Endgames Statistical Question

Number needed to treat II

BMJ 2011; 342 doi: http://dx.doi.org/10.1136/bmj.d2664 (Published 04 May 2011) Cite this as: BMJ 2011;342:d2664
  1. Philip Sedgwick, senior lecturer in medical statistics
  1. 1Section of Medical and Healthcare Education, St George’s, University of London, Tooting, London, UK
  1. p.sedgwick{at}sgul.ac.uk

Researchers assessed the efficacy and safety of varenicline, a smoking cessation aid for users of smokeless tobacco. A double blind, placebo controlled, randomised controlled trial was performed. In total, 213 participants were allocated to varenicline and 218 to placebo. Treatment was for 12 weeks, with 14 weeks of follow-up after treatment.1

The primary end point was continuous abstinence from smoking for four weeks at the end of treatment (weeks 9 to 12). Continuous abstinence was achieved by 59% of participants in the varenicline group and 39% in the placebo group, an absolute risk difference of 0.2. The relative risk of continuous abstinence between weeks 9 and 12 for varenicline compared with placebo was 1.60 (95% confidence interval 1.32 to 1.87; P<0.001).

Which one of the following is the number needed to treat for the comparison of varenicline with placebo in the primary end point?

  • a) 20

  • b) 5

  • c) −5

  • d) −20

  • e) 1.6

Answers

Answer b is correct.

This is the value of the number needed to treat for the comparison of varenicline with placebo in continuous abstinence from smoking for four weeks at the end of treatment. The number needed to treat is calculated as the reciprocal of the absolute risk difference between varenicline and placebo in the primary outcome. The percentage difference in the primary outcome between varenicline and placebo was 20%—that is, a difference in risks of 0.20. Therefore, the number needed to treat was 1÷0.20, or 5. The number needed to treat is always a positive number.

The number needed to treat was described in last week’s question.2 It quantifies the effectiveness or benefit of treatment in comparison with control and can be used to describe any outcome in a trial. The rate of continuous abstinence was greater in the varenicline group than in the placebo group. The number needed to treat summarises this treatment effect: five participants need to be treated with varenicline for one more person to benefit from treatment (continuous abstinence between weeks 9 and 12) than if they had been treated with placebo. The number needed to treat is obviously based on an estimated long term average.

The value of the number needed to treat depends only on the difference in risks between the varenicline and placebo groups. Therefore, a number needed to treat of 5 would have been obtained regardless of the absolute risks for the two treatment groups, so long as the absolute risk difference between them was 0.20. Therefore, to assess the overall benefits of treatment the number needed to treat should be presented with other measures of risk, including the absolute risks of continuous abstinence for both the varenicline and placebo groups.

The number needed to treat is typically defined as the reciprocal of the reduction in risk of an outcome between the intervention and control groups. However, this definition is suitable only when the primary outcome is undesirable, such as wound infection after minor dermatological surgery; the aim of the trial would be to establish whether the intervention reduces the rate. When the primary outcome is desirable, as in the above trial, then the aim would be to establish whether the intervention increases the rate. Therefore, the standard definition described above would not be appropriate. A more suitable definition of the number needed to treat would be the reciprocal of the absolute risk difference in the primary outcome between the intervention and control groups.

The number needed to treat describes the benefit of treatment over the control. If, however, intervention was harmful when compared with control, then the harm is quantified by the statistic of number needed to harm. The number needed to harm will be described in next week’s question.

Notes

Cite this as: BMJ 2011;342:d2664

Footnotes

  • Competing interests: None declared.

References