Systematic analysis of the number needed to treat

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The number needed to treat is often used to measure the efficacy of a binary outcome in randomized clinical trials. There are three different available measures of the number needed to treat. Two of these measures, Furukawa and Leucht’s and Kraemer and Kupfer’s, focus on converting Cohen’s δ index into the number needed to treat, while Laupacis et al.’s measure deals primarily with the number needed to treat’s estimation rather than with a reformulation. Mathematical and numerical analysis of numbers needed to treat and their estimators was conducted. Three novel number needed to treat estimators were introduced to supplement the numbers needed to treat introduced by Laupacis, Furukawa and Leucht, and Kraemer and Kupfer. The analysis showed that Laupacis et al.’s number needed to treat is intrinsically different from Kraemer and Kupfer’s number needed to treat, and that Furukawa and Leucht’s estimator is appropriate to use only for normally distributed outcomes with equal standard deviations. Based on the numerical analysis, the novel numbers needed to treat outperformed the existing ones under correct model specifications. Asymptotic analysis was used to test three different types of confidence intervals to supplement the numbers needed to treat. An R-package to calculate these numbers needed to treat and their confidence intervals has been developed and made available for users online.

Original languageEnglish
Pages (from-to)2393-2410
Number of pages18
JournalStatistical Methods in Medical Research
Issue number9
StatePublished - 1 Sep 2020

Bibliographical note

Publisher Copyright:
© The Author(s) 2020.


  • Number needed to treat
  • confidence intervals
  • estimation
  • maximum likelihood estimator
  • model misspecification
  • randomized controlled trial

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability
  • Health Information Management


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