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

ABSTRACT

We propose a new nonparametric method for
assessing non-inferiority of an experimental therapy compared to a standard of
care. The ratio *μ*_{E}/*μ*_{R} 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 *m*_{E}/*m*_{R} of the sample medians as a point estimate of the ratio*μ*_{E}/*μ*_{R}. 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 *μ*_{E}/*μ*_{R} 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
ratio*μ*_{E}/*μ*_{R}. 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.

Cite this paper

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.

K. Koti, "New Tests for Assessing Non-Inferiority and Equivalence from Survival Data,"

References

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[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

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[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. http://ftp.sas.com/techsup/download/stat/jackboot.htm/

[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.

[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. http://ftp.sas.com/techsup/download/stat/jackboot.htm/

[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.