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Incorrect calculation of numbers needed to treat affects confidence intervals more often than point estimates

  • Ralf Bender
    Correspondence
    Corresponding author. Tel.: +49-221-35685-451; fax: +49-221-35685-10.
    Affiliations
    Department of Medical Biometry, Institute for Quality and Efficiency in Health Care (IQWiG), Im Mediapark 8, D-50670 Cologne, Germany
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      To the Editor:
      In a recent article on the estimation of the number needed to treat (NNT) in studies with varying follow-up times, Suissa et al. [
      • Suissa D.
      • Brassard P.
      • Smiechowski B.
      • Suissa S.
      Number needed to treat is incorrect without proper time-related considerations.
      ] concluded that 6 of 10 studies published in four major medical journals in 2009 did not compute the NNT correctly. This confirms and extends the previous result, that 17 of 34 articles published in the same journals between 2003 and 2005 applied an inappropriate calculation method to derive NNTs from time-to-event outcomes [
      • Hildebrandt M.
      • Vervölgyi E.
      • Bender R.
      Calculation of NNTs in RCTs with time-to-event outcomes: a literature review.
      ]. There are two frequently used inadequate methods to calculate NNTs from time-to-event outcomes, namely the use of naive proportions neglecting censoring and the application of incidence rates rather than absolute risks [
      • Suissa D.
      • Brassard P.
      • Smiechowski B.
      • Suissa S.
      Number needed to treat is incorrect without proper time-related considerations.
      ,
      • Hildebrandt M.
      • Vervölgyi E.
      • Bender R.
      Calculation of NNTs in RCTs with time-to-event outcomes: a literature review.
      ,
      • Stang A.
      • Poole C.
      • Bender R.
      Common problems related to the use of number needed to treat.
      ]. Suissa et al. [
      • Suissa D.
      • Brassard P.
      • Smiechowski B.
      • Suissa S.
      Number needed to treat is incorrect without proper time-related considerations.
      ] presented published examples where the application of naive proportions or incidence rates leads to incorrect NNT point estimates. Besides incorrect point estimates, an additional problem is the incorrect calculation of confidence intervals (CIs) if naive proportions or incidence rates are used to estimate NNTs. This is important because in practice incorrectly calculated NNT point estimates are frequently close to the corresponding estimates calculated by an appropriate method [
      • Hildebrandt M.
      • Vervölgyi E.
      • Bender R.
      Calculation of NNTs in RCTs with time-to-event outcomes: a literature review.
      ]. However, even if the use of an incorrect method has little effect on the point estimate, the corresponding incorrectly calculated CI may be misleading. For example, if naive proportions are used to estimate NNTs in the case of varying follow-up times and a large proportion of censored data, the corresponding CIs will be too narrow because censoring is not taken into account and the values used for the effective sample sizes are too large [
      • Hildebrandt M.
      • Vervölgyi E.
      • Bender R.
      Calculation of NNTs in RCTs with time-to-event outcomes: a literature review.
      ].

      References

        • Suissa D.
        • Brassard P.
        • Smiechowski B.
        • Suissa S.
        Number needed to treat is incorrect without proper time-related considerations.
        J Clin Epidemiol. 2012; 65: 42-46
        • Hildebrandt M.
        • Vervölgyi E.
        • Bender R.
        Calculation of NNTs in RCTs with time-to-event outcomes: a literature review.
        BMC Med Res Methodol. 2009; 9: 21
        • Stang A.
        • Poole C.
        • Bender R.
        Common problems related to the use of number needed to treat.
        J Clin Epidemiol. 2010; 63: 820-825