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In epidemiology, the absolute risk reduction, risk difference or excess risk is the change 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.
In general, absolute risk reduction is the difference between the control group’s event rate (CER) and the experimental group’s event rate (EER). The difference is usually calculated with respect to two treatments A and B, with A typically a drug and B a placebo. For example, A could be a 5-year treatment with a hypothetical drug, and B is treatment with placebo, i.e. no treatment. A defined endpoint has to be specified, such as a survival or a response rate. For example: the appearance of lung cancer in a 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.
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.
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|
|EER − CER||< 0: absolute risk reduction||ARR||(−)0.3, or (−)30%||N/A|
|> 0: absolute risk increase||ARI||N/A||0.1, or 10%|
|(EER − CER) / CER||< 0: relative risk reduction||RRR||(−)0.75, or (−)75%||N/A|
|> 0: relative risk increase||RRI||N/A||0.25, or 25%|
|1 / (EER − CER)||< 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|