CER = CE / CS = 0.4, or 40% EER = 0.5 (50%) CER = 0.4 (40%)
Equation Variable Abbr. Example 1 Example 2
CER − EER < 0: absolute risk reduction ARR (−)0.3, or (−)30% N/A
> 0: absolute risk increase ARI N/A 0.1, or 10%
(CER − EER) / CER < 0: relative risk reduction RRR (−)0.75, or (−)75% N/A
> 0: relative risk increase RRI N/A 0.25, or 25%
1 / (CER − EER) < 0: number needed to treat NNT (−)3.33 N/A
> 0: number needed to harm NNH N/A 10
EER / CER relative risk RR 0.25 1.25
(EE / EN) / (CE / CN) odds ratio OR 0.167 1.5
EER − CER attributable risk AR (−)0.30, or (−)30% 0.1, or 10%
(RR − 1) / RR attributable risk percent ARP N/A 20%
1 − RR (or 1 − OR) preventive fraction PF 0.75, or 75% N/A


  1. An overview of measurements in epidemiology. URL accessed on 2010-02-01.
  2. Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment. N Engl J Med 1988;318:1728-33. PMID 3374545.
  3. Ben Goldacre (2008). Bad Science, 239–260, New York: Fourth Estate.

See alsoEdit

External linksEdit

es:Riesgo absoluto

nl:Absolute risicoreductie

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