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Estimation of numbers needed to treat should be based on absolute risks

Published:November 04, 2013DOI:https://doi.org/10.1016/j.jclinepi.2013.08.009
      In reply:
      We thank Girerd et al. [
      • Girerd N.
      • Rabilloud M.
      • Duarte K.
      • Roy P.
      Number needed to treat from absolute risk and incidence rate: How to make apples and oranges comparable?.
      ] for their interest in the recent article by Bender et al. [
      • Bender R.
      • Kromp M.
      • Kiefer C.
      • Sturtz S.
      Absolute risks rather than incidence rates should be used to estimate the number needed to treat from time-to-event data.
      ], in which we compared the two methods to estimate the numbers needed to treat (NNTs) from time-to-event data, namely inverting risk differences (RD approach) and inverting incidence differences (ID approach). We totally agree that, in principal, both methods lead to two different effect measures, a fact that is already explained in detail [
      • Bender R.
      • Kromp M.
      • Kiefer C.
      • Sturtz S.
      Absolute risks rather than incidence rates should be used to estimate the number needed to treat from time-to-event data.
      ,
      • Stang A.
      • Poole C.
      • Bender R.
      Common problems related to the use of number needed to treat.
      ,
      • Suissa D.
      • Brassard P.
      • Smiechowski B.
      • Suissa S.
      Number needed to treat is incorrect without proper time-related considerations.
      ]. However, as in current practice the ID approach is inappropriately used to estimate the classical patient-based NNT [
      • Suissa D.
      • Brassard P.
      • Smiechowski B.
      • Suissa S.
      Number needed to treat is incorrect without proper time-related considerations.
      ], it makes sense to explore the estimation and coverage properties of this approach in relevant data situations [
      • Bender R.
      • Kromp M.
      • Kiefer C.
      • Sturtz S.
      Absolute risks rather than incidence rates should be used to estimate the number needed to treat from time-to-event data.
      ]. Our simulations clearly showed that the ID approach frequently has considerable bias and low coverage probabilities and should therefore not be used to estimate the classical patient-based NNT [
      • Bender R.
      • Kromp M.
      • Kiefer C.
      • Sturtz S.
      Absolute risks rather than incidence rates should be used to estimate the number needed to treat from time-to-event data.
      ].
      The consideration of the inverse of an ID as an alternative effect measure that expresses the required average amount of person-time, which results in one less event in the intervention group compared with the control group, is only valid under the strong assumption of a constant hazard difference [
      • Bender R.
      • Kromp M.
      • Kiefer C.
      • Sturtz S.
      Absolute risks rather than incidence rates should be used to estimate the number needed to treat from time-to-event data.
      ,
      • Stang A.
      • Poole C.
      • Bender R.
      Common problems related to the use of number needed to treat.
      ,
      • Suissa D.
      • Brassard P.
      • Smiechowski B.
      • Suissa S.
      Number needed to treat is incorrect without proper time-related considerations.
      ]. In this case, we agree with Girerd et al. [
      • Girerd N.
      • Rabilloud M.
      • Duarte K.
      • Roy P.
      Number needed to treat from absolute risk and incidence rate: How to make apples and oranges comparable?.
      ] that the use of the ID approach gives complementary information regarding the absolute benefit of a treatment. However, the conversion formula used by Girerd et al. [
      • Girerd N.
      • Rabilloud M.
      • Duarte K.
      • Roy P.
      Number needed to treat from absolute risk and incidence rate: How to make apples and oranges comparable?.
      ] to calculate one NNT measure from the other is only valid in the case of the exponential distribution. This means that this conversion is inappropriate for all other survival time distributions. Thus, we do not agree that in general “the conversion between these two NNT can be easily done.” The application of the ID approach in situations without constant hazard differences such as the Gompertz distribution leads to an effect measure with unclear interpretation and no useful information regarding the absolute benefit of a treatment [
      • Bender R.
      • Kromp M.
      • Kiefer C.
      • Sturtz S.
      Absolute risks rather than incidence rates should be used to estimate the number needed to treat from time-to-event data.
      ].
      The inverted incidence differences calculated by Girerd et al. [
      • Girerd N.
      • Rabilloud M.
      • Duarte K.
      • Roy P.
      Number needed to treat from absolute risk and incidence rate: How to make apples and oranges comparable?.
      ] from the Colon Cancer Study data set on a yearly basis varied from 21 to 84. Therefore, the assumptions of a constant hazard difference and exponentially distributed survival times are questionable in this example. This means that the usual applications of the ID approach and of the conversion formula are invalid for these data. Without further discussion and explanation, Girerd et al. [
      • Girerd N.
      • Rabilloud M.
      • Duarte K.
      • Roy P.
      Number needed to treat from absolute risk and incidence rate: How to make apples and oranges comparable?.
      ] applied the conversion formula on a yearly basis, which makes the results of the different methods more comparable. However, one reason for the application of the ID approach was to get an effect measure, which is independent of time [
      • Lubsen J.
      • Hoes A.
      • Grobbee D.
      Implications of trial results: the potentially misleading notations of number needed to treat and average duration life gained.
      ]. The application of the ID approach on a yearly basis may improve the validity of the corresponding approximations but the goal to have an effect measure that is independent of time is not achieved. We think that the presentation of two time-dependent NNT measures, the classical patient-based NNT, and a more or less adequate approximation of a person-time NNT is more confusing than helpful to assess the absolute benefit of a treatment.
      In summary, the application of the ID approach to estimate NNT measures leads to useful information only under strong assumptions. In general, the estimation of NNTs from time-to-event outcomes should be based on absolute risks estimated by means of appropriate survival time methods.

      References

        • Girerd N.
        • Rabilloud M.
        • Duarte K.
        • Roy P.
        Number needed to treat from absolute risk and incidence rate: How to make apples and oranges comparable?.
        J Clin Epidemiol. 2014; 67 ([in this issue]): 236-238
        • Bender R.
        • Kromp M.
        • Kiefer C.
        • Sturtz S.
        Absolute risks rather than incidence rates should be used to estimate the number needed to treat from time-to-event data.
        J Clin Epidemiol. 2013; 66: 1038-1044
        • Stang A.
        • Poole C.
        • Bender R.
        Common problems related to the use of number needed to treat.
        J Clin Epidemiol. 2010; 63: 820-825
        • 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
        • Lubsen J.
        • Hoes A.
        • Grobbee D.
        Implications of trial results: the potentially misleading notations of number needed to treat and average duration life gained.
        Lancet. 2000; 356: 1757-1759

      Linked Article

      • Number needed to treat from absolute risk and incidence rate: How to make apples and oranges comparable?
        Journal of Clinical EpidemiologyVol. 67Issue 2
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          We read with great interest the article of Bender et al. [1] focusing on number needed to treat (NNT) calculation. In this article, the authors compare a “risk difference” (RD) method based on cumulative risk calculated from the Kaplan–Meier Method and an “incidence rate difference” (IRD) method based on classical epidemiological incidence rate (IR) calculation. In this simulation study, the authors compared NNT estimated with the RD and the IRD methods with the “true” NNT calculated with the RD method.
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