Multiple testing to establish superiority/equivalence of a new treatment compared with k standard treatments for unbalanced designs.
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.
Kwong
Koon Shing
KS
Department of Statistics and Applied Probability, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. stakks@nus.edu.sg
Cheung
Siu Hung
SH
Chan
Wai Sum
WS
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*
D000700:Analgesics