Research Article
Assessing non‐inferiority of a new treatment in a three‐arm trial in the presence of heteroscedasticity
Abstract
In this paper, we describe an adjusted method to facilitate non‐inferiority tests in a three‐arm design. While the methodology is readily available in the situation of homogeneous group variances, the adjusted method will also maintain the α‐level in the presence of heteroscedasticity. We propose explicit criteria for an optimal allocation. Depending on the pattern of heterogeneity, remarkably unbalanced designs are power optimal. We will apply the method to a randomized clinical trial and a toxicological experiment. Copyright © 2007 John Wiley & Sons, Ltd.
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Number of times cited according to CrossRef: 33
- Niansheng Tang, Bin Yu, Simultaneous confidence interval for assessing non‐inferiority with assay sensitivity in a three‐arm trial with binary endpoints, Pharmaceutical Statistics, 10.1002/pst.2010, 19, 5, (518-531), (2020).
- Michael J. Adjabui, Nathaniel K. Howard, Mathias Akamba, Biostatistical Assessment of Mutagenicity Studies: A Stepwise Confidence Procedure, Journal of Probability and Statistics, 10.1155/2019/3249097, 2019, (1-8), (2019).
- Gosuke Homma, Takashi Daimon, Sequential parallel comparison design for “gold standard” noninferiority trials with a prespecified margin, Biometrical Journal, 10.1002/bimj.201800394, 61, 6, (1493-1506), (2019).
- Santu Ghosh, Arpita Chatterjee, Samiran Ghosh, Non-inferiority test based on transformations for non-normal distributions, Computational Statistics & Data Analysis, 10.1016/j.csda.2016.10.004, 113, (73-87), (2017).
- Tobias Mütze, Tim Friede, Blinded sample size re‐estimation in three‐arm trials with ‘gold standard’ design, Statistics in Medicine, 10.1002/sim.7356, 36, 23, (3636-3653), (2017).
- Ying Wu, Yiqun Li, Yan Hou, Kang Li, Xiaohua Zhou, Study duration for three-arm non-inferiority survival trials designed for accrual by cohorts, Statistical Methods in Medical Research, 10.1177/0962280216633908, 27, 2, (507-520), (2016).
- Tobias Mütze, Frank Konietschke, Axel Munk, Tim Friede, A studentized permutation test for three‐arm trials in the ‘gold standard’ design, Statistics in Medicine, 10.1002/sim.7176, 36, 6, (883-898), (2016).
- Toshimitsu Ochiai, Toshimitsu Hamasaki, Scott R. Evans, Koko Asakura, Yuko Ohno, Group-sequential three-arm noninferiority clinical trial designs, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2016.1148710, 27, 1, (1-24), (2016).
- Toshimitsu Hamasaki, Koko Asakura, Scott R. Evans, Toshimitsu Ochiai, Toshimitsu Hamasaki, Koko Asakura, Scott R. Evans, Toshimitsu Ochiai, Group-Sequential Three-Arm Non-inferiority Clinical Trials, Group-Sequential Clinical Trials with Multiple Co-Objectives, 10.1007/978-4-431-55900-9_6, (81-95), (2016).
- Ming Zhou, Sudeep Kundu, Some practical considerations in three‐arm non‐inferiority trial design, Pharmaceutical Statistics, 10.1002/pst.1779, 15, 6, (550-559), (2016).
- Hezhi Lu, Hua Jin, Weixiong Zeng, A more efficient three-arm non-inferiority test based on pooled estimators of the homogeneous variance, Statistical Methods in Medical Research, 10.1177/0962280216681036, (096228021668103), (2016).
- Huang Li-Ching, Wen Miin-Jye, Cheung Siu Hung, Kwong Koon Shing, Noninferiority studies with multiple reference treatments, Statistical Methods in Medical Research, 10.1177/0962280215576017, 26, 3, (1295-1307), (2015).
- Tobias Mütze, Axel Munk, Tim Friede, Design and analysis of three‐arm trials with negative binomially distributed endpoints, Statistics in Medicine, 10.1002/sim.6738, 35, 4, (505-521), (2015).
- David A Kim, Alison R Hwong, Derek Stafford, D Alex Hughes, A James O'Malley, James H Fowler, Nicholas A Christakis, Social network targeting to maximise population behaviour change: a cluster randomised controlled trial, The Lancet, 10.1016/S0140-6736(15)60095-2, 386, 9989, (145-153), (2015).
- Ludwig Hothorn, References, Statistics in Toxicology Using R, 10.1201/b19659-12, (209-232), (2015).
