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How to calculate risk

These are the relationships among various terms used to describe risk, changes in risk, and significant statistical differences.

Risk terms

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

Examples

  1. RR of 0.8 means a RRR of 20% (meaning a 20% reduction in the relative risk of the specified outcome in the treatment group compared with the control group).
  2. 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.
  3. 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.
  4. 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 a NNT of 200.

Significant difference

  • 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.

Note

  • To express decimals as percentages, multiply by 100.