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.[1] It is the inverse of the number needed to treat.[2]
For instance, 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.
Contents |
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 non-experts.
| 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 |
|
||||||||||||||||||||||||||