Skip to main content
SpringerLink
Log in

Identification of the minimum non-inferior dose in a three-arm non-inferiority trial

  • Research Article
  • Published:
Journal of the Korean Statistical Society Aims and scope Submit manuscript

Abstract

Non-inferiority (NI) trials have gained recognition as an effective tool with which to search for substitutes for a standard treatment that is associated with certain undesirable features, such as adverse side-effects, an exorbitant cost, or an extremely complicated therapeutic regimen. Statistical methods have been developed for NI studies with multiple experimental treatments. However, experimental treatments sometimes represent a new treatment with various dose levels, and in such circumstances, identification of the minimum non-inferior dose is a reasonable objective of the trial. Thus, we examine several potential testing procedures with respect to this testing objective. A simulation study is conducted to evaluate their performance, and determination of the sample size is discussed. Two clinical examples are provided to illustrate the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bachelez, H., Van de Kerkhof, P., Strohal, R., Kubanov, A., Valenzuela, F., Lee, J. H., et al. (2015). Tofacitinib versus etanercept or placebo in moderate-to-severe chronic plaque psoriasis: A phase 3 randomised non-inferiority trial. Lancet, 386, 552–561.

    Article  Google Scholar 

  • Beeh, K. M., Derom, E., Kanniess, F., Cameron, R., Higgins, M., & Van As, A. (2007). Indacaterol, a novel inhaled beta 2-agonist, provides sustained 24-hour bronchodilation in asthma. European Respiratory Journal, 29, 871–878.

    Article  Google Scholar 

  • Bossche, L. V., & Vanderstraeten, G. (2015). A multi-center, double-blind, randomized, placebo-controlled trial protocol to assess traumeel injection vs dexamethasone injection in rotator cuff syndrome: the TRAumeel in ROtator cuff syndrom (TRARO) study protocol. BMC Musculoskeletal Disorders, 16, 8.

    Article  Google Scholar 

  • Burger, H. U., Beyer, U., & Abt, M. (2011). Issues in the assessment of non-inferiority: Perspectives drawn from case studies. Pharmaceutical Statistics, 10, 433–439.

    Article  Google Scholar 

  • Cazzola, M., & Matera, M. G. (2009). Emerging inhaled bronchodilators: An update. European Respiratory Journal, 34, 757–769.

    Article  Google Scholar 

  • Donohue, J. F., Fogarty, C., Lötvall, J., Worth, H., Yorgancioglu, A., Iqbal, A., et al. (2010). Once-daily bronchodilators for chronic obstructive pulmonary disease: Indacaterol versus tiotropium. American Journal of Respiratory and Critical Care Medicine, 182, 155–162.

    Article  Google Scholar 

  • Dunnett, C. W. (1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50, 1096–1121.

    Article  Google Scholar 

  • Dunnett, C. W., & Tamhane, A. C. (1992). A step-up multiple test procedure. Journal of the American Statistical Association, 87, 162–170.

    Article  MathSciNet  Google Scholar 

  • Ellenberg, S. S., & Temple, R. (2000). Placebo-controlled trials and active-control trials in the evaluation of new treatments. Part 2: Practical issues and specific cases. Annals of Internal Medicine, 133, 464–470.

    Article  Google Scholar 

  • European Medicines Agency. (2006). Guideline on the Choice of the Non-inferiority Margin. London: EMA. https://www.ema.europa.eu/en/documents/scientific-guideline/guideline-choice-non-inferiority-margin_en.pdf. Retrieved 12 June 2019.

  • Fleming, T. R., Odem-Davis, K., Rothmann, M. D., & Yan, L. S. (2011). Some essential considerations in the design and conduct of non-inferiority trials. Clinical Trials, 8, 432–439.

    Article  Google Scholar 

  • Fleming, T. R., & Powers, J. H. (2008). Issues in noninferiority trials: The evidence in community-acquired pneumonia. Clinical Infectious Diseases, 47, S108–S120.

    Article  Google Scholar 

  • Food and Drug Administration. (2016). Guidance for Industry Non-inferiority Clinical Trials-Draft Guidance. Rockville: FDA. https://www.fda.gov/media/78504/download. Retrieved 12 June 2019.

