Published 24 June 2009, doi:10.1136/bmj.b2493
Cite this as: BMJ 2009;338:b2493

Endgames

Statistical question

Number needed to treat

John Fletcher, clinical epidemiologist

1 BMJ, London WC1H 9JR

jfletcher{at}bmj.com

Two weeks after entry to a trial of antibiotics to treat symptoms of chest infection, 25% of people receiving placebo and 15% of people receiving antibiotics still had symptoms. What is the number needed to treat in this trial for antibiotics to cure symptoms at two weeks?

a) 10
b) 1.18
c) 10%
d) 4
e) 6.7

Show Answers

Answer

a—Number needed to treat reflects in this context how many people must be treated with the antibiotic for one extra person to improve over and above those who would have improved taking the placebo. The difference between the two groups in those who benefit is 10% or 10 in 100, which is 1 in 10. So 10 patients must be treated for one extra than the placebo group to benefit.

Answer b is 1/0.85 and reflects the number needed to treat ignoring the recovery rate in the placebo arm; that is, for every 118 people treated, 100 experienced improvement in their symptoms. This is the "cure rate" experienced by clinicians because, outside of a research setting, doctors do not usually give half their patients a placebo!

Answer c is the difference between groups in the percentage of people who benefit. The number needed to treat is the reciprocal of this.

Answer d is the number of people that would need to be treated with placebo in order for one person to still have symptoms at two weeks. Of those patients receiving placebo, 25%, or 1 in 4, still had symptoms at two weeks. The maximum possible benefit in this trial would be if every single one of these patients were cured by antibiotics. Hence in this setting, four is the lowest possible number needed to treat if antibiotics were 100% effective.

Answer e is 1/0.15 and is just misguided maths.

Cite this as: BMJ 2009;338:b2493


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