Quick Multiple Test Procedures and p-Value Adjustments

References

• Aickin, M., and Gensler, H. (1996), “Adjusting for Multiple Testing When Reporting Research Results: The Bonferroni vs Holm Methods,” American Journal of Public Health, 86, 726–728. DOI: 10.2105/ajph.86.5.726.
   PubMed Web of Science ®Google Scholar
• Andrew, A. (1979), “Another Efficient Algorithm for Convex Hulls in Two Dimensions,” Information Processing Letters, 9, 216–219. DOI: 10.1016/0020-0190(79)90072-3.
   Web of Science ®Google Scholar
• Bretz, F., Hothorn, T., and Westfall, P. (2010), Multiple Comparisons Using R, Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• 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. DOI: 10.1002/sim.3495.
   PubMed Web of Science ®Google Scholar
• Cai, G., and Sarkar, S. K. (2008), “Modified Simes’ Critical Values Under Independence,” Statistics & Probability Letters, 78, 1362–1368.
   Web of Science ®Google Scholar
• Dmitrienko, A., Tamhane, A. C., and Bretz, F. (2009), Multiple Testing Problems in Pharmaceutical Statistics, Boca Raton, FL: Taylor & Francis.
   Google Scholar
• Dunn, O. J. (1961), “Multiple Comparisons Among Means,” Journal of the American Statistical Association, 56, 52–64. DOI: 10.1080/01621459.1961.10482090.
   Web of Science ®Google Scholar
• Finner, H., and Roters, M. (1994), “On the Limit Behaviour of the Joint Distribution Function of Order Statistics,” Annals of the Institute of Statistical Mathematics, 46, 343–349. DOI: 10.1007/BF01720590.
   Web of Science ®Google Scholar
• Fortune, S. (1989), “Stable Maintenance of Point Set Triangulations in Two Dimensions,” in 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, eds. Y Benjamini, F. bretz, and S. Sarkar, Los Alamitos, CA: IEEE Computer Society, pp. 494–499.
   Google Scholar
• Gou, J., and Tamhane, A. C. (2014), “On Generalized Simes Critical Constants,” Biometrical Journal, 56, 1035–1054. DOI: 10.1002/bimj.201300258.
   PubMed Web of Science ®Google Scholar
• Gou, J., and Tamhane, A. C. (2018a), “A Flexible Choice of Critical Constants for the Improved Hybrid Hochberg-Hommel Procedure,” Sankhya B, 80, 85–97.
   Google Scholar
• Gou, J., and Tamhane, A. C. (2018b), “Hochberg Procedure Under Negative Dependence,” Statistica Sinica, 28, 339–362.
   Web of Science ®Google Scholar
• Gou, J., Tamhane, A. C., Xi, D., and Rom, D. M. (2014), “A Class of Improved Hybrid Hochberg–Hommel Type Step-Up Multiple Test Procedures,” Biometrika, 101, 899–911. DOI: 10.1093/biomet/asu032.
   Web of Science ®Google Scholar
• Gou, J., and Xi, D. (2019), “Hierarchical Testing of a Primary and a Secondary Endpoint in a Group Sequential Design With Different Information Times,” Statistics in Biopharmaceutical Research, 11, 398–406. DOI: 10.1080/19466315.2018.1546613.
   Web of Science ®Google Scholar
• Graham, R. (1972), “An Efficient Algorith for Determining the Convex Hull of a Finite Planar Set,” Information Processing Letters, 1, 132–133. DOI: 10.1016/0020-0190(72)90045-2.
   Google Scholar
• Guilbaud, O. (2014), “Sharper Confidence Intervals for Hochberg- and Hommel-Related Multiple Tests Based on an Extended Simes Inequality,” Statistics in Biopharmaceutical Research, 6, 123–136. DOI: 10.1080/19466315.2013.872999.
   Web of Science ®Google Scholar
• Hamasaki, T., Asakura, K., Evans, S. R., Sugimoto, T. and Sozu, T. (2015), “Group-Sequential Strategies in Clinical Trials With Multiple Co-Primary Outcomes,” Statistics in Biopharmaceutical Research, 7, 36–54. DOI: 10.1080/19466315.2014.1003090.
