MRCGP AKT · Statistics & EBP · Flagship

Measures of effect: RR, RRR, ARR, NNT, NNH and odds ratios

The highest-yield arithmetic in the AKT. Turn any trial result into absolute terms, calculate NNT and NNH with their time frame, and know when an odds ratio can stand in for a relative risk.

Reviewed and kept current

Last editorial review: 28 September 2026 · Next scheduled refresh: March 2027.

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Clinical vignette

Begin with the patient. Read the case, weigh the options, then work through the unit.

Mrs F has high blood pressure. She has read that a new antihypertensive “cuts the risk of stroke by 25%”. She asks whether she should take it.

The figure comes from a five-year trial. A stroke occurred in 4% of patients taking placebo and in 3% of patients taking the new drug. Symptomatic postural hypotension occurred in 12% of patients on the drug and in 7% on placebo.

Mrs F wants to know what the drug would do for her. She dislikes taking tablets and will not take one without a good reason.

Options to weigh

  • Quote the relative risk reduction of 25%.
  • Convert the result to an absolute risk reduction and a number needed to treat over the trial’s five years.
  • Present benefit and harm with a common denominator: out of 100 people treated for five years, how many avoid a stroke and how many have postural hypotension.
  • Recommend the drug without discussing postural hypotension.

Reflect

How would you explain this result so that Mrs F can decide, and what would you be careful not to say?

Unit overview

What this unit covers

Pocket-sized and self-contained: three AKT-style questions, the answers explained, an expanded discussion with hyperlinked guidance, a decision algorithm and a certificate.

Unit code
MDA-AKT-EBP-EIP-05
AKT domain
Evidence-based practice≈10% (16 of 160 items)
Study time
25 minutesCPD, self-certified
Pass mark
2 of 3unlocks your certificate
RCGP Topic Guide: Evidence in practice, research, teaching and lifelong learningRCGP Topic Guide: Continuity and quality of care, safety and prescribingRCGP · Applied Knowledge Test

By the end of this unit you will be able to

✓Calculate CER, EER, RR, RRR, ARR and NNT from raw trial data or percentages.
✓Calculate NNH and balance it against NNT for shared decisions.
✓Distinguish risk from odds, and explain when the OR approximates the RR.
✓Explain why relative measures exaggerate benefit in low-risk patients (population vs individual risk).
The unit

Five steps, in order

Answer first, then learn. Each section unlocks as you progress, and your progress is saved in this browser.

1Three single best answer questions

Commit to an answer for all three single best answer questions, then submit. Sections 2–4 open on submission; your certificate opens at 2/3 or better.

Question 1 of 3

In a five-year trial, 4% of patients taking placebo and 3% of patients taking a new antihypertensive had a stroke.

How many patients need to be treated for five years to prevent one stroke?

Question 2 of 3

In the same trial, 12% of patients on the new drug and 7% on placebo developed symptomatic postural hypotension.

What is the number needed to harm over five years?

Question 3 of 3

A case–control study compares 200 patients with Stevens–Johnson syndrome with 800 controls. 40 cases and 40 controls had taken a particular antiepileptic in the preceding eight weeks.

What is the odds ratio for exposure to the antiepileptic?

2Answers explained

Question 1

Correct answer D. 100

ARR = CER − EER = 4% − 3% = 1% = 0.01 NNT = 1 / 0.01 = 100 (over five years)

The relative risk reduction is 25% (1/4), which sounds impressive; the NNT of 100 puts it in perspective. Option B (25) confuses RRR with NNT; option C (33) is 1/EER; option E (133) is 1/(0.03 × 0.25).

Question 2

Correct answer C. 20

Absolute risk increase (ARI) = 12% − 7% = 5% = 0.05 NNH = 1 / 0.05 = 20

So, over five years, for every 100 patients treated, about 5 extra experience postural hypotension and 1 stroke is prevented. That is the conversation to have with the patient. Convention: round NNT up and NNH down to the nearest whole person (the cautious direction).

Question 3

Correct answer D. 4.75

Exposed Not exposed Cases 40 160 Controls 40 760 OR = (40 × 760) / (160 × 40) = 30,400 / 6,400 = 4.75

A case–control study can only give an odds ratio, because the investigator fixed the number of cases and controls and so cannot calculate incidence (risk). Option C (4.0) comes from comparing the proportions exposed (20% vs 5%), which is not an odds ratio.

