Multiple Testing to Establish Noninferiority of k Treatments with a Reference Based on the Ratio of Two Means
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MULTIPLE TESTING TO ESTABLISH NONINFERIORITY OF k TREATMENTS WITH A REFERENCE BASED ON THE RATIO OF TWO MEANS DIETER HAUSCHKE, PHD Department of Biometry, Byk Gulden Pharmaceuticals, Konstanz, Germany
MEINHARD KIESER, PHD Department of Biometry, Dr. Willmar Schwabe Pharmaceuticals, Karlsruhe, Germany
It is the aim of most active control trials to show that the treatment(s)under investigation is (are) not inferior to the reference by more than a prespecifed clinically irrelevant amount. In the situation of a multiarmed trial with more than one test treatment it may be required that noninferiority of all these groups to the reference be demonstrated. Alternatively, it may by suflcient to prove noninferiority of at least one of the test treatments to the reference. These clinical questions correspond to the concepts of global and partial noninferiority. For both scenarios test procedures are given f o r the situation that the noninferiority margin is expressed as a proportion of the unknown reference mean. Key Words: Noninferioritytrial; Therapeutic equivalence; Multiple comparison procedure; Intersection-union principle; Union-intersection principle
INTRODUCTION DUE TO PROGRESS in medical research, there has been an increase in attention to studies with an active control. Unlike placebo-controlled trials, these studies are designed to show that the treatment(s) under investigation is (are) not inferior to the established reference drug by more than a predefined quantity judged to be acceptable. Such so-called therapeutic equivalence trials exhibit a number of design features that are different than those of superiority trials (see, eg, [1,2,3] and references given there). If
Reprint address: Dr. Dieter Hauschke, Department of Biometry, Byk Gulden Pharmaceuticals, P.O. Box 10 03 10, 78403 Konstanz, Germany. E-mail: dieter. hauschke @ byk.de.
more than one treatment is compared with the active control, a further methodological challenge arises from the corresponding multiplicity of hypothesis testing. In this paper, we provide a solution to this problem for the situation of normally distributed random variables with the closeness between the test and reference treatments expressed as a fraction of the population mean for the reference. This formulation addresses the question, “Is at least f percent of the effectiveness of the reference preserved by the investigated treatment?’ If we deal with log-normally distributed data, logarithmic transformation of the relating test problem leads to an acceptance range formulated in terms of the difference of means, and standard methods can be used for noninferiority assessment. However, there are many situations in which the origi-
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Dieter Hauschke and Meinhard Kieser
nal (untransformed) observations of the primary variable follow a normal distribution. The purpose of this paper is to provide test procedures for esta
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