IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0234432.html
   My bibliography  Save this article

The generalized inference on the ratio of mean differences for fraction retention noninferiority hypothesis

Author

Listed:
  • Hsin-Neng Hsieh
  • Hung-Yi Lu

Abstract

The fraction retention non-inferiority hypothesis is often measured for the ratio of the effects of a new treatment to those of the control in medical research. However, the fraction retention non-inferiority test that the new treatment maintains the efficacy of control can be affected by the nuisance parameters. Herein, a heuristic procedure for testing the fraction retention non-inferiority hypothesis is proposed based on the generalized p-value (GPV) under normality assumption and heteroskedasticity. Through the simulation study, it is demonstrated that, the performance of the GPV-based method not only adequately controls the type I error rate at the nominal level but also is uniformly more powerful than the ratio test, Rothmann’s and Wang’s tests, the comparable extant methods. Finally, we illustrate the proposed method by employing a real example.

Suggested Citation

  • Hsin-Neng Hsieh & Hung-Yi Lu, 2020. "The generalized inference on the ratio of mean differences for fraction retention noninferiority hypothesis," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-12, June.
    • Handle: RePEc:plo:pone00:0234432
    DOI: 10.1371/journal.pone.0234432
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0234432
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0234432&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0234432?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Lin, Tsai-Yu & Liao, Chen-Tuo, 2006. "A [beta]-expectation tolerance interval for general balanced mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 911-925, February.
    2. Marsaglia, George, 2006. "Ratios of Normal Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(i04).
    3. Wei-Ya Wu & Wei-Hwa Wu & Hsin-Neng Hsieh & Meng-Chih Lee, 2018. "The generalized inference on the sign testing problem about the normal variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(5), pages 956-970, April.
    4. Wei-Hwa Wu & Hsin-Neng Hsieh, 2014. "Generalized confidence interval estimation for the mean of delta-lognormal distribution: an application to New Zealand trawl survey data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1471-1485, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael Keane & Timothy Neal, 2021. "A Practical Guide to Weak Instruments," Discussion Papers 2021-05b, School of Economics, The University of New South Wales.
    2. Dennis Wichelns, 2015. "Water productivity and water footprints are not helpful in determining optimal water allocations or efficient management strategies," Water International, Taylor & Francis Journals, vol. 40(7), pages 1059-1070, November.
    3. Carson, Richard T. & Czajkowski, Mikołaj, 2019. "A new baseline model for estimating willingness to pay from discrete choice models," Journal of Environmental Economics and Management, Elsevier, vol. 95(C), pages 57-61.
    4. Guy P. Nason & Ben Powell & Duncan Elliott & Paul A. Smith, 2017. "Should we sample a time series more frequently?: decision support via multirate spectrum estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 353-407, February.
    5. Caginalp, Carey & Caginalp, Gunduz, 2018. "The quotient of normal random variables and application to asset price fat tails," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 457-471.
    6. Stokes, Barrie, 2012. "mathStatica 2.5," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(s01).
    7. Eloísa Díaz-Francés & Francisco Rubio, 2013. "On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables," Statistical Papers, Springer, vol. 54(2), pages 309-323, May.
    8. Philip L.H. Yu & Thomas Mathew & Yuanyuan Zhu, 2017. "A generalized pivotal quantity approach to portfolio selection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1402-1420, June.
    9. Carlotta Galeone & Angiola Pollastri, 2012. "Confidence intervals for the ratio of two means using the distribution of the quotient of two normals," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 13(3), pages 451-472, December.
    10. Caginalp, Carey & Caginalp, Gunduz, 2019. "Price equations with symmetric supply/demand; implications for fat tails," Economics Letters, Elsevier, vol. 176(C), pages 79-82.
    11. Clark, Adam Thomas & Neuhauser, Claudia, 2018. "Harnessing uncertainty to approximate mechanistic models of interspecific interactions," Theoretical Population Biology, Elsevier, vol. 123(C), pages 35-44.
    12. Bagos Pantelis G, 2008. "A Unification of Multivariate Methods for Meta-Analysis of Genetic Association Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-35, October.
    13. Alvarez, Eduardo J. & Ribaric, Adrijan P., 2018. "An improved-accuracy method for fatigue load analysis of wind turbine gearbox based on SCADA," Renewable Energy, Elsevier, vol. 115(C), pages 391-399.
    14. Erhard Reschenhofer, 2017. "Using Ratios of Successive Returns for the Estimation of Serial Correlation in Return Series," Noble International Journal of Economics and Financial Research, Noble Academic Publsiher, vol. 2(9), pages 125-130, September.
    15. Gatta, Valerio & Marcucci, Edoardo & Scaccia, Luisa, 2015. "On finite sample performance of confidence intervals methods for willingness to pay measures," Transportation Research Part A: Policy and Practice, Elsevier, vol. 82(C), pages 169-192.
    16. Gunduz Caginalp, 2020. "Fat tails arise endogenously in asset prices from supply/demand, with or without jump processes," Papers 2011.08275, arXiv.org, revised Mar 2021.
    17. Michael Keane & Timothy Neal, 2021. "A New Perspective on Weak Instruments," Discussion Papers 2021-05a, School of Economics, The University of New South Wales.
    18. Fernández, Arturo J., 2010. "Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 151-162, January.
    19. Christopher Withers & Saralees Nadarajah, 2014. "A unified method for constructing expectation tolerance intervals," Statistical Papers, Springer, vol. 55(4), pages 951-965, November.
    20. Frantisek Duris & Juraj Gazdarica & Iveta Gazdaricova & Lucia Strieskova & Jaroslav Budis & Jan Turna & Tomas Szemes, 2018. "Mean and variance of ratios of proportions from categories of a multinomial distribution," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-20, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0234432. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.