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Research Article

Reverse graphical approaches for multiple test procedures

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Pages 90-110 | Received 16 Jan 2021, Accepted 17 Jan 2023, Published online: 09 Feb 2023

References

  • Benjamini, Y., and Y. Hochberg. 1997. Multiple hypotheses testing with weights. Scandinavian Journal of Statistics 24 (3):407–418. doi:10.1111/1467-9469.00072.
  • Brannath, W., and F. Bretz. 2010. Shortcuts for locally consonant closed test procedures. Journal of the American Statistical Association 105 (490):660–669. doi:10.1198/jasa.2010.tm08127.
  • Bretz, F., W. Maurer, W. Brannath, and M. Posch. 2009. A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine 28 (4):586–604. doi:10.1002/sim.3495.
  • Bretz, F., M. Posch, E. Glimm, F. Klinglmueller, W. Maurer, and K. Rohmeyer. 2011. Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal 53 (6):894–913. doi:10.1002/bimj.201000239.
  • Burman, C. -F., C. Sonesson, and O. Guilbaud. 2009. A recycling framework for the construction of Bonferroni-based multiple tests. Statistics in Medicine 28 (5):739–761. doi:10.1002/sim.3513.
  • Gabriel, K. R. 1969. Simultaneous test procedures–some theory of multiple comparisons. Annals of Mathematical Statistics 40 (1):224–250. doi:10.1214/aoms/1177697819.
  • Genz, A., and F. Bretz. 2009. Computation of multivariate normal and t probabilities. Heidelberg: Springer-Verlag.
  • Gou, J. 2022. Sample size optimization and initial allocation of the significance levels in group sequential trials with multiple endpoints. Biometrical Journal 64 (2):301–311. doi:10.1002/bimj.202000081.
  • Gou, J. 2023a. On dependence assumption in p-value based multiple test procedures. Journal of Biopharmaceutical Statistics 1–15. doi:10.1080/10543406.2022.2162066.
  • Gou, J. 2023b. A test of the dependence assumption for the Simes-test-based multiple test procedures. Manuscript submitted.
  • Gou, J. 2023c. Trigger strategy in repeated tests on multiple hypotheses. Statistics in Biopharmaceutical Research 15 (1):133-140 doi:10.1080/19466315.2021.1947361.
  • Gou, J., and A. C. Tamhane. 2018. Hochberg procedure under negative dependence. Statistica Sinica 28:339–362. doi:10.5705/ss.202016.0306.
  • Gou, J., A. C. Tamhane, D. Xi, and D. Rom. 2014. A class of improved hybrid Hochberg- Hommel type step-up multiple test procedures. Biometrika 101 (4):899–911. doi:10.1093/biomet/asu032.
  • Gou, J., and D. Xi. 2019. Hierarchical testing of a primary and a secondary endpoint in a group sequential design with different information times. Statistics in Biopharmaceutical Research 11 (4):398–406. doi:10.1080/19466315.2018.1546613.
  • Hochberg, Y. 1988. A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75 (4):800–802. doi:10.1093/biomet/75.4.800.
  • Hochberg, Y., and D. M. Rom. 1995. Extensions of multiple testing procedures based on Simes’ test. Journal of Statistical Planning and Inference 48 (2):141–152. doi:10.1016/0378-3758(95)00005-T.
  • Hochberg, Y., and A. C. Tamhane. 1987. Multiple comparison procedures. New York, New York: John Wiley and Sons.
  • Holm, S. 1979. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6:65–70.
  • Hommel, G. 1988. A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika 75 (2):383–386. doi:10.1093/biomet/75.2.383.
  • Krum, H., B. Massie, W. T. Abraham, K. Dickstein, L. Kober, J. J. McMurray, A. Desai, C. Gimpelewicz, A. Kandra, B. Reimund, et al. 2011. and on behalf of the ATMOSPHERE investigators. European Journal of Heart Failure 13 (1):107–114. doi:10.1093/eurjhf/hfq212.
  • Marcus, R., E. Peritz, and K. R. Gabriel. 1976. On closed testing procedures with special reference to ordered analysis of variance. Biometrika 63 (3):655–660. doi:10.1093/biomet/63.3.655.
