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This is a really important and interesting article. I would like to congratulate the authors with their work.
I do have one question with regard to figure 3B. The numbers needed to treat to harm (NNTH) in this table seem to have counterintuitive values, for instance see the value from the direct thrombin inhibitor, which is listed as 153, with a corresponding OR of harm of 2.63. This NNTH value is more or less equal to that of aspirin, which has a listed NNTH of 155, however, its corresponding OR for harm is much lower, namely 1.07. Similarly, the point estimate of the NNTH for standard dose Xa is 270 which is higher than that listed for low dose Xa inhibitor (187), while the respective ORs for harm show that standard-dose Xa inhibitor has a higher odds for harm. I realize that there is a possible logical explanation for these counterintuitive results, namely that the base rates of the placebo/observation condition vary significantly, but that would not be expected. Could the authors elaborate on this? Thank you very much in advance.
This is our response to a concern raised by a reader regarding the estimates and credible intervals of those numbers needed to treat to harm presented in our article titled “Extended treatment of venous thromboembolism: a systematic review and network meta-analysis.”
First, we confirm that data published in the Journal are valid and correct.
We also like to thank the reader to point it out as a number needed (either for benefit or harm) derived from an effect estimate that crosses the unity has been intuitively challenging to visualize (Hutton JL. Br J Haematol. 2009;146:27-30). Because it is given by the reciprocal of the absolute risk difference, a number needed can never include zero but straddles plus and minus infinity ∞ when the absolute risk difference include zero. By the frequentist approach based on inverting the confidence interval of the absolute risk difference, it represents that the number needed encompasses two disjoint regions: one from upper confidence interval to plus ∞ and the other from lower confidence interval to minus ∞ (Altman DG. BMJ. 1998;317:1309-12). Some had argued that for those non-significant results, a number needed should be presented as a single number without its confidence interval as it includes the possibility of no benefit or harm (McQuay HJ. Ann Intern Med. 1997;126:712-20). Other had suggested that it should not be reported when being non-significant (McAlister FA. CMAJ. 2008;179:549-53).
Our analyses with t...
Our analyses with the Bayesian approach based on probability derived a number needed from the posterior distribution of the reciprocal of the absolute risk difference. Mathematically, its distribution stretches from minus ∞ to plus ∞ and can be bi-modal (as the probability of a number needed being zero is zero) (Thabane L. Biostatistics. 2003;4:365-70). The median of a number needed falls within its credible interval.
We also provided the estimates of the absolute risk difference in Supplementary table 3. When using them by the frequentist approach, the number needed to treat to harm (95% credible interval) is 4560 (-368, 110), 95 (16, 3461), 87(23, 348), 805 (-381, 56), 363 (-854, 56), and 184 (-1103, 17) for aspirin, low-intensity vitamin K antagonist, standard-intensity vitamin K antagonist, low-dose factor Xa inhibitor, standard-dose factor Xa inhibitor, and direct thrombin inhibitor, respectively.
We opted for presenting all numbers needed with their credible intervals by the Bayesian approach. However, neither the frequentist approach nor the Bayesian approach is ideal when reporting non-significant results. It should take extra caution when using and interpreting a number needed derived from an effect estimate that crosses the unity.
Finally, thank you for letting us clarify this.
Kang-Ling Wang and Marc Carrier
General Clinical Research Center, Taipei Veterans General Hospital, Taipei, Taiwan
Department of Medicine, Ottawa Hospital Research Institute, University of Ottawa, Ottawa, Ontario, Canada