Relative risk reduction

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Relative risk reduction

In epidemiology, the relative risk reduction (RRR) or efficacy is the relative decrease in the risk of an adverse event in the exposed group compared to an unexposed group. It is computed as , where is the incidence in the exposed group, and is the incidence in the unexposed group. If the risk of an adverse event is increased by the exposure rather than decreased, the term relative risk increase (RRI) is used, and it is computed as .[1][2] If the direction of risk change is not assumed, the term relative effect is used, and it is computed in the same way as relative risk increase.[3]

Thumb
The group exposed to treatment (left) has the risk of an adverse outcome (black) reduced by 50% (RRR = 0.5) compared to the unexposed group (right).

Numerical examples

Risk reduction

More information Quantity, Experimental group (E) ...
Example of risk reduction
Quantity Experimental group (E) Control group (C) Total
Events (E) EE = 15 CE = 100 115
Non-events (N) EN = 135 CN = 150 285
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400
Event rate (ER) EER = EE / ES = 0.1, or 10% CER = CE / CS = 0.4, or 40%
Close
More information Variable, Abbr. ...
Variable Abbr. Formula Value
Absolute risk reduction ARR CER EER 0.3, or 30%
Number needed to treat NNT 1 / (CER EER) 3.33
Relative risk (risk ratio) RR EER / CER 0.25
Relative risk reduction RRR (CER EER) / CER, or 1 RR 0.75, or 75%
Preventable fraction among the unexposed PFu (CER EER) / CER 0.75
Odds ratio OR (EE / EN) / (CE / CN) 0.167
Close

Risk increase

More information Quantity, Experimental group (E) ...
Example of risk increase
Quantity Experimental group (E) Control group (C) Total
Events (E) EE = 75 CE = 100 175
Non-events (N) EN = 75 CN = 150 225
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400
Event rate (ER) EER = EE / ES = 0.5, or 50% CER = CE / CS = 0.4, or 40%
Close
More information Variable, Abbr. ...
Variable Abbr. Formula Value
Absolute risk increase ARI EER CER 0.1, or 10%
Number needed to harm NNH 1 / (EER CER) 10
Relative risk (risk ratio) RR EER / CER 1.25
Relative risk increase RRI (EER CER) / CER, or RR 1 0.25, or 25%
Attributable fraction among the exposed AFe (EER CER) / EER 0.2
Odds ratio OR (EE / EN) / (CE / CN) 1.5
Close

See also

References

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