NNT, NNH and absolute risk reduction: which number to quote

Study cases written by our editors, not BPS items. The real BCPS exam is computer-based multiple choice, answered in order with no going back.

1. Case 01

   In a 2-year randomized trial, stroke occurred in 4% of patients receiving placebo and 3% of patients receiving a new drug (p=0.01). Which measure best conveys the absolute clinical benefit when counseling an individual patient?

   1. AOption A: Relative risk of 0.75
   2. BOption B: p-value of 0.01
   3. COption C: NNT of 100 over 2 years
   4. DOption D: Relative risk reduction of 25%

   Pick an option: the verdict and a note on every option open here.

   Best answer: C.

   The absolute risk reduction is 4% − 3% = 1%, so the NNT is 1 ÷ 0.01 = 100 patients treated for 2 years to prevent one stroke, which conveys benefit in absolute terms. The 25% relative risk reduction is tempting but makes a small absolute benefit sound large because it ignores the baseline risk. The relative risk restates the same relative effect, and the p-value shows only that chance is an unlikely explanation, not how large the effect is.

   A

   A relative risk of 0.75 restates the relative effect and hides the 1% absolute difference.

   B

   The p-value shows that chance is an unlikely explanation, not how large the benefit is.

   C

   Correct. The absolute risk reduction is 1%, so 100 patients must be treated for 2 years to prevent one stroke.

   D

   A 25% relative reduction sounds large but ignores the low 4% baseline risk.

2. Case 02

   A new antihypertensive lowers 5-year stroke risk by 25% relative to placebo, and the relative effect is similar across risk groups. Patient 1 is a 45-year-old with a 5-year stroke risk of 2%. Patient 2 is a 78-year-old with a prior TIA and a 5-year stroke risk of 20%. Which statement about the expected benefit over 5 years is correct?

   1. AOption A: Both benefit equally, since each gets the same 25% risk reduction
   2. BOption B: The NNT is about 200 for patient 1 and about 20 for patient 2
   3. COption C: The NNT is about 20 for patient 1 and about 2 for patient 2
   4. DOption D: The NNT is 4 for both, the reciprocal of the 25% reduction

   Pick an option: the verdict and a note on every option open here.

   Best answer: B.

   Absolute risk reduction (ARR) = baseline risk × relative risk reduction (RRR). For patient 1, 2% × 0.25 = 0.5%, so the NNT is 1 ÷ 0.005 = 200 over 5 years. For patient 2, 20% × 0.25 = 5%, so the NNT is 1 ÷ 0.05 = 20. The same 25% RRR means ten times more absolute benefit at the higher baseline risk. This is why the CONSORT 2025 statement asks trials with binary outcomes to report both absolute and relative effect sizes: a relative reduction alone hides the baseline risk.

   A

   The relative reduction is the same, but the absolute benefit is ten times larger for patient 2.

   B

   Correct. ARR is 2% × 0.25 = 0.5% (NNT 200) for patient 1 and 20% × 0.25 = 5% (NNT 20) for patient 2.

   C

   This slips a decimal: 0.5% is 0.005, not 0.05, so 1 ÷ 0.005 = 200, and 1 ÷ 0.05 = 20.

   D

   An NNT comes from the absolute risk reduction, not the relative one, so it changes with baseline risk.

3. Case 03

   In a 3-year randomized trial, myocardial infarction occurred in 6.0% of patients receiving placebo and 4.2% of patients receiving a new lipid-lowering drug. How many patients must be treated for 3 years to prevent one myocardial infarction?

   1. AOption A: 56
   2. BOption B: 556
   3. COption C: 4
   4. DOption D: 55

   Pick an option: the verdict and a note on every option open here.

   Best answer: A.

   The absolute risk reduction is 6.0% − 4.2% = 1.8%, and the NNT is 1 ÷ 0.018 = 55.6, which is rounded up to 56 so that at least one event is prevented. Rounding down to 55 is the common error. Entering 1.8% as 0.0018 gives the decimal-slip answer 556, and dividing 1 by the 30% relative risk reduction gives 4, which is not an NNT.

   A

   Correct. ARR is 6.0% − 4.2% = 1.8%, and 1 ÷ 0.018 is 55.6, rounded up to 56.

   B

   556 is the decimal slip that comes from entering 1.8% as 0.0018.

   C

   4 comes from dividing 1 by the relative risk reduction (30%), but the NNT must use the absolute difference.

   D

   Rounding 55.6 down to 55 is the common error; NNT is always rounded up.

