A statement such as “the programme reduced the risk by half” leaves a reader with a crucial unanswered question: half of what? A change from 40 in 100 to 20 in 100 and a change from 2 in 100 to 1 in 100 both halve risk. They describe very different absolute differences.
For PT students reading research, the practical skill is to keep the event, denominator, comparison and follow-up together. Relative and absolute measures answer different questions about the same data. The Cochrane Handbook distinguishes ratios of risks from differences between risks and warns against treating an odds ratio as a risk ratio. Cochrane, Chapter 6.
The datasets here are invented for arithmetic practice. They are not evidence for a rehabilitation intervention.
Start with counts before percentages
Imagine a fictional trial comparing two approaches to supporting participation in a rehabilitation programme. The event is stopping the programme before the eight-week follow-up. Each group begins with 200 participants, and the exercise assumes complete outcome information.
| Group | Stopped the programme | Did not stop | Total |
|---|---|---|---|
| Comparison support | 40 | 160 | 200 |
| Additional support | 20 | 180 | 200 |
The comparison risk is 40/200 = 0.20, or 20%. The additional-support risk is 20/200 = 0.10, or 10%.
Writing the denominator first helps prevent a surprisingly easy error: comparing the 20 additional-support events with all 400 participants. The risk within that group uses its own 200 participants.
Calculate three descriptions
Risk ratio: 0.10 / 0.20 = 0.50. In this dataset, the additional-support group has half the observed risk of stopping.
Relative risk reduction: 1 − 0.50 = 0.50, or 50%.
Absolute risk reduction: 0.20 − 0.10 = 0.10, or 10 percentage points. That is 10 fewer people stopping per 100 participants over eight weeks.
“Ten percent lower” can be ambiguous. “Ten percentage points lower” describes the absolute difference clearly. You can avoid the distinction altogether when speaking by using natural counts: 20 in 100 compared with 10 in 100.
A careful explanation is: “In this fictional study, 10% stopped with additional support compared with 20% under comparison support over eight weeks. The observed absolute difference was 10 percentage points; the risk ratio was 0.50.”
That sentence preserves the numbers without suggesting certainty about the underlying effect or suitability for an individual.
Add number needed to treat carefully
For the observed reduction in this undesirable event, the arithmetic number needed to treat is the reciprocal of the absolute risk reduction expressed as a proportion:
NNT = 1 / 0.10 = 10
If the comparison provides a credible estimate of a causal effect, this corresponds to an average of 10 people receiving additional support rather than comparison support for one fewer person to stop over eight weeks. The arithmetic alone cannot establish that support caused the difference: group differences, missing outcomes and other biases still require appraisal. NNT also does not identify who benefits or promise one extra success in every group of 10. Cochrane on interpreting NNT.
Keep the comparison and eight-week period attached to the result. Changing either can change its meaning. A proper appraisal would also examine uncertainty around the estimate, adverse effects, workload and the trial’s methods before using the number in a decision.
Keep the relative effect and change the baseline
Now consider a second fictional setting with 1,000 participants per group:
| Group | Stopped within eight weeks | Risk |
|---|---|---|
| Comparison support | 20 of 1,000 | 2% |
| Additional support | 10 of 1,000 | 1% |
The risk ratio remains 0.50 and the relative risk reduction remains 50%. However, the absolute risk reduction is now one percentage point, and the arithmetic NNT is 100.
The same “halves the risk” headline fits both examples. The additional-support programme might require very different resources per additional person who continues. Whether it is worthwhile still depends on how much the outcome matters to people, the burden of support and the quality of the evidence. Arithmetic does not make that value judgement for you.
Do not quietly change the event
In the first dataset, 80% of comparison participants and 90% of additional-support participants continued. The ratio for continuing is 0.90/0.80 = 1.125. That is not the reciprocal of the risk ratio for stopping.
The events are complements, but their risk ratios are different descriptions. Name the event before you calculate. A note that just says “RR = 0.50” is incomplete because another reader cannot tell whether the event is beneficial or undesirable.
Likewise, do not substitute odds for risk. In the first comparison group, the odds of stopping are 40/160, while the risk is 40/200. They use different denominators. Read the study’s reported measure before translating a headline.
Practise the explanation
A third fictional comparison reports 12 events among 120 people receiving usual support and 6 among 120 receiving an additional service, with complete six-month follow-up. Calculate the absolute difference, relative risk and NNT before reading on.
The risks are 10% and 5%. The absolute reduction is five percentage points, the risk ratio is 0.50, and NNT is 20 over six months. The sentence “50 fewer events per 100 people” is wrong. It confuses a relative reduction of 50% with an absolute reduction of 50 percentage points.
For your next paper, copy the raw counts and follow-up period into your notes. Write one sentence using natural frequencies, then one using the reported effect measure. If the two sentences appear to tell different stories, check the denominator and event definition before you trust either one.
Sources and further reading
- Cochrane Handbook Chapter 6 — Choosing effect measures — Risk ratio, risk difference and distinction between odds and risks.
- Cochrane Handbook Chapter 15 — Interpreting results — Interpretation of NNT as an expected comparative effect over a specified time, with uncertainty.