Unconditional Exact Tests for Dichotomous Data in the Comparison of Two Treatments with One Control Group
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Seung-Ho Kang, PhD Department of Applied Statistics. Yonsei Universitv. Seoul, Korea
Key Words Dunnett‘s test; Multiple comparison; Exact power; 2 x 3 contingency table; Hochberg procedure Correspondence Address Seung-Ho Kang, PhD, Department of Applied Statistics, Yonsei University, 134, Sinchon-Dong. SeoDaeMun-Gu. Seoul, Korea, 120-749 (ernail: [email protected]).
Unconditional Exact Tests for Dichotomous Data in the Comparison of Two Treatments With One Control Group
INTRODUCTION In clinical drug trials, it is often of interest to conduct a parallel placebo-controlled study with multiple doses of a test drug. The primary objective of such a trial is to demonstrate that one or more doses of the drug are effective. In this article we are mainly concerned with the comparison of two treatments with one control group for dichotomous data. The real example that motivated this study is provided in Kang and Choi (1).Dunnett’s test based on the large sample theory might be employed for such comparisons to control the familywise type I error rate under the nominal level. However, Dunnett’s test for binary data based on the large sample theory might be unreliable in small samples (2).When asymptotic tests are not reliable, exact tests have been used as alternatives, because the exact tests guarantee that the type I errors are controlled under the nominal level. Recently Kang and Choi (1) compared the two-step closed Fisher’s exact test, the conditional Dunnett test, and the new conditional exact test in terms of the unconditional exact power. The conditional exact tests have two kinds of power, the conditional exact power PHl(reject H,IS) and the unconditional exact power pH1 (reject H,) where S is a suffcient statistic for unknown nuisance parameters. Kang and Choi (1) thought that the unconditional exact power was
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In this article 1 discuss four procedures that compare each of two treatments against the control for dichotomous data while maintaining the familywtse type I error rate at a level a The four procedures are two unconditional exact tests, the Hochberg procedure, and the Bonferroni procedure, and they are compared in terms of exact powm After that, the numerical results of this article are also compared with those of Kang and Choi (Drug Information Journal 2008; 42:337-347). The best procedures are recommended depending on the values of the parameters under the alternative hypothesis.
a more appropriate criterion to compare the above three conditional exact tests. Since there is only one unknown nuisance parameter (denoted by p in the next section) in the comparison of two treatments with one control group for binary data under the null hypothesis, the unconditional exact tests are also feasible (3). This raises the question of which exact test produces greater power. In small samples the unconditional exact test is known to be more powerful than the conditional exact test for testing the homogeneity of two binomial proportions (4-6). Which exact test has greater power depends on which exact test is
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