  • Gallwitz, B., Rosenstock, J., Rauch, T., Bhattacharya, S., Patel, S., von Eynatten, M., et al. (2012). 2-year efficacy and safety of linagliptin compared with glimepiride in patients with type 2 diabetes inadequately controlled on metformin: A randomised, double-blind, non-inferiority trial. Lancet, 380, 475–483.

    Article  Google Scholar 

  • Gamalo-Siebers, M., Gao, A., Lakshminarayanan, M., Liu, G., Natanegara, F., Railkar, R., et al. (2016). Bayesian methods for the design and analysis of noninferiority trials. Journal of Biopharmaceutical Statistics, 26, 823–841.

    Article  Google Scholar 

  • Ghosh, S., Ghosh, S., & Tiwari, R. C. (2014). Bayesian approach for assessing non-inferiority in a three-arm trial with pre-specified margin. Statistics in Medicine, 35, 695–708.

    Article  MathSciNet  Google Scholar 

  • Hung, H. M., Wang, S. J., & O’Neill, R. (2009). Challenges and regulatory experiences with non-inferiority trial design without placebo arm. Biometrical Journal, 51, 324–334.

    Article  MathSciNet  Google Scholar 

  • Jendle, J., Grunberger, G., Blevins, T., Giorgino, F., Hietpas, R. T., & Botros, F. T. (2016). Efficacy and safety of dulaglutide in the treatment of type 2 diabetes: A comprehensive review of the dulaglutide clinical data focusing on the AWARD phase 3 clinical trial program. Diabetes Metabolism Research and Reviews, 32, 776–790.

    Article  Google Scholar 

  • Kwong, K. S., Cheung, S. H., & Hayter, A. J. (2016). Step-up procedures for non-inferiority tests with multiple experimental treatments. Statistical Methods in Medical Research, 25, 1290–1302.

    Article  MathSciNet  Google Scholar 

  • Kwong, K. S., Cheung, S. H., Hayter, A. J., & Wen, M. J. (2012). Extension of three-arm non-inferiority studies to trials with multiple new treatments. Statistics in Medicine, 31, 2833–2843.

    Article  MathSciNet  Google Scholar 

  • Kwong, K. S., & Liu, W. (2000). Calculation of critical values for Dunnett and Tamhane’s step-up multiple test procedure. Statistics and Probability Letters, 49, 411–416.

    Article  MathSciNet  Google Scholar 

  • Madsbad, S., Schmitz, O., Ranstam, J., Jakobsen, G., & Matthews, D. R. (2004). Improved glycemic control with no weight increase in patients with type 2 diabetes after once-daily treatment with the long-acting glucagon-like peptide 1 analog liraglutide (NN2211): A 12-week, double-blind, randomized, controlled trial. Diabetes Care, 27, 1335–1342.

    Article  Google Scholar 

  • Nauck, M., Frid, A., Hermansen, K., Shah, N. S., Tankova, T., Mitha, I. H., et al. (2009). Efficacy and safety comparison of liraglutide, glimepiride, and placebo, all in combination with metformin, in type 2 diabetes. Diabetes Care, 32, 84–90.

    Article  Google Scholar 

  • Nauck, M., Weinstock, R. S., Umpierrez, G. E., Guerci, B., Skrivanek, Z., & Millicevic, Z. (2014). Efficacy and safety of dulaglutide versus sitagliptin after 52 weeks in type 2 diabetes in a randomized controlled trial. Diabetes Care, 37, 2149–2158.

    Article  Google Scholar 

  • Ridderstråle, M., Andersen, K. R., Zeller, C., Kim, G., Woerle, H. J., Broedl, U. C., & EMPA-REG H2H-SU trial investigators. (2014). Comparison of empagliflozin and glimepiride as add-on to metformin in patients with type 2 diabetes: A 104-week randomised, active-controlled, double-blind, phase 3 trial. The Lancet Diabetes and Endocrinology, 2, 691–700.

  • Roberts, V. L., Stewart, J., Issa, M., Lake, B., & Melis, R. (2005). Triple therapy with glimepiride in patients with type 2 diabetes mellitus inadequately controlled by metformin and a thiazolidinedione: Results of a 30-week, randomized, double-blind, placebo-controlled, parallel-group study. Clinical Therapeutics, 27, 1535–1547.

