title: Multiple testing to establish superiority/equivalence of a new treatment compared with k standard treatments for unbalanced designs.
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.
authors.affiliation: Department of Statistics and Applied Probability, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. stakks@nus.edu.sg
authors.forename: Koon Shing
authors.initials: KS
authors.lastname: Kwong
authors.forename: Siu Hung
authors.initials: SH
authors.lastname: Cheung
authors.forename: Wai Sum
authors.initials: WS
authors.lastname: Chan
mesh_terms: D000700:Analgesics / Q000627:therapeutic use; D001699:Biometry; D003814:Dentistry, Operative; D006801:Humans; D015233:Models, Statistical; D010149:Postoperative Pain / Q000188:drug therapy; D013812:Therapeutics / Q000706:statistics & numerical data*
chemical_list: D000700:Analgesics