4. Case 04

   In an 18-month HFrEF trial, the primary outcome (cardiovascular death or HF hospitalization) occurred in 21.2% of patients on a new drug and 26.5% on placebo (HR 0.74; 95% CI 0.65–0.85). Which statement is correct?

   1. AOption A: About 4 patients must be treated for 18 months to prevent one event
   2. BOption B: The drug prevented the outcome in 26% of treated patients
   3. COption C: The absolute risk of the outcome fell by 26 percentage points
   4. DOption D: The hazard of the outcome was 26% lower with the drug

   Pick an option: the verdict and a note on every option open here.

   Best answer: D.

   An HR of 0.74 means a 26% lower instantaneous risk (hazard) of the outcome over time, and the CI excluding 1 makes it significant. The absolute risk reduction is only 26.5% − 21.2% = 5.3%, so the NNT is 1 ÷ 0.053 ≈ 19, not 4; reading the relative 26% as an absolute change is the classic trap. The 26% does not describe the proportion of patients who benefited.

   A

   The NNT uses the absolute difference of 5.3%, which gives about 19, not 4.

   B

   The 26% is a relative reduction in hazard, not the share of treated patients who benefited.

   C

   The absolute drop is 26.5% − 21.2% = 5.3 percentage points, not 26.

   D

   Correct. An HR of 0.74 means a 26% lower hazard of the outcome, and the CI excluding 1 makes it significant.

5. Case 05

   In a 1-year trial, hypoglycemia requiring assistance occurred in 9% of patients receiving a new insulin regimen and 3% of patients receiving standard therapy. What is the number needed to harm (NNH) for one additional patient with severe hypoglycemia over 1 year?

   1. AOption A: 33
   2. BOption B: 8
   3. COption C: 17
   4. DOption D: 16.7

   Pick an option: the verdict and a note on every option open here.

   Best answer: C.

   The absolute risk increase is 9% − 3% = 6%, so NNH = 1 ÷ 0.06 = 16.7, which is rounded up to 17 by convention (the same rule as for NNT). Reporting the unrounded 16.7 is an error, since patients come in whole numbers. 33 comes from using only the control-group rate (1 ÷ 0.03), and 8 comes from adding the two rates instead of subtracting them.

   A

   33 comes from using only the standard-therapy rate (1 ÷ 0.03) instead of the difference.

   B

   8 comes from adding the two rates (12%) instead of subtracting them.

   C

   Correct. The absolute risk increase is 6%, so NNH is 1 ÷ 0.06, or 16.7, rounded up to 17.

   D

   16.7 is the unrounded value; NNH is reported as a whole number of patients.

6. Case 06

   A 64-year-old man with stable coronary disease asks which of two add-on drugs offers more benefit. Trial X followed similar patients for 5 years: major cardiovascular events occurred in 10.0% on placebo and 8.0% on drug X, so the NNT is 50. Trial Y followed similar patients for 1 year: events occurred in 4.0% on placebo and 3.0% on drug Y, so the NNT is 100. The outcome definitions match. Which statement about these NNTs is correct?

   1. AOption A: Drug X works better, since its NNT of 50 is half of drug Y’s
   2. BOption B: Drug Y works better, since a larger NNT means a larger benefit
   3. COption C: Per year, drug X’s NNT is 10 (50 ÷ 5), so X is ten times better
   4. DOption D: They cover different periods, so 50 vs 100 does not rank them

   Pick an option: the verdict and a note on every option open here.

   Best answer: D.

   An NNT is the number of patients who must get the treatment instead of the comparator for one extra patient to avoid an event in a given time frame (Cochrane Handbook, chapter 15, 2024). It is 1 divided by the absolute risk reduction, and it should always be reported with its follow-up time. Trial X gives an NNT of 50 over 5 years, and trial Y gives 100 over 1 year, so the two numbers cannot be ranked side by side. If risk builds at a steady rate, drug X reduces risk by about 0.4% a year (NNT near 250 per year) against 1% a year for drug Y. That steady-rate assumption needs checking, but it shows the raw comparison can even reverse.

   A

   A lower NNT means more benefit only when both NNTs cover the same follow-up time. Here one covers 5 years and the other 1 year.

   B

   This reverses the meaning. A larger NNT means more patients must be treated to prevent one event, so a smaller benefit per patient treated.

   C

   Dividing an NNT by years moves it the wrong way. If risk builds steadily, a 2% reduction over 5 years is 0.4% a year, an NNT near 250 per year.

   D

   Correct. Every NNT belongs to its own time frame. Both must be put on the same period, with an assumption about how risk builds, before ranking.