3Expanded discussion, worked examples & guidance

1. The core formulas

CER (control event rate) = events in control / total control EER (experimental event rate) = events in treatment / total treatment RR = EER / CER (<1 = fewer events with treatment) RRR = (CER − EER) / CER = 1 − RR ARR = CER − EER NNT = 1 / ARR → round UP; always quote the time period and the outcome NNH = 1 / ARI → ARI = EER(harm) − CER(harm) Odds = events / non-events OR = odds(treatment) / odds(control) = ad/bc

Try it · live calculator

Treatment-effect calculator

2. Worked examples

Worked example 1 — from raw numbers

Statin trial over 5 years: 80 of 2,000 on placebo and 60 of 2,000 on statin had a myocardial infarction.

  1. CER = 80/2000 = 4%; EER = 60/2000 = 3%.
  2. RR = 0.75; RRR = 25%.
  3. ARR = 1%; NNT = 100.

Answer. Treat 100 people for 5 years to prevent one MI.

Worked example 2 — same RRR, different baseline risk (population vs individual risk)

A treatment gives an RRR of 25% for cardiovascular events. Patient A has a 10-year QRISK3 of 4%; patient B has 20%.

  1. Patient A: ARR = 25% × 4% = 1% → NNT 100 over 10 years.
  2. Patient B: ARR = 25% × 20% = 5% → NNT 20 over 10 years.

Answer. The relative effect is constant; the absolute benefit — and therefore the value to the individual — depends on baseline risk. This is the logic behind NICE’s QRISK3 threshold for offering a statin (10%).

Worked example 3 — relative framing in the media

A headline says: “Drug doubles the risk of blood clots.” The risk rises from 2 per 10,000 to 4 per 10,000 women per year.

  1. RR = 2 (a 100% relative increase).
  2. ARI = 2 per 10,000 = 0.0002.
  3. NNH = 1/0.0002 = 5,000.

Answer. One extra clot per 5,000 women treated per year. Always convert relative risks to absolute numbers when counselling.

3. Risk vs odds, RR vs OR

Risk = events / total; odds = events / non-events. With 20 events in 100 people, the risk is 0.20 and the odds are 20/80 = 0.25.

  • Cohort studies and RCTs can report RR and OR.
  • Case–control studies can report only the OR.
  • When the outcome is rare (below about 10%), OR ≈ RR. When the outcome is common, the OR exaggerates the effect: it is further from 1 than the RR.
  • Logistic regression produces adjusted odds ratios, which is why observational studies so often report ORs.

4. Using these numbers with patients

NICE recommends presenting risks as absolute numbers with a common denominator (for example “out of 100 people like you”), over a stated time, with both benefits and harms, using visual aids such as Cates plots (Unit 11). Relative risk reductions alone overstate benefit and mislead.

Exam traps
  • Percentages: 4% − 3% = 1 percentage point (ARR), not a 1% relative reduction.
  • NNT has no meaning without a time frame and an outcome.
  • If the treatment increases events, 1/|ARR| is an NNH.
  • An RR or OR of exactly 1 means no difference.

References and further reading

Guidance checked at the last editorial review (28 September 2026). Always use the current version.

  1. RCGP — Data interpretation topics in the AKT (PDF)
  2. NICE NG197 — Shared decision making
  3. NICE NG238 — Cardiovascular disease: risk assessment and reduction, including lipid modification
  4. Oxford CEBM — Number needed to treat
  5. Winton Centre for Risk and Evidence Communication
4Decision algorithm

From any trial result to a patient-ready number

1

Start

Identify the outcome, the time period and the two groups.

2

Decision

Are you given raw counts?

YesCER = control events ÷ control total; EER = treatment events ÷ treatment total.
NoUse the percentages given as CER and EER.
3

Action

RR = EER/CER · RRR = 1 − RR · ARR = CER − EER

4

Decision

Is ARR positive (fewer events with treatment)?

YesNNT = 1/ARR, rounded up.
NoThe treatment increases events: NNH = 1/ARI.
5

Decision

Is the study case–control?

YesOnly an odds ratio is valid: OR = ad/bc.
NoRR is preferred; OR ≈ RR if the outcome affects fewer than about 10%.
6

Outcome

Tell the patient: “Out of 100 people like you treated for X years, about N avoid the outcome and M experience the harm.”

Revision summary; apply clinical judgement and local pathways.

5Certificate of completion

You have met the pass mark. Enter your details to issue your personalised certificate of completion, then save it as a PDF for your appraisal or revalidation portfolio.

Where next?

← Diagnostic tests II: likelihood ratios and pre- to post-test probabilityP-values, confidence intervals, type I and II errors, and power →📐 AKT statistics formula sheet✉️ enquiry@mdacumen.com
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