Background When the efficacy of a treatment in a randomized controlled trial is required for multiple primary endpoints, trial design and analysis differ from trial requiring efficacy in only one of the multiple endpoints.
Methods We consider a two-arm clinical trial requiring efficacy analysis for multiple primary endpoints, formulating the appropriate null and alternative hypotheses for the test of treatment efficacy. We study the significance level/statistical power of an intersection-union test (IUT) in this situation. We compare IUT with the intuitive approach (selecting the maximum sample size over those obtained from testing individual primary endpoints one by one) for determination of sample size.
Results The proposed IUT reserves the same Type I error rate as shared by all endpoint-specific tests. The statistical power of the proposed IUT is no more than the minimum from the individual tests. The maximum sample size from multiple endpoint-specific tests is often inadequate for the test of treatment efficacy, especially when the standardized effect sizes are similar. Finally, the IUT can be applied to Alzheimer's disease treatment trials in which two primary endpoints are typically used.
Conclusions The IUT is a valid method for use in the design and analysis of clinical trials requiring efficacy at multiple primary endpoints.
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References
1.
1. Pocock SJ. Clinical trials with multiple outcomes: a statistical perspective on their design, analysis, and interpretation. Control Clin Trial1997; 18: 530–545.
2.
2. Gong J, Pinheiro JC, DeMets DL. Estimating significance level and power comparisons for testing multiple endpoints in clinical trials. Control Clin Trial2000; 21: 313–329.
3.
3. McMahon RP, Harrell FR. Power calculation for clinical trials when the outcome is a composite ranking of survival and a nonfatal outcome. Control Clin Trial2000; 21: 305–312.
4.
4. O'Brien PC. Procedures for comparing samples with multiple endpoints. Biometrics1984; 40: 1079–1087.
5.
5. Pocock SJ, Geller NL, Tsiatis AA. The analysis of multiple endpoints in clinical trials. Biometrics1987; 43: 487–498.
6.
6. Gent M. Some issues in the comparison and use of clusters of outcome events. Control Clin Trial1997; 18: 546–549.
7.
7. Prentice RL. On the role and analysis of secondary outcomes in clinical trials. Control Clin Trial1997; 18: 561–567.
8.
8. Lehmann EL. Testing multiparameter hypotheses. Ann Math Statist1952; 23: 541–552.
9.
9. Gleser LJ. On a theory of intersection-union tests. Inst Math Stat Bull1973; 2: 233-233 (abstract).
11. Cohen A, Gatsonis C, Marden JI. Hypothesis testing for marginal probabilities in a 2 × 2 × 2 contingency table with conditional independence. J Am Statist Assoc1983; 78: 920–929.
12.
12. Berger RL. Likelihood ratio tests and intersection-union tests. In Panchapakesan S, Balakrishnan N eds. Advances in statistical decision theory and applications. Boston: Birkhauser, 1997; 225–237.
13.
13. Berger RL, Sinclair DF. Testing hypotheses concerning unions of linear subspaces. J Am Statist Assoc1984; 79: 158–163.
14.
14. Berger RL. Uniformly more powerful tests for hypotheses concerning linear inequalities and normal means. J Am Statist Assoc1989; 84: 192–199.
15.
15. Liu H, Berger RL. Uniformly more powerful, one-sided tests for hypotheses about linear inequalities. Ann Statist1995; 23: 55–72.
16.
16. Saikali KG. Uniformly more powerful tests for linear inequalities. PhD Dissertation, North Carolina State University, Raleigh, NC, 1996.
17.
17. Genz A. Numerical computation of multivariate normal probabilities. J Comput Graphical Statist1992; 1: 141–149.
18.
18. MathSoft. S-Plus 6.0 guide to statistics, Vol 1. Seattle, WA: MathSoft Data Analysis Division, 2000.
19.
19. SAS Institute, Inc.SAS language (Version 8). Cary, NC: SAS Institute, Inc., 1999.
20.
20. Rogers SL, Farlow MR, Doody RS, Mohs R, Friedhoff LT, and the Donepezil Study Group. A 24-week, double-blind, placebo-controlled trial of donepezil in patients with Alzheimer's disease. Neurology1998; 50: 136–145.
21.
21. Farlow M, Anand R, Messina J Jr, Hartman R, Veach J. A 52-week study of the efficacy of Rivastigmine in patients with mild to moderately severe Alzheimer's disease. Eur Neurol2000; 44: 236–241.
22.
22. Tariot PN, Soloman PR, Morris JC, Kershaw P, Lilienfeld S, Ding C, and the Galantamine USA-10 Study Group. A 5-month, randomized, placebo-controlled trial of galantamine in AD. Neurology2000; 54: 2269–2276.
23.
23. Rosen W, Mohs R. A new rating scale for Alzheimer's Disease. Am J Psychiatry1984; 141, 1356–1364.
24.
24. Schneider LS, Olin JT. Clinical global impressions in Alzheimer's clinical trials. Int Psychogeriatr1996; 8: 277–288.
25.
25. Little RJA, Rubin DB. Statistical analysis with missing data. New York: John Wiley, 1987.
