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Miscellaneous: Applied biostatistics: number needed to treat

Free question published 22 September 2026

MiscellaneousApplied biostatistics: number needed to treat

A randomised trial of adjuvant therapy reports that 3-year overall survival is 70% in the treatment arm and 60% in the control arm. A trainee is asked to express the benefit as the number needed to treat (NNT) to gain one additional survivor at 3 years. Which value is correct, and what does it represent?

  1. ANNT = 100, derived from the relative risk reduction
  2. BNNT = 10, meaning 10 patients must be treated for one additional patient to survive to 3 years
  3. CNNT = 1.17, the ratio of the two survival rates
  4. DNNT = 0.10, which is the absolute risk reduction itself
  5. ENNT = 7, derived from the hazard ratio

Why B is correct

The number needed to treat is the reciprocal of the absolute risk reduction (the absolute difference in survival). Here the absolute survival difference is 70% minus 60% = 10% = 0.10, so NNT = 1/0.10 = 10. It represents the number of patients who need to be treated for one additional patient to benefit, here surviving to 3 years; it is derived from the absolute, not the relative, treatment effect.

And why the others are not

  • A100 would require an absolute difference of 1%, but the absolute difference here is 10%.
  • C1.17 is the ratio of the two survival probabilities, not the NNT, which is the reciprocal of the absolute difference.
  • D0.10 is the absolute risk reduction itself; the NNT is its reciprocal (10), not the difference.
  • ENNT is calculated from the absolute risk reduction, not from the hazard ratio, so 7 is incorrect.

Source Number needed to treat (NNT) in survival analysis — Altman DG, Andersen PK. Calculating the number needed to treat for trials where the outcome is time to an event. BMJ. 1999;319(7223):1492-1495.

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