Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests

Biometrical Journal

Volumn 53, Issue 6, 2011, Pages 894-913

  Bretz, Frank ^a   Posch, Martin ^b   Glimm, Ekkehard ^a   Klinglmueller, Florian ^b   Maurer, Willi ^a   Rohmeyer, Kornelius ^c  

^a NOVARTIS PHARMA AG   (Switzerland)

^b MEDICAL UNIVERSITY OF VIENNA   (Austria)

^c LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Dunnett test; Gatekeeping procedure; Min p test; Non inferiority; Truncated Holm

Indexed keywords

DRUG DOSAGE;

DUNNETT TEST; GATEKEEPING; GATEKEEPING PROCEDURE; GRAPHICAL APPROACH; MIN-P TEST; MULTIPLE TEST; NON-INFERIORITY; PARAMETRIC TEST; TEST PROCEDURES; TRUNCATED HOLM;

STATISTICAL TESTS;

EID: 80755127019     PISSN: 03233847     EISSN: 15214036     Source Type: Journal    
DOI: 10.1002/bimj.201000239     Document Type: Article

References (49)

1. Alosh, M. and Huque, M. F. (2009). A flexible strategy for testing subgroups and overall population. Statistics in Medicine 28, 3-23.
2. Alosh, M. and Huque, M. F. (2010). A consistency-adjusted alpha-adaptive strategy for sequential testing. Statistics in Medicine 29, 1559-1571.
3. Bauer, P. (1991). Multiple testing in clinical trials. Statistics in Medicine 10, 871-890.
4. Bauer, P., Röhmel, J., Maurer, W. and Hothorn, L. (1998). Testing strategies in multi-dose experiments including active control. Statistics in Medicine 17, 2133-2146.
5. Benjamini, Y. and Heller, R. (2007). False discovery rates for spatial signals. Journal of the American Statistical Association 102, 1272-1281.
6. Benjamini, Y. and Hochberg, Y. (1997). Multiple hypothesis testing with weights. Scandinavian Journal of Statistics 24, 407-418.
7. Benjamini, Y. and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29, 1165-1188.
8. Brannath, W. and Bretz, F. (2010). Shortcuts for locally consonant closed test procedures. Journal of the American Statistical Association 105, 660-669.
9. Bretz, F., Maurer, W., Brannath, W. and Posch, M. (2009). A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine 28, 586-604.
10. Bretz, F., Maurer, W. and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical procedures. Statistics in Medicine 30, 1489-1501.
11. Burman, C. F., Sonesson, C. and Guilbaud, O. (2009). A recycling framework for the construction of Bonferroni-based multiple tests. Statistics in Medicine 28, 739-761.
12. Chen, X., Luo, X. and Capizzi, T. (2005). The application of enhanced parallel gatekeeping strategies. Statistics in Medicine 24, 1385-1397.
13. Dmitrienko, A., Offen, W., Wang, O. and Xiao, D. (2006). Gatekeeping procedures in dose-response clinical trials based on the Dunnett test. Pharmaceutical Statistics 5, 19-28.
14. Dmitrienko, A., Offen, W. W. and Westfall, P. H. (2003). Gatekeeping strategies for clinical trials that do not require all primary effects to be significant. Statistics in Medicine 22, 2387-2400.
15. Dmitrienko, A. and Tamhane, A. C. (2009). Gatekeeping procedures in clinical trials. In Multiple Testing Problems in Pharmaceutical Statistics, Dmitrienko, A., Tamhane, A. C. and Bretz, F. (Eds.). Chapman & Hall/CRC Biostatistics Series, Boca Raton.
16. Dmitrienko, A., Tamhane, A. and Wiens, B. (2008). General multi-stage gatekeeping procedures. Biometrical Journal 50, 667-677.
17. Genz, A. and Bretz, F. (2009). Computation of Multivariate Normal and t Probabilities. Springer, Heidelberg.
18. Guilbaud, O. (2008). Simultaneous confidence regions corresponding to Holm's stepdown procedure and other closed-testing procedures. Biometrical Journal 50, 678-692.
19. Guilbaud, O. (2009). Alternative confidence regions for Bonferroni-based closed-testing procedures that are not alpha-exhaustive. Biometrical Journal 51, 721-735.
20. Guilbaud, O. and Karlsson, P. (2011). Confidence regions for Bonferroni-based closed tests extended to more general closed tests. Journal of Biopharmaceutical Statistics 21, 682-707.
21. Hochberg, Y. and Tamhane, A. C. (1987). Multiple Comparison Procedures. Wiley, New York.
22. Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65-70.
23. Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika 75, 383-386.
