Unlike risk in lay terms, which is generally associated with a bad event, risk in statistical terms refers simply to the probability (usually statistical probability) that an event will occur, whether it be a good or a bad event.
These are the relationships among various terms used to describe risk, changes in risk, and significant statistical differences.
AR (absolute risk) = the number of events (good or bad) in treated or control groups, divided by the number of people in that group
ARC = the AR of events in the control group
ART = the AR of events in the treatment group
ARR (absolute risk reduction) = ARC – ART
RR (relative risk) = ART / ARC
RRR (relative risk reduction) = (ARC – ART) / ARC
RRR = 1 – RR
NNT (number needed to treat) = 1 / ARR
- RR of 0.8 means an RRR of 20% (meaning a 20% reduction in the relative risk of the specified outcome in the treatment group compared with the control group).
- RRR is usually constant across a range of absolute risks. But the ARR is higher and the NNT lower in people with higher absolute risks.
- If a person’s AR of stroke, estimated from his age and other risk factors, is 0.25 without treatment but falls to 0.20 with treatment, the ARR is 25% – 20% = 5%. The RRR is (25% – 20%) / 25% = 20%. The NNT is 1 / 0.05 = 20.
- In a person with an AR of stroke of only 0.025 without treatment, the same treatment will still produce a 20% RRR, but treatment will reduce her AR of stroke to 0.020, giving a much smaller ARR of 2.5% – 2% = 0.5%, and an NNT of 200.
- If the RR (the relative risk) or the OR (the odds ratio) = 1, or the CI (the confidence interval) = 1, then there is no significant difference between treatment and control groups.
- If the RR >1, and the CI does not include 1, events are significantly more likely in the treatment than the control group.
- If the RR <1, and the CI does not include 1, events are significantly less likely in the treatment than the control group.
- To express decimals as percentages, multiply by 100.