Correspondence

Calculation of Number Needed to Treat

N Engl J Med 2009; 361:424-425July 23, 2009

Article

To the Editor:

The number of patients who would need to be treated to prevent a given adverse outcome in one patient, called the number needed to treat, is often used in randomized trials and observational studies to provide a simple measure of the effect of a treatment. The computation of the number needed to treat can, however, be inaccurate and its interpretation misleading in trials with varying follow-up times. In this case, the cumulative incidence of an outcome cannot simply be calculated as a proportion of subjects but must instead be estimated over time by means of the Kaplan–Meier approach that accounts for varying follow-up times.

Trials that based the computation of the number needed to treat on the simple proportion of patients with the outcome, rather than the Kaplan–Meier estimates, may have distorted values of the number needed to treat.1-3 Other trials have accounted for varying follow-up times by using, instead, the incidence rate computed as the number of patients with the outcome divided by the total amount of person-time.4,5 However, the corresponding number needed to treat, although based on the incidence rates, was interpreted as the number needed to treat to prevent one occurrence of the outcome among patients treated for a given period, which may be incorrect.

For example, in the recent trial of 3845 elderly patients who had hypertension, with follow-up times varying from 0 to 6.5 years, the incidence rate of stroke was 12.4 per 1000 patient-years for active treatment compared with 17.7 per 1000 patient-years for placebo.5 These rates were converted to 2-year rates and the number needed to treat was computed as 1÷(0.0354−0.0248)=94.3, interpreted as “1 stroke being prevented because 94 patients were treated for 2 years.”5 This interpretation is not accurate, since this number needed to treat does not represent patients, but rather patient-years. Indeed, 94 patients treated for 2 years is not necessarily the same as 188 patient-years: the former implies 94 distinct patients treated for 2 years, whereas the latter can equally imply 188 patients treated for 1 year or 47 patients treated for 4 years. The study in fact provided the Kaplan–Meier curves for the cumulative incidence of stroke, which resulted in a 2-year cumulative incidence of stroke of around 2.2% for active treatment and 3.8% for placebo. These values correspond to a more accurate number needed to treat of 63 patients needing to be treated for 2 years to prevent 1 stroke, rather than the reported 94 patients.

Although the number needed to treat is a simple and intuitively appealing measure of the effect of a treatment, its computation must be performed with care in trials with varying follow-up times.

Samy Suissa, Ph.D.
McGill University, Montreal, QC H3A 2T5, Canada
samy.suissa@mcgill.ca

Dr. Suissa reports receiving consulting fees from Boehringer Ingelheim, Pfizer, GlaxoSmithKline, and Schering-Plough; lecture fees from Boehringer Ingelheim, Pfizer, and AstraZeneca; and grant support from Boehringer Ingelheim and Pfizer. No other potential conflict of interest relevant to this letter was reported.

5 References

1. 1

   Corey L, Wald A, Patel R, et al. Once-daily valacyclovir to reduce the risk of transmission of genital herpes. N Engl J Med 2004;350:11-20
   Full Text | Web of Science | Medline

2. 2

   Tu JV, Bowen J, Chiu M, et al. Effectiveness and safety of drug-eluting stents in Ontario. N Engl J Med 2007;357:1393-1402
   Full Text | Web of Science | Medline

3. 3

   Gnant M, Mlineritsch B, Schippinger W, et al. Endocrine therapy plus zoledronic acid in premenopausal breast cancer. N Engl J Med 2009;360:679-691[Erratum, N Engl J Med 2009;360:2379.]
   Full Text | Web of Science | Medline

4. 4

   Hurlen M, Abdelnoor M, Smith P, Erikssen J, Arnesen H. Warfarin, aspirin, or both after myocardial infarction. N Engl J Med 2002;347:969-974
   Full Text | Web of Science | Medline

5. 5

   Beckett NS, Peters R, Fletcher AE, et al. Treatment of hypertension in patients 80 years of age or older. N Engl J Med 2008;358:1887-1898
   Full Text | Web of Science | Medline

Citing Articles (6)

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   Vern L. Katz. 2013. Evidence–Based Medicine and Clinical Epidemiology. , 97-103.
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   Daniel Suissa, Paul Brassard, Brielan Smiechowski, Samy Suissa. (2012) Number needed to treat is incorrect without proper time-related considerations. Journal of Clinical Epidemiology 65:1, 42-46
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   Alexander A. Leung, Adam Wright, Valeria Pazo, Andrew Karson, David W. Bates. (2011) Risk of Thiazide-induced Hyponatremia in Patients with Hypertension. The American Journal of Medicine 124:11, 1064-1072
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