Multiple testing to establish superiority/equivalence of a new treatment compared with k standard treatments for unbalanced designs |
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Authors: | Kwong Koon Shing Cheung Siu Hung Chan Wai Sum |
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Affiliation: | Department of Statistics and Applied Probability, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. stakks@nus.edu.sg |
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Abstract: | In clinical studies, multiple superiority/equivalence testing procedures can be applied to classify a new treatment as superior, equivalent (same therapeutic effect), or inferior to each set of standard treatments. Previous stepwise approaches (Dunnett and Tamhane, 1997, Statistics in Medicine16, 2489-2506; Kwong, 2001, Journal of Statistical Planning and Inference 97, 359-366) are only appropriate for balanced designs. Unfortunately, the construction of similar tests for unbalanced designs is far more complex, with two major difficulties: (i) the ordering of test statistics for superiority may not be the same as the ordering of test statistics for equivalence; and (ii) the correlation structure of the test statistics is not equi-correlated but product-correlated. In this article, we seek to develop a two-stage testing procedure for unbalanced designs, which are very popular in clinical experiments. This procedure is a combination of step-up and single-step testing procedures, while the familywise error rate is proved to be controlled at a designated level. Furthermore, a simulation study is conducted to compare the average powers of the proposed procedure to those of the single-step procedure. In addition, a clinical example is provided to illustrate the application of the new procedure. |
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Keywords: | Coherence property Equivalent efficacy Familywise error rate Multivariate t-distribution |
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