Risk, Odds & Absolute Treatment Effects
Translate comparative results into understandable numbers with a stated population and time horizon.
Quick revision ↓ Medical Dictionary
01Risk and rate
Risk is the proportion of initially at-risk people who develop an outcome during a specified period. An incidence rate divides events by person-time at risk and is not itself a probability. Prevalence describes existing cases in a population at a defined time or period. State the denominator and time horizon before comparing measures. Ten events per thousand person-years cannot simply be relabelled as a ten-year percentage.
02Relative and absolute effects
A risk ratio divides one group's risk by the comparison group's risk. A risk difference subtracts risks. For an undesirable event, absolute risk reduction is control risk minus intervention risk. Relative risk reduction is one minus the risk ratio. Relative effects help compare proportional changes, but absolute effects show how many events differ in a population and depend on the starting risk.
03Number needed to treat
For a beneficial reduction in an undesirable binary outcome, NNT is the reciprocal of the absolute risk reduction expressed as a proportion, usually rounded up to a whole person. Always state the follow-up duration and comparison. When harm increases, the analogous reciprocal describes a number needed to harm. If uncertainty crosses no effect, a single apparently neat NNT conceals important uncertainty about benefit versus harm.
04Odds are not risks
Odds equal probability divided by one minus probability. With a risk of 20%, odds are 0.2 divided by 0.8, or 0.25. An odds ratio compares odds, not probabilities, and can differ substantially from a risk ratio for common outcomes. The rare-outcome approximation is context dependent. Never translate an odds ratio of two into twice the risk without checking the design and baseline probability.
05Worked event table
In a one-year trial, 20 of 100 control participants and 10 of 100 intervention participants experience the adverse event. Risks are 20% and 10%; RR is 0.5, relative reduction 50%, absolute reduction 10 percentage points and NNT 10 for one year. The odds ratio is (10/90)/(20/80), approximately 0.44. Describe both relative and absolute effects alongside uncertainty and adverse effects.
Worked example • One-year adverse events
| Group | Events | No event | Risk |
|---|---|---|---|
| Intervention | 10 | 90 | 10% |
| Control | 20 | 80 | 20% |
RR = 0.5 • Absolute reduction = 10 percentage points • NNT = 10 over one year.
High-Yield Revision
- For a risk ratio, no difference is 1; for a risk difference, it is 0.
- Use a proportion, not a percentage number, when calculating NNT.
- An absolute effect requires a baseline risk and time horizon.
Common Pitfalls
- A 50% relative reduction does not mean 50 fewer events per 100 people.
- Do not treat odds ratios as risk ratios when outcomes are common.
References & Further Reading
Use the full methods and relevant chapters when appraising a paper. These sources support further study; the examples and questions above are original teaching exercises.
- Oxford CEBM — Critical appraisal tools
- Cochrane Handbook — Methods for evidence synthesis
- CDC — Analysing and interpreting epidemiological data
- ASA — Statement on p-values and statistical significance
- Oxford CEBM — Likelihood ratios
- Cochrane — GRADE and summary of findings
- WMA — Declaration of Helsinki, 2024 revision
- EQUATOR — Reporting guideline library
- NIH OBSSR — Mixed-methods research resources
- Institute for Healthcare Improvement — Model for Improvement