Multiplicity Testing Procedure Selection in Clinical Trials Rachael Wen Ph.D JSM 2018 of 8

Background Multiple endpoints Repeated measurements 2/22/2011 Multiple endpoints Repeated measurements Correlations between hypotheses Hypotheses: Inherent clinical importance order Varied treatment effect sizes Case Study: Hypotheses: Primary: H1 and H2 Secondary: H3 and H4 Considerations: Clinical priority: H1>> H2 > H3> H4 Correlations: H1 and H2, H3 and H4 Individual marginal power: H3>>H2>(H1, H4) JSM 2018 of 8

Methods     Simes test Weighted Bonferroni test

Simulation Scenarios Graph 1 Graph 2 JSM2018 of 8

Simulation Results (Different MTPs) 2/22/2011

Simulation Results (How much power will gain?) 2/22/2011 Table: Power and power gain by alpha propagation in graphical approach Initial alpha Corr(H1,H2) H1 H2 H1* H2* (0.04, 0.01, 0, 0) -0.5 0.792 (2%) 0.833 (24.7%) 0.776 0.668 0.5 0.791 (1.9%) 0.799 (19.6%) (0.025, 0.025, 0, 0) 0.776 (8.8%) 0.843 (7.4%) 0.713 0.785 0.764 (7.2%) 0.831 (5.9%) (0.01, 0.04, 0, 0) 0.756 (29.9%) 0.852 (1.7%) 0.582 0.838 0.739 (27%) 0.851 (1.6%) Note: * power at initial assigned alpha level; Weighted closed parametric approach JSM 2018 of 8

Conclusions 2/22/2011 Hochberg and Hommel: reserved power, not flexible and Robust Graphical approach Attractive power, flexible and proper for complicate design with multiple endpoints with varied clinical importance and correlations Understandable and communicable to non-statistician Power gain extend depends on specific transition matrix, correlation between hypotheses, and marginal power of individual hypotheses ‘Optimal’ initial graph determined by exhaustive simulations JSM 2018 of 8

References: Bretz F., Mauer W., Brannath W., and Posch M., A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine (2009); 28: 586-604 Bretz F., Posch M., Glimm E., Klinglmueller F., Maurer W., and Rohmeyer K., Grphial approaches for multiple comparison procedures using Bonferroni, Simes, or parametric test. Biometrical Journal (2011); 6: 894-913 Hochberg, Y. A sharper Bonferroni procedure for multiple tests of significance. Biometrika (1988); 75: 800–803 Holm S. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics (1979); 6: 65–70. Hommel, G. A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika (1998); 75: 383–386. Lu. K, Graphical approaches using a Bonferroni mixture of weighted Simes test. Statistics in Medicine (2016); 35: 4041-4055 of 8 JSM2018