New Tests for Assessing Non-Inferiority and Equivalence from Survival Data

DOI: 10.4236/ojs.2013.32008   PDF   HTML   XML   4,317 Downloads   7,398 Views   Citations


We propose a new nonparametric method for assessing non-inferiority of an experimental therapy compared to a standard of care. The ratio μE/μR of true median survival times is the parameter of interest. This is of considerable interest in clinical trials of generic drugs. We think of the ratio mE/mR of the sample medians as a point estimate of the ratioμE/μR. We use the Fieller-Hinkley distribution of the ratio of two normally distributed random variables to derive an unbiased level-α test of inferiority null hypothesis, which is stated in terms of the ratio μE/μR and a pre-specified fixed non-inferiority margin δ. We also explain how to assess equivalence and non-inferiority using bootstrap equivalent confidence intervals on the ratioμE/μR. The proposed new test does not require the censoring distributions for the two arms to be equal and it does not require the hazard rates to be proportional. If the proportional hazards assumption holds good, the proposed new test is more attractive. We also discuss sample size determination. We claim that our test procedure is simple and attains adequate power for moderate sample sizes. We extend the proposed test procedure to stratified analysis. We propose a “two one-sided tests” approach for assessing equivalence.

Share and Cite:

K. Koti, "New Tests for Assessing Non-Inferiority and Equivalence from Survival Data," Open Journal of Statistics, Vol. 3 No. 2, 2013, pp. 55-64. doi: 10.4236/ojs.2013.32008.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] “E-10: Guidance on Choice of Control Group in Clinical Trials,” International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH), Vol. 64, No. 185, 2000, pp. 51767-51780.
[2] R. B. D’Agostino, J. M. Massaro and L. M. Sullivan, “Non-Inferiority Trials: Design Concepts and Issues— The Encounters of Academic Consultants in Statistics,” Statistics in Medicine, Vol. 22, No. 2, 2003, pp. 169-186. doi:10.1002/sim.1425
[3] G. G. Koch, “Non-Inferiority in Confirmatory Active Control Clinical Trials: Concepts and Statistical Methods,” American Statistical Association: FDA/Industry Workshop, Washington, D.C., 2004.
[4] S. Wellek, “Testing Statistical Hypothesis of Equivalence,” CHAPMAN & HALL/CRC, New York, 2003.
[5] B. Efron, “Censored Data and the Bootstrap,” Journal of the American Statistical Association, Vol. 76, No. 374, 1981, pp. 312-319. doi:10.1080/01621459.1981.10477650
[6] R. Simon, “Confidence Intervals for Reporting Results of Clinical Trials,” Annals of Internal Medicine, Vol. 105, No. 3, 1986, pp. 429-435.
[7] L. Rubinstein, M. Gail and T. Santner, “Planning the Duration of a Comparative Clinical Trial with Loss to Follow-Up and a Period of Continued Observation,” Journal of Chronic Disease, Vol. 34, No. 9-10, 1981, pp. 469-479. doi:10.1016/0021-9681(81)90007-2
[8] D. R. Bristol, “Planning Survival Studies to Compare a Treatment to an Active Control,” Journal of Biopharma ceutical Statistics, Vol. 3, No. 2, 1993, pp. 153-158. doi:10.1080/10543409308835056
[9] R. L. Berger and J. C. Hsu, “Bioequivalence Trials, Inter section-Union Tests and Equivalence Confidence Sets,” Statistical Science, Vol. 11, No. 4, 1996, pp. 283-319. doi:10.1214/ss/1032280304
[10] D. Hauschke and L. A. Hothorn, “Letter to the Editor,” Statistics in Medicine, Vol. 26, No. 1, 2007, pp. 230-236. doi:10.1002/sim.2665
[11] SAS Institute Inc., “SAS/STAT User’s Guide,” Version 8, Cary, 2000.
[12] R. Brookmeyer and J. Crowley, “A Confidence Interval for the Median Survival Time,” Biometrics, Vol. 38, No. 1, 1982, pp. 29-41. doi:10.2307/2530286
[13] D. Collett, “Modeling Survival Data in Medical Research,” 1st Edition, Chapman & Hall, London, 1994.
[14] N. Reid, “Estimating the Median Survival Time,” Bio metrika, Vol. 68, No. 3, 1981, pp. 601-608. doi:10.1093/biomet/68.3.601
[15] G. J. Babu, “A Note on Bootstrapping the Variance of Sample Quantiles,” Annals of the Institute of Statistical Mathematics, Vol. 38, 1985, pp. 439-443. doi:10.1007/BF02482530
[16] The University of Texas at Austin, “Setting and Resam pling in SAS,” 1996.
[17] K. M. Keaney and L. J. Wei, “Interim Analyses Based on Median Survival Times,” Biometrika, Vol. 81, No. 2, 1994, pp. 279-286. doi:10.1093/biomet/81.2.279
[18] E. C. Fieller, “The Distribution of the Index in a Normal Bivariate Population,” Biometrika, Vol. 24, No. 3-4, 1932, pp. 428-440. doi:10.1093/biomet/24.3-4.428
[19] D. V. Hinkley, “On the Ratio of Two Correlated Normal Variables,” Biometrika, Vol. 56, No. 3, 1969, pp. 635-639. doi:10.1093/biomet/56.3.635
[20] K. M. Koti, “Use of the Fieller-Hinkley Distribution of the Ratio of Random Variables in Testing for Non-Inferiority and Equivalence,” Journal of Biopharmaceutical Statistics, Vol. 17, No. 2, 2007, pp. 215-228. doi:10.1080/10543400601177335
[21] K. M. Koti, “New Tests for Null Hypothesis of Non Unity Ratio of Proportions,” Journal of Biopharmaceuti cal Statistics, Vol. 17, No. 2, 2007, pp. 229-245. doi:10.1080/10543400601177426
[22] B. Efron and R. J. Tibshirani, “An Introduction to the Bootstrap,” Chapman & Hall, New York, 1993.
[23] M. E. Stokes, C. S. Davis and G. G. Koch, “Categorical Data Analysis Using the SAS System,” SAS Institute Inc., Cary, 1995.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.