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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. It is the inverse of the number needed to treat.
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.
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"). Natural numbers, which are used in the number needed to treat approach, are easily understood by non-experts.
|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|
- ↑ An overview of measurements in epidemiology. URL accessed on 2010-02-01.
- ↑ 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.
- ↑ Ben Goldacre (2008). Bad Science, 239–260, New York: Fourth Estate.
- Measures of effect size of an intervention - unmc.edu.
Biomedical research: Clinical study design / Design of experiments
| Controlled study|
(EBM I to II-1; A to B)
| Observational study|
(EBM II-2 to II-3; B to C)
|Analysis of clinical trials|
|Interpretation of results|