- Mario Hasler, Heteroscedasticity: multiple degrees of freedom vs. sandwich estimation, Statistical Papers, 10.1007/s00362-014-0640-4, 57, 1, (55-68), (2014).
- Li-Ching Huang, Miin-Jye Wen, Siu Hung Cheung, Noninferiority Studies with Multiple New Treatments and Heterogeneous Variances, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2014.920346, 25, 5, (958-971), (2014).
- Nian-Sheng Tang, Bin Yu, Man-Lai Tang, Testing non-inferiority of a new treatment in three-arm clinical trials with binary endpoints, BMC Medical Research Methodology, 10.1186/1471-2288-14-134, 14, 1, (2014).
- Karola Kombrink, Axel Munk, Tim Friede, Design and semiparametric analysis of non‐inferiority trials with active and placebo control for censored time‐to‐event data, Statistics in Medicine, 10.1002/sim.5769, 32, 18, (3055-3066), (2013).
- Patrick Schlömer, Werner Brannath, Group sequential designs for three‐arm ‘gold standard’ non‐inferiority trials with fixed margin, Statistics in Medicine, 10.1002/sim.5950, 32, 28, (4875-4889), (2013).
- Eisuke Hida, Toshiro Tango, Three-Arm Noninferiority Trials with a Prespecified Margin for Inference of the Difference in the Proportions of Binary Endpoints, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2013.789893, 23, 4, (774-789), (2013).
- M Amper Gamalo, Rui Wu, Ram C Tiwari, Bayesian approach to non-inferiority trials for normal means, Statistical Methods in Medical Research, 10.1177/0962280212448723, 25, 1, (221-240), (2012).
- Kathrin Stucke, Meinhard Kieser, A general approach for sample size calculation for the three‐arm ‘gold standard’ non‐inferiority design, Statistics in Medicine, 10.1002/sim.5461, 31, 28, (3579-3596), (2012).
- Mario Hasler, Multiple comparisons to both a negative and a positive control, Pharmaceutical Statistics, 10.1002/pst.503, 11, 1, (74-81), (2012).
- Nicolas Simonis, Jean-François Rual, Irma Lemmens, Mathieu Boxus, Tomoko Hirozane-Kishikawa, Jean-Stéphane Gatot, Amélie Dricot, Tong Hao, Didier Vertommen, Sébastien Legros, Sarah Daakour, Niels Klitgord, Maud Martin, Jean-François Willaert, Franck Dequiedt, Vincent Navratil, Michael E Cusick, Arsène Burny, Carine Van Lint, David E Hill, Jan Tavernier, Richard Kettmann, Marc Vidal, Jean-Claude Twizere, Host-pathogen interactome mapping for HTLV-1 and -2 retroviruses, Retrovirology, 10.1186/1742-4690-9-26, 9, 1, (26), (2012).
- Daniel F. Jimenez, Peter A. Heuch, Crawford W. Revie, George Gettinby, Confidence in assessing the effectiveness of bath treatments for the control of sea lice on Norwegian salmon farms, Aquaculture, 10.1016/j.aquaculture.2012.03.029, 344-349, (58-65), (2012).
- Mark A Gamalo, Saman Muthukumarana, Pulak Ghosh, Ram C Tiwari, A generalized p -value approach for assessing noninferiority in a three-arm trial , Statistical Methods in Medical Research, 10.1177/0962280210395739, 22, 3, (261-277), (2011).
- Pulak Ghosh, Farouk Nathoo,, Mithat Gönen, Ram C. Tiwari, Assessing noninferiority in a three‐arm trial using the Bayesian approach, Statistics in Medicine, 10.1002/sim.4244, 30, 15, (1795-1808), (2011).
- Mark A. Gamalo, Ram C. Tiwari, Testing Noninferiority Through Generalized p -values , Statistics in Biopharmaceutical Research, 10.1198/sbr.2010.09028, 3, 1, (87-96), (2011).
- Ivan Chan, Three-Arm Non-Inferiority Trials, Design and Analysis of Non-Inferiority Trials, 10.1201/b11039-7, (149-165), (2011).
- Eisuke Hida, Toshiro Tango, On the three‐arm non‐inferiority trial including a placebo with a prespecified margin, Statistics in Medicine, 10.1002/sim.4099, 30, 3, (224-231), (2010).
- Ludwig A. Hothorn, Gemechis D. Djira, A ratio‐to‐control Williams‐type test for trend, Pharmaceutical Statistics, 10.1002/pst.464, 10, 4, (289-292), (2010).
- Ullrich Munzel, Nonparametric non‐inferiority analyses in the three‐arm design with active control and placebo, Statistics in Medicine, 10.1002/sim.3727, 28, 29, (3643-3656), (2009).
