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Absolute risk reduction
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.^{[1]} It is the inverse of the number needed to treat.^{[2]}
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 5year 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 5year 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.
Presenting results
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 fiveyear period. The rate of colon cancer for a fiveyear 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").^{[3]} Natural numbers, which are used in the number needed to treat approach, are easily understood by nonexperts.
Worked example
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 
Nonevents (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 
See also
References
 ^ "An overview of measurements in epidemiology" (PDF). Retrieved 20100201.
 ^ Laupacis, A; Sackett, DL; Roberts, RS (1988). "An assessment of clinically useful measures of the consequences of treatment.". The New England Journal of Medicine 318 (26): 1728–33. PMID 3374545. doi:10.1056/NEJM198806303182605.
 ^ Ben Goldacre (2008). Bad Science. New York: Fourth Estate. pp. 239–260. ISBN 0007240198.
External links
 Measures of effect size of an intervention – unmc.edu.