    Article  Google Scholar 

  • Skrivanek, Z., Gaydos, B. L., Chien, J. Y., Geiger, M. J., Heathman, M. A., Berry, S., et al. (2014). Dose-finding results in an adaptive, seamless, randomized trial of once-weekly dulaglutide combined with metformin in type 2 diabetes patients (AWARD5). Diabetes, Obesity and Metabolism, 16, 748–756.

    Article  Google Scholar 

  • Sundar, S., Sinha, P. K., Rai, M., Verma, D. K., Nawin, K., Alam, S., et al. (2011). Comparison of short-course multidrug treatment with standard therapy for visceral leishmaniasis in India: An open-label, non-inferiority, randomised controlled trial. Lancet, 377, 477–486.

    Article  Google Scholar 

  • Tamhane, A. C., Dunnett, C. W., Green, J., & Wetherington, J. (2001). Multiple test procedures for identifying the maximum safe dose. Journal of the American Statistical Association, 96, 835–843.

    Article  MathSciNet  Google Scholar 

  • Tamhane, A. C., Hochberg, Y., & Dunnett, C. W. (1996). Multiple test procedures for dose finding. Biometrics, 52, 21–37.

    Article  Google Scholar 

  • Tamhane, A. C., & Logan, B. R. (2002). Multiple test procedures for identifying the minimum effective and maximum safe doses of a drug. Journal of the American Statistical Association, 97, 293–301.

    Article  MathSciNet  Google Scholar 

  • Tamhane, A. C., Shi, K., & Strassburger, K. (2006). Power and sample size determination fot a stepwise test procedure for finding the maximum safe dose. Journal of Statistical Planning and Inference, 136, 2163–2181.

    Article  MathSciNet  Google Scholar 

  • Vilsbøll, T., Zdravkovic, M., Le-Thi, T., Krarup, T., Schmitz, O., Courrges, J. P., et al. (2007). Liraglutide, a long-acting human glucagon-like peptide-1 analog, given as monotherapy significantly improves glycemic control and lowers body weight without risk of hypoglycemia in patients with type 2 diabetes. Diabetes Care, 30, 1608–1610.

    Article  Google Scholar 

  • Wolfsegger, M. J., Gutjahr, G., Engl, W., & Jaki, T. (2014). A hybrid method to estimate the minimum effective dose for monotone and non-monotone dose-response relationships. Biometrics, 70, 103–109.

    Article  MathSciNet  Google Scholar 

  • Xu, W., Hu, F., & Cheung, S. H. (2018). Adaptive design for non-inferiority trials with multiple experimental treatments. Statistical Methods in Medical Research, 27, 3255–3270.

    Article  MathSciNet  Google Scholar 

  • Zhong, J., Wen, M. J., Kwong, K. S., & Cheung, S. H. (2018). Testing of non-inferiority and superiority for three-arm clinical studies with multiple experimental treatments. Statistical Methods in Medical Research, 27, 1751–1765.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We are grateful to the referees who provided very helpful suggestions and comments. Zhong’s research was supported by the Natural Science Foundation of Fujian Province, China (2018J01430) and a research grant from Xiamen University of Technology, China (YKJ17003R). Wen’s research was supported by the Ministry of Science and Technology, Taiwan, MOST 108-2118-M-006-008, and MOST 107-2118-M-006-005. Cheung’s research was supported by the Research Grants Council of the Hong Kong Special Administrative Region (CUHK14304916) and a direct grant from The Chinese University of Hong Kong.

Author information

Authors and Affiliations

  1. School of Applied Mathematics, Xiamen University of Technology, Xiamen, China

    Junjiang Zhong

  2. Department of Statistics, Institute of Data Science, and Institute of International Management, National Cheng Kung University, Tainan, Taiwan

    Miin-Jye Wen

  3. Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China

    Siu Hung Cheung

  4. Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, China

    Siu Hung Cheung

Authors
  1. Junjiang Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miin-Jye Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Siu Hung Cheung
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Siu Hung Cheung.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhong, J., Wen, MJ. & Cheung, S.H. Identification of the minimum non-inferior dose in a three-arm non-inferiority trial. J. Korean Stat. Soc. 49, 1238–1254 (2020). https://doi.org/10.1007/s42952-020-00053-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42952-020-00053-w

Keywords

Mathematics Subject Classification

Search

Navigation