   PubMed Web of Science ®Google Scholar
• Hochberg, Y. (1988), “A Sharper Bonferroni Procedure for Multiple Tests of Significance,” Biometrika, 75, 800–802. DOI: 10.1093/biomet/75.4.800.
   Web of Science ®Google Scholar
• Hochberg, Y. and Tamhane, A. C. (1987), Multiple Comparison Procedures, New York: Wiley.
   Google Scholar
• Holm, S. (1979), “A Simple Sequentially Rejective Multiple Test Procedure,” Scandinavian Journal of Statistics, 6, 65–70.
   Web of Science ®Google Scholar
• Hommel, G. (1983), “Tests of the Overall Hypothesis for Arbitrary Dependence Structures,” Biometrical Journal, 25, 423–430. DOI: 10.1002/bimj.19830250502.
   Google Scholar
• Hommel, G. (1986), “Multiple Test Procedures for Arbitrary Dependence Structures,” Metrika, 33, 321–336.
   Google Scholar
• Hommel, G. (1988), “A Stagewise Rejective Multiple Test Procedure Based on a Modified Bonferroni Test,” Biometrika, 75, 383–386.
   Web of Science ®Google Scholar
• Hommel, G. (1989), “A Comparison of Two Modified Bonferroni Procedures,” Biometrika, 76, 624–625.
   Web of Science ®Google Scholar
• Horn, M. and Dunnett, C. W. (2004), “Power and Sample Size Comparisons of Stepwise FWE and FDR Controlling Test Procedures in the Normal Many-One Case,” in Recent Developments in Multiple Comparison Procedures (Vol. 47), Lecture Notes–Monograph Series, Beachwood, OH: Institute of Mathematical Statistics, pp. 48–64.
   Google Scholar
• Hsu, J. C. (1996), Multiple Comparisons – Theory and Methods, London: Chapman and Hall.
   Google Scholar
• Huang, Y., and Hsu, J. C. (2007), “Hochberg’s Step-Up Method: Cutting Corners Off Holm’s Step-Down Method,” Biometrika, 94, 965–975. DOI: 10.1093/biomet/asm067.
   Web of Science ®Google Scholar
• Huque, M. F., Dmitrienko, A., and D’Agostino, R. (2013), “Multiplicity Issues in Clinical Trials With Multiple Objectives,” Statistics in Biopharmaceutical Research, 5, 321–337. DOI: 10.1080/19466315.2013.807749.
   Web of Science ®Google Scholar
• Liu, W. (1996), “On Multiple Tests of a Non-Hierarchical Finite Family of Hypotheses,” Journal of the Royal Statistical Society, Series B, 58, 455–461. DOI: 10.1111/j.2517-6161.1996.tb02093.x.
   Google Scholar
• Marcus, R., Peritz, E., and Gabriel, K. R. (1976), “On Closed Testing Procedures With Special Reference to Ordered Analysis of Variance,” Biometrika, 63, 655–660. DOI: 10.1093/biomet/63.3.655.
   Web of Science ®Google Scholar
• Maurer, W., and Bretz, F. (2013), “Multiple Testing in Group Sequential Trials Using Graphical Approaches,” Statistics in Biopharmaceutical Research, 5, 311–320. DOI: 10.1080/19466315.2013.807748.
   Web of Science ®Google Scholar
• Meijer, R. J., Krebs, T. J. P., and Goeman, J. J. (2019), “Hommel’s Procedure in Linear Time,” Biometrical Journal, 61, 73–82. DOI: 10.1002/bimj.201700316.
   PubMed Web of Science ®Google Scholar
• Metcalfe, A., Green, D., Greenfield, T., Mansor, M., Smith, A., and Tuke, J. (2019), Statistics in Engineering: With Examples in MATLAB and R (2nd ed.), Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Newson, R. B. (2010), “Frequentist q-Values for Multiple-Test Procedures,” Stata Journal, 10, 568–584. DOI: 10.1177/1536867X1101000403.
   Web of Science ®Google Scholar
• Porter, K. E. (2018), “Statistical Power in Evaluations That Investigate Effects on Multiple Outcomes: A Guide for Researchers,” Journal of Research on Educational Effectiveness, 11, 267–295. DOI: 10.1080/19345747.2017.1342887.
