In epidemiology, the relative risk reduction is a measure calculated by dividing the absolute risk reduction by the control event rate.[1][2][3][4]
The relative risk reduction can be more useful than the absolute risk reduction in determining an appropriate treatment plan, because it accounts not only for the effectiveness of a proposed treatment, but also for the relative likelihood of an incident (positive or negative) occurring in the absence of treatment.
Like many other epidemiological measures, the same equations can be used to measure a benefit or a harm (although the signs may need to be adjusted, depending upon how the data was collected.)
| Example 1: risk reduction | Example 2: risk increase | ||||
|---|---|---|---|---|---|
| Experimental group (E) | Control group (C) | Total | (E) | (C) | |
| Events (E) | EE = 15 | CE = 100 | 115 | EE = 75 | CE = 100 |
| Non-events (N) | EN = 135 | CN = 150 | 285 | EN = 75 | CN = 150 |
| Total subjects (S) | ES = EE + EN = 150 | CS = CE + CN = 250 | 400 | ES = 150 | CS = 250 |
| Event rate (ER) | EER = EE / ES = 0.1, or 10% | CER = CE / CS = 0.4, or 40% | N/A | 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 |