  • Maurer, W., and F. Bretz. 2013. Multiple testing in group sequential trials using graphical approaches. Statistics in Biopharmaceutical Research 5 (4):311–320. doi:10.1080/19466315.2013.807748.
  • Maurer, W., and F. Bretz. 2014. A note on testing families of hypotheses using graphical procedures. Statistics in Medicine 33 (30):5340–5346. doi:10.1002/sim.6267.
  • Maurer, W., E. Glimm, and F. Bretz. 2011. Multiple and repeated testing of primary, coprimary, and secondary hypotheses. Statistics in Biopharmaceutical Research 3 (2):336–352. doi:10.1198/sbr.2010.10010.
  • Proschan, M. A., and E. H. Brittain. 2020. A primer on strong vs weak control of familywise error rate. Statistics in Medicine 39 (9):1407–1413. doi:10.1002/sim.8463.
  • Robertson, D. S., J. M. S. Wason, and F. Bretz. 2020. Graphical approaches for the control of generalized error rates. Statistics in Medicine 39 (23):3135–3155. doi:10.1002/sim.8595.
  • Samuel-Cahn, E. 1996. Is the Simes improved Bonferroni procedure conservative? Biometrika 83 (4):928–933. doi:10.1093/biomet/83.4.928.
  • Sarkar, S. K. 1998. Some probability inequalities for ordered $\rm MTP\sb 2$ random variables: A proof of the Simes conjecture. Annals of Statistics 26 (2):494–504. doi:10.1214/aos/1028144846.
  • Sarkar, S. K., and C. K. Chang. 1997. The Simes method for multiple hypothesis testing with positively dependent test statistics. Journal of the American Statistical Asociation 92 (440):1601–1608. doi:10.1080/01621459.1997.10473682.
  • Simes, R. J. 1986. An improved Bonferroni procedure for multiple tests of significance. Biometrika 73 (3):751–754. doi:10.1093/biomet/73.3.751.
  • Sugitani, T., F. Bretz, and W. Maurer. 2016. A simple and flexible graphical approach for adaptive group-sequential clinical trials. Journal of Biopharmaceutical Statistics 26 (2):202–216. doi:10.1080/10543406.2014.972509.
  • Sugitani, T., and T. Morikawa. 2017. Gatekeeping strategies and graphical approaches in clinical trials with hierarchically structured study objectives: A review. Japanese Journal of Biometrics 38 (1):41–78. doi:10.5691/jjb.38.41.
  • Tamhane, A. C., and J. Gou. 2018. Advances in p-value based multiple test procedures. Journal of Biopharmaceutical Statistics 28 (1):10–27. doi:10.1080/10543406.2017.1378666.
  • Tamhane, A. C., and J. Gou. 2022. Multiple test procedures based on p-values. In Handbook of multiple comparisons, ed. X. Cui, T. Dickhaus, Y. Ding, and J. C. Hsu, pp. 11–34. New York: Chapman and Hall/CRC.
  • Tamhane, A. C., J. Gou, C. Jennison, C. R. Mehta, and T. Curto. 2018. A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks. Biometrics 74 (1):40–48. doi:10.1111/biom.12732.
  • Tamhane, A. C., and L. Liu. 2008. On weighted Hochberg procedures. Biometrika 95 (2):279–294. doi:10.1093/biomet/asn018.
  • Tamhane, A. C., D. Xi, and J. Gou. 2021. Group sequential Holm and Hochberg procedures. Statistics in Medicine 40 (24):5333–5350. doi:10.1002/sim.9128.
  • Wright, S. P. 1992. Adjusted p-values for simultaneous inference. Biometrics 48 (4):1005–1013. doi:10.2307/2532694.
  • Xi, D., and F. Bretz. 2019. Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine 38 (27):5268–5282. doi:10.1002/sim.8375.
  • Xi, D., and F. Bretz. 2022. Graphical approaches for multiple comparison procedures. In Handbook of multiple comparisons, ed. X. Cui, T. Dickhaus, Y. Ding, and J. C. Hsu, pp. 91–119. New York: Chapman and Hall/CRC.
  • Xi, D., and A. C. Tamhane. 2015. Allocating recycled significance levels in group sequential procedures for multiple endpoints. Biometrical Journal 57 (1):90–107. doi:10.1002/bimj.201300157.
  • Ye, Y., A. Li, L. Liu, and B. Yao. 2013. A group sequential Holm procedure with multiple primary endpoints. Statistics in Medicine 32 (7):1112–1124. doi:10.1002/sim.5700.

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