24. Hommel, G., Bretz, F. and Maurer, W. (2007). Powerful short-cuts for multiple testing procedures with special reference to gatekeeping strategies. Statistics in Medicine 26, 4063-4073.
25. Hung, H. M. J. and Wang, S. J. (2009). Some controversial multiple testing problems in regulatory applications. Journal of Biopharmaceutical Statistics 19, 1-11.
26. Hung, H. M. J. and Wang, S. J. (2010). Challenges to multiple testing in clinical trials. Biometrical Journal 52, 747-756.
27. Huque, M. F. and Alosh, M. (2008). A flexible fixed-sequence testing method for hierarchically ordered correlated multiple endpoints in clinical trials. Journal of Statistical Planning and Inference 138, 321-335.
28. Huque, M. F., Alosh, M. and Bhore, R. (2011). Addressing multiplicity issues of a composite endpoint and its components in clinical trials. Journal of Biopharmaceutical Statistics 21, 610-634.
29. Ihaka, R. and Gentleman, R. (1996). R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics 5, 299-314.
30. Kling, Y. (2005). Issues of Multiple Hypothesis Testing in Statistical Process Control. Thesis, The Neiman Library of Exact Sciences & Engineering, Tel-Aviv University.
31. Lawrence, J. (2011). Testing non-inferiority and superiority for two endpoints for several treatments with a control. Pharmaceutical Statistics. DOI: 10.1002/pst.468.
32. Li, J. and Mehrotra, D. (2008). An efficient method for accommodating potentially underpowered primary endpoints. Statistics in Medicine 27, 5377-5391.
33. Liu, Y. and Hsu, J. (2009). Testing for efficacy in primary and secondary endpoints by partitioning decision paths. Journal of the American Statistical Association 104, 1661-1670.
34. Marcus, R., Peritz, E. and Gabriel, K. R. (1976). On closed testing procedure with special reference to ordered analysis of variance. Biometrika 63, 655-660.
35. Maurer, W., Glimm, E. and Bretz, F. (2011). Multiple and repeated testing of primary, co-primary and secondary hypotheses. Statistics in Biopharmaceutical Research 3, 336-352.
36. Maurer, W., Hothorn, L. and Lehmacher, W. (1995). Multiple comparisons in drug clinical trials and preclinical assays: a-priori ordered hypotheses. In: Biometrie in der Chemisch-Pharmazeutischen Industrie, Vollmar, J. (Ed.). Fischer Verlag, Stuttgart 3-18.
37. Millen, B. A. and Dmitrienko, A. (2011). Chain procedures: A class of flexible closed testing procedures with clinical trial applications. Statistics in Biopharmaceutical Research 3, 14-30.
38. O'Neill, R. T. (1997). Secondary endpoints cannot be validly analyzed if the primary endpoint does not demonstrate clear statistical significance. Controlled Clinical Trials 18, 550-556.
39. R Development Core Team. (2011). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
40. Rohmeyer, K. and Klinglmueller, F. (2011). gMCP: A graphical approach to sequentially rejective multiple test procedures. R package version 0.6-5.
41. Romano, J. R., Shaikh, A. and Wolf, M. (2011). Consonance and the closure method in multiple testing. The International Journal of Biostatistics 7, Article 12.
42. Sidak, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association 62, 626-633.
43. Simes, R. J. (1986). An improved Bonferroni procedure for multiple tests of significance. Biometrika 73, 751-754.
44. Strassburger, K. and Bretz, F. (2008). Compatible simultaneous lower confidence bounds for the Holm procedure and other Bonferroni based closed tests. Statistics in Medicine 27, 4914-4927.
45. Westfall, P. H. and Krishen, A. (2001). Optimally weighted, fixed sequence, and gatekeeping multiple testing procedures. Journal of Statistical Planning and Inference 99, 25-40.
46. Westfall, P. H., Krishen, A. and Young, S. S. (1998). Using prior information to allocate significance levels for multiple endpoints. Statistics in Medicine 17, 2107-2119.
47. Westfall, P. H., Young, S. S. (1993). Resampling-based Multiple Testing. Wiley, New York.
48. Wiens, B. L. (2003). A fixed sequence Bonferroni procedure for testing multiple endpoints. Pharmaceutical Statistics 2, 211-215.
49. Xu, H. Y., Nuamah, I., Liu, J. Y., Lim, P. and Sampson, A. (2009). A Dunnett-Bonferroni-based parallel gatekeeping procedure for dose-response clinical trials with multiple endpoints. Pharmaceutical Statistics 8, 301-316.