   Web of Science ®Google Scholar
• Rom, D. M. (1990), “A Sequentially Rejective Test Procedure Based on a Modified Bonferroni Inequality,” Biometrika, 77, 663–665. DOI: 10.1093/biomet/77.3.663.
   Web of Science ®Google Scholar
• Rom, D. M. (2013), “An Improved Hochberg Procedure for Multiple Tests of Significance,” British Journal of Mathematical and Statistical Psychology, 66, 189–196.
   PubMed Web of Science ®Google Scholar
• Rosenthal, R., and Rubin, D. B. (1983), “Ensemble-Adjusted p Values,” Psychological Bulletin, 94, 540–541. DOI: 10.1037/0033-2909.94.3.540.
   Web of Science ®Google Scholar
• Samuel-Cahn, E. (1996), “Is the Simes Improved Bonferroni Procedure Conservative?” Biometrika, 83, 928–933. DOI: 10.1093/biomet/83.4.928.
   Web of Science ®Google Scholar
• Sarkar, S. K. (1998), “Some Probability Inequalities for Ordered MTP2 Random Variables: A Proof of the Simes Conjecture,” The Annals of Statistics, 494–504.
   Web of Science ®Google Scholar
• Sarkar, S. K., and Chang, C. K. (1997), “The Simes Method for Multiple Hypothesis Testing With Positively Dependent Test Statistics,” Journal of the American Statistical Asociation, 92, 1601–1608. DOI: 10.1080/01621459.1997.10473682.
   Web of Science ®Google Scholar
• Shaffer, J. P. (1995), “Multiple Hypothesis Testing,” Annual Review of Psychology, 46, 561–584. DOI: 10.1146/annurev.ps.46.020195.003021.
   Web of Science ®Google Scholar
• Simes, R. J. (1986), “An Improved Bonferroni Procedure for Multiple Tests of Significance,” Biometrika, 73, 751–754. DOI: 10.1093/biomet/73.3.751.
   Web of Science ®Google Scholar
• Tamhane, A. C., and Gou, J. (2018), “Advances in p-Value Based Multiple Test Procedures,” Journal of Biopharmaceutical Statistics, 28, 10–27. DOI: 10.1080/10543406.2017.1378666.
   PubMed Web of Science ®Google Scholar
• Tamhane, A. C., Gou, J., Jennison, C., Mehta, C. R. and Curto, T. (2018), “A Gatekeeping Procedure to Test a Primary and a Secondary Endpoint in a Group Sequential Design With Multiple Interim Looks,” Biometrics, 74, 40–48. DOI: 10.1111/biom.12732.
   PubMed Web of Science ®Google Scholar
• Tamhane, A. C., and Liu, L. (2008), “On Weighted Hochberg Procedures,” Biometrika, 95, 279–294. DOI: 10.1093/biomet/asn018.
   Web of Science ®Google Scholar
• Wang, B., and Cui, X. (2012), “A New Partition Testing Strategy for Multiple Endpoints,” Statistics in Medicine, 31, 2151–2168. DOI: 10.1002/sim.5366.
   PubMed Web of Science ®Google Scholar
• Westfall, P. H., Tobias, R. D., Rom, D. M., Wolfinger, R. D. and Hochberg, Y. (2011), Multiple Comparisons and Multiple Tests Using The SAS System, Cary, NC: SAS Institute.
   Google Scholar
• Wright, S. P. (1992), “Adjusted p-Values for Simultaneous Inference,” Biometrics, 48, 1005–1013. DOI: 10.2307/2532694.
   Web of Science ®Google Scholar
• Zhang, F., and Gou, J. (2016), “A p-Value Model for Theoretical Power Analysis and Its Applications in Multiple Testing Procedures,” BMC Medical Research Methodology, 16, 135. DOI: 10.1186/s12874-016-0233-0.
   PubMed Web of Science ®Google Scholar
• Zhang, F., and Gou, J. (2019), “Control of False Positive Rates in Clusterwise fMRI Inferences,” Journal of Applied Statistics, 46, 1956–1972.
   Web of Science ®Google Scholar