1. Multiplicity Testing Procedure Selection in Clinical Trials Rachael Wen Ph.D
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2. 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)
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3. Methods
Simes test
Weighted Bonferroni test

4. Simulation Scenarios
Graph 1
Graph 2
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5. Simulation Results (Different MTPs)
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6. 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
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7. 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
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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:
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:
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:
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