An alternative approach for estimating the number needed to treat for survival endpoints

Autoři: Zhao Yang aff001;  Guosheng Yin aff001
Působiště autorů: Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong SAR, China aff001;  Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas, United States of America aff002
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: 10.1371/journal.pone.0223301


To investigate the issues of the NNT based on the absolute risk reduction (ARR), namely NNTARR; and to propose an alternative definition and an estimation procedure based on the restricted mean survival time (RMST), namely NNTRMST, for RCTs. Three recent clinical trials with survival endpoints, representing different scenarios, were selected to compare the performance of the NNTARR and NNTRMST. For each trial, both versions of NNT were estimated using the reconstructed individual-level data, and the average life gain (ALG) was derived to show the differences between the NNTARR and NNTRMST. Four hypothetical scenarios were constructed to further explore the advantages and disadvantages of each definition of the NNT for survival endpoints. For the illustrative trial examples, the NNTARR failed to capture the profile of the treatment effect over time as it is calculated at a specific time point. Sometimes it may even result in misinterpretations of the treatment benefit. In particular, when either the observed event rates are low, the two survival curves cross, or a mixture of survival patterns exist. In contrast, the NNTRMST based on the average survival (or event-free) time can quantify the treatment effect more accurately and its interpretation is more intuitive and clinically meaningful. The NNTRMST can be used as an alternative measure for quantifying treatment effect in RCTs, especially so in the case of the ALG, which helps practitioners to better understand the magnitude of the benefit conferred by treatment.

Klíčová slova:

Cancer treatment – Clinical trials – Decision making – Patient advocacy – Platelets – Prostate cancer – Randomized controlled trials – Radical prostatectomy


1. Guyatt GH, Sackett DL, Sinclair JC, Hayward R, Cook DJ, Cook RJ. Users' guides to the medical literature. IX. A method for grading health care recommendations. Evidence-Based Medicine Working Group. JAMA. 1995;274(22):1800–4. doi: 10.1001/jama.274.22.1800 7500513

2. Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment. N Engl J Med. 1988;318(26):1728–33. doi: 10.1056/NEJM198806303182605 3374545

3. Altman DG, Andersen PK. Calculating the number needed to treat for trials where the outcome is time to an event. BMJ. 1999;319(7223):1492–5. doi: 10.1136/bmj.319.7223.1492 10582940

4. Altman DG. Confidence intervals for the number needed to treat. BMJ. 1998;317(7168):1309–12. doi: 10.1136/bmj.317.7168.1309 9804726

5. Nuovo J, Melnikow J, Chang D. Reporting number needed to treat and absolute risk reduction in randomized controlled trials. JAMA. 2002;287(21):2813–4. doi: 10.1001/jama.287.21.2813 12038920

6. Saver JL, Lewis RJ. Number needed to treat: Conveying the likelihood of a therapeutic effect. JAMA. 2019; 321(8):798–799. doi: 10.1001/jama.2018.21971 30730545

7. Higgins JPT, Green S. Cochrane handbook for systematic reviews of interventions. 2008.

8. Altman DG, Schulz KF, Moher D, Egger M, Davidoff F, Elbourne D, et al. The revised CONSORT statement for reporting randomized trials: Explanation and elaboration. Ann Intern Med. 2001;134(8):663–94. doi: 10.7326/0003-4819-134-8-200104170-00012 11304107

9. Moher D, Hopewell S, Schulz KF, Montori V, Gotzsche PC, Devereaux PJ, et al. CONSORT 2010 explanation and elaboration: Updated guidelines for reporting parallel group randomised trials. BMJ. 2010;340:c869. doi: 10.1136/bmj.c869 20332511

10. Osiri M, Suarez-Almazor ME, Wells GA, Robinson V, Tugwell P. Number needed to treat (NNT): Implication in rheumatology clinical practice. Ann Rheum Dis. 2003;62(4):316–21. doi: 10.1136/ard.62.4.316 12634229

11. Hutton JL. Number needed to treat: Properties and problems. J R Statl Soc Ser A Stat Soc. 2000;163(3):381–402.

12. Hutton JL. Number needed to treat and number needed to harm are not the best way to report and assess the results of randomised clinical trials. Br J Haematol. 2009;146(1):27–30. doi: 10.1111/j.1365-2141.2009.07707.x 19438480

