Measuring the effect of an exposure or treatment
Clinical trials and epidemiological studies compare how often an event happens in two groups: treated and untreated, exposed and unexposed. Several measures describe the difference, and each answers a slightly different question.
The 2 × 2 table
| Event | No event | |
|---|---|---|
| Exposed or treated | a | b |
| Control | c | d |
The formulas
- Risk in each group: a ÷ (a + b) and c ÷ (c + d)
- Relative risk RR = risk in exposed ÷ risk in control
- Odds ratio OR = (a × d) ÷ (b × c)
- Absolute risk reduction ARR = risk in control − risk in exposed
- Number needed to treat NNT = 1 ÷ |ARR|
- Relative risk reduction RRR = 1 − RR
- Confidence interval for RR: exp(ln RR ± z × √(1/a − 1/(a + b) + 1/c − 1/(c + d)))
Worked example
In a trial, 15 of 100 treated patients and 25 of 100 control patients have a heart attack.
- Risks: 15% and 25%.
- RR = 0.15 ÷ 0.25 = 0.60: treatment lowers the risk by 40% in relative terms.
- ARR = 25% − 15% = 10 points.
- NNT = 1 ÷ 0.10 = 10: treating 10 patients prevents one heart attack.
- OR = (15 × 75) ÷ (85 × 25) ≈ 0.53.
- 95% confidence interval for RR: 0.34 to 1.07. It includes 1, so with only 200 patients the result is not statistically significant.
Relative or absolute?
Relative measures sound more impressive. A drug that cuts risk from 2% to 1% has an RRR of 50% but an ARR of only 1 point and an NNT of 100. Good reporting gives both, so patients can weigh the benefit against side effects and cost.
Odds ratio or relative risk?
- In cohort studies and trials, use the relative risk, which is easier to interpret.
- In case-control studies, participants are chosen by outcome, so risks cannot be computed and the odds ratio is used.
- When the event is rare (under about 10%), the OR is close to the RR. When it is common, the OR exaggerates the effect.
Number needed to harm
When the exposure increases the risk, 1 ÷ |ARR| is the number needed to harm: how many people must be exposed for one extra adverse event.
This calculator is for general information and education. It is not medical advice and does not replace the judgment of a doctor, nurse or pharmacist who knows the full clinical picture.