Choice of Delta: A Special Case
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0092-86 15/2001 Copyright 0 2001 Drug Information Association h c .
CHOICE OF DELTA: A SPECIAL CASE DIETERHAUSCHKE,PHD Department of Biometry, Byk Gulden Pharmaceuticals, Konstanz, Germany
From a scientific point of view the proof of efJicacy of a new investigational (test) treatment is persuasively established by demonstrating superiority to a concurrent placebo group in a randomized double-blind clinical trial. Howeve6 in the case where a standard treatment (reference) has already proved effective the comparison against placebo may be considered unethical and efJicacy can only be derived in a randomized active control study by showing noninferiority or equivalence. Inherent for these trials is the necessiry of an a priori specification of what constitutes an irrelevant difference. The purpose of this paper is to derive a methodology when this difference is defined as a fraction of the reference mean. Key Words: Noninferiority; Equivalence; Ratio of Means
INTRODUCTION
has been historically demonstrated that no placebo effect exists, a solution is provided IN THE INTERNATIONAL Conference on by defining the margins as a proportion of Harmonization (ICH) tripartite guideline the unknown reference mean. This paper adStatistical Principles for Clinical Trials (l), dresses the statistical methodology for testthe statistical analysis of active controlled ing noninferiority or equivalence, assuming trials is addressed. Obviously, the comparinormally distributed data, but the correson to placebo in a randomized double-blind sponding nonparametric methods can be eastrial provides the most convincing way to ily derived for continuous data following a demonstrateefficacy of the new test treatment. location family (2). Recently, Rohmel and However, if a widely accepted reference treatMansmann (3) and Munzel and Hauschke ment exists which has shown superiority in (unpublished data; 2000) derived related staformer placebo-controlledtrials, the investigatistical procedures for binomial and ordered tion of the new test treatment against placebo categorical data, respectively. cannot be regarded as feasible. Hence, active control studies are performed and the efficacy of the test treatment is indirectly derived by PROOF OF NONINFERIORITY showing either noninferiority or equivalence A two-sample situation is considered. Let the to the reference treatment. clinical endpoint by noted by X, and X, for The inherent issue in noninferiority and the test and reference treatments, respecequivalence studies is the definition of what tively. Suppose that these random variables constitutes a clinically irrelevant difference are mutually independent and normally disin effectiveness. For the situation where it tributed with unknown but common variance o2and population means pT and pR, that is Reprint address: Dr. Dieter Hauschke, Department of Biometry, Byk Gulden Pharmaceuticals, P.O. Box 10 03 10, 78403 Konstanz, Germany. E-mail: dieter. [email protected].
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- N(pT,02),j = 1, . . . , nT x, - N(pR,02),j = 1, . . , nR. X,
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