Relative Risk, Absolute Risk and NNT for EDAIC
Calculate relative risk, absolute risk reduction and NNT from one worked example, then see why baseline risk and follow-up change the answer.
Relative risk compares two event probabilities by division. Absolute risk reduction compares them by subtraction. The number needed to treat, or NNT, is the reciprocal of the absolute reduction expressed as a proportion. For EDAIC statistics, the reliable sequence is to identify the outcome, calculate each group's risk, and only then choose the comparison.
These measures answer different questions. A large relative reduction can accompany a small absolute benefit when the starting risk is low. None should be interpreted without the outcome and observation period. Cochrane's guide to effect measures explains the distinction between ratio and difference measures.
Start with one clearly defined event
Consider an original teaching trial, unrelated to any particular medicine. Investigators compare intervention A with a control and count participants experiencing at least one specified complication within 30 days. Assume complete follow-up, equal-sized groups, and one binary outcome per participant.
| Group | Participants | Participants with the complication | Risk |
|---|---|---|---|
| Control | 400 | 80 | 80/400 = 0.20 |
| Intervention A | 400 | 48 | 48/400 = 0.12 |
The denominator is participants, not the total number of complications. If one participant experiences three episodes, that does not turn this particular binary outcome into three affected people. Write the outcome definition beside the table before using a formula.
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Calculate four results from the same table
The relative risk, using intervention divided by control, is 0.12/0.20 = 0.60. The intervention group has 60% of the control group's observed event risk.
The relative risk reduction is 1 − 0.60 = 0.40, or 40%. This is a reduction relative to the control risk. It is not a reduction of 40 percentage points.
The absolute risk reduction is 0.20 − 0.12 = 0.08. Express it as eight percentage points, or eight fewer affected participants per 100 over 30 days.
The NNT is 1/0.08 = 12.5, conventionally rounded upward to 13. Its interpretation is an estimated 13 participants treated with A instead of control for one additional participant to avoid the specified complication over the stated 30 days. It is not a guarantee that every thirteenth person benefits. Oxford CEBM's NNT explanation supports this absolute-risk interpretation.
Notice that the arithmetic uses 0.08, not the number 8. Inverting 8 produces 0.125, which is a warning that percentage notation has been mixed with a proportion.
Change the baseline risk, keeping the relative effect
Now create a second hypothetical population with a control event risk of 5%. Assume, specifically for this exercise, that the same relative risk of 0.60 applies.
The predicted intervention risk is 0.05 × 0.60 = 0.03. The absolute reduction is 0.02, or two percentage points. NNT is therefore 50 over the same observation period.
The relative reduction remains 40%, yet the NNT has changed from 13 to 50. This follows directly from the different starting risk. In a real appraisal, transporting a relative effect to another population is an assumption requiring justification, not a permission to invent an individual treatment benefit. Cochrane's interpretation chapter discusses presenting absolute effects using an appropriate baseline risk.
Answer an EDAIC-style question
This is one exam-format Part 1 multiple-true-false question from our bank. Mark each statement true or false, then see the worked answer.
Regarding the pathophysiology of oxygen delivery and consumption in circulatory shock:
Mark each statement true or false:
In healthy adults at rest, systemic oxygen delivery is approximately 1000 mL/min while oxygen consumption is about 250 mL/min, creating a physiological oxygen reserve.
When systemic oxygen delivery decreases, oxygen consumption immediately falls in direct proportion, indicating supply dependency at all levels of DO₂.
Cardiac output is determined by the product of heart rate and stroke volume, with stroke volume being influenced by preload, afterload, and myocardial contractility.
The unifying feature of all forms of shock, regardless of aetiology, is acute circulatory failure associated with inadequate cellular oxygen utilisation.
In septic shock, early goal-directed therapy targeting supranormal oxygen delivery values has been shown to consistently reduce mortality across all patient populations.
Three traps worth putting in your error log
First, risk is not odds. In the first control group, risk is 80/400, whereas odds are 80/320. An odds ratio cannot simply be relabelled a risk ratio when answering a statement.
Second, the direction of subtraction matters. If the intervention increases a harmful outcome, the absolute difference represents harm rather than benefit. State which event is being counted; a reduction in death and a reduction in survival have opposite implications.
Third, an NNT without its time horizon is incomplete. A 30-day result and a five-year result do not describe the same exposure period. Confidence intervals also matter: the point estimate alone does not describe uncertainty, and crossing no effect makes a single simple NNT interval misleading.
Test yourself before reading the answers
In another invented study, a harmful event occurs in 30 of 600 controls and 18 of 600 intervention participants during identical follow-up.
- The relative risk is 0.60.
- The absolute risk reduction is 40 percentage points.
- The NNT point estimate is 50.
- The result identifies exactly which individuals benefit.
Answers: 1 true: 0.03/0.05 = 0.60. 2 false: the difference is two percentage points; 40% is the relative reduction. 3 true: 1/0.02 = 50. 4 false: group differences do not identify individual responders.
For a second practice pass, reverse the comparison and explain why the relative risk becomes approximately 1.67 rather than 1.40. Dividing is directional; a percentage decrease and its reverse increase are not numerically symmetric.
Use the EDAIC statistics overview to connect these calculations with other study designs. When practising in the AnesCORE question bank, write the denominator and follow-up period before selecting a statistics answer.
Sources
- Cochrane Handbook: choosing effect measures
- Cochrane Handbook: interpreting results
- Oxford CEBM: Number Needed to Treat
Prepared with AI assistance for examination revision; this article is not a patient-care protocol or a substitute for current primary guidance. Sources checked 7 October 2026.
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