13. Suissa D, Brassard P, Smiechowski B, Suissa S. Number needed to treat is incorrect without proper time-related considerations. J Clin Epidemiol. 2012;65(1):42–6. doi: 10.1016/j.jclinepi.2011.04.009 21816576

14. Andersen PK, Perme MP. Pseudo-observations in survival analysis. Stat Methods Med Res. 2010;19(1):71–99. doi: 10.1177/0962280209105020 19654170

15. Austin PC. Absolute risk reductions and numbers needed to treat can be obtained from adjusted survival models for time-to-event outcomes. J Clin Epidemiol. 2010;63(1):46–55. doi: 10.1016/j.jclinepi.2009.03.012 19595575

16. Bowry SK, Schoder V, Apel C. An inadvertent but explicable error in calculating number needed to treat for reporting survival data. J Am Soc Nephrol. 2014;25(5):875–6. doi: 10.1681/ASN.2014020188 24722435

17. Uno H, Claggett B, Tian L, Inoue E, Gallo P, Miyata T, et al. Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis. J Clin Oncol. 2014;32(22):2380–5. doi: 10.1200/JCO.2014.55.2208 24982461

18. Uno H, Wittes J, Fu H, Solomon SD, Claggett B, Tian L, et al. Alternatives to hazard ratios for comparing the efficacy or safety of therapies in noninferiority studies. Ann Intern Med. 2015;163(2):127–34. doi: 10.7326/M14-1741 26054047

19. Yin G. Clinical Trial Design: Bayesian and Frequentist Adaptive Methods: John Wiley & Sons; 2012.

20. Guyot P, Ades AE, Ouwens MJ, Welton NJ. Enhanced secondary analysis of survival data: Reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol. 2012;12:9. doi: 10.1186/1471-2288-12-9 22297116

21. Zhao L, Tian L, Uno H, Solomon SD, Pfeffer MA, Schindler JS, et al. Utilizing the integrated difference of two survival functions to quantify the treatment contrast for designing, monitoring, and analyzing a comparative clinical study. Clin Trials. 2012;9(5):570–7. doi: 10.1177/1740774512455464 22914867

22. Bill-Axelson A, Holmberg L, Garmo H, Taari K, Busch C, Nordling S, et al. Radical prostatectomy or watchful waiting in prostate cancer—29-year follow-up. N Engl J Med. 2018;379(24):2319–29. doi: 10.1056/NEJMoa1807801 30575473

23. Schmid P, Adams S, Rugo HS, Schneeweiss A, Barrios CH, Iwata H, et al. Atezolizumab and nab-paclitaxel in advanced triple-negative breast cancer. N Engl J Med. 2018;379(22):2108–21. doi: 10.1056/NEJMoa1809615 30345906

24. Scully M, Cataland SR, Peyvandi F, Coppo P, Knobl P, Kremer Hovinga JA, et al. Caplacizumab treatment for acquired thrombotic thrombocytopenic purpura. N Engl J Med. 2019;380(4):335–46. doi: 10.1056/NEJMoa1806311 30625070

25. Mendes D, Alves C, Batel-Marques F. Number needed to treat (NNT) in clinical literature: An appraisal. BMC Med. 2017;15(1):112. doi: 10.1186/s12916-017-0875-8 28571585

26. Trinquart L, Jacot J, Conner SC, Porcher R. Comparison of treatment effects measured by the hazard ratio and by the ratio of restricted mean survival times in oncology randomized controlled trials. J Clin Oncol. 2016;34(15):1813–9. doi: 10.1200/JCO.2015.64.2488 26884584

27. Pak K, Uno H, Kim DH, Tian L, Kane RC, Takeuchi M, et al. Interpretability of cancer clinical trial results using restricted mean survival time as an alternative to the hazard ratio. JAMA Oncol. 2017;3(12):1692–6. doi: 10.1001/jamaoncol.2017.2797 28975263

28. Uno H, Claggett B, Tian L, Fu H, Huang B, Kim DH, et al. Adding a new analytical procedure with clinical interpretation in the tool box of survival analysis. Ann Oncol. 2018;29(5):1092–4. doi: 10.1093/annonc/mdy109 29617717

29. Liang F, Zhang S, Wang Q, Li W. Treatment effects measured by restricted mean survival time in trials of immune checkpoint inhibitors for cancer. Ann Oncol. 2018;29(5):1320–4. doi: 10.1093/annonc/mdy075 29788167

Článek vyšel v časopise


2019 Číslo 10