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Multiple comparisons to both a negative and a positive control
Author(s) -
Hasler Mario
Publication year - 2012
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.503
Subject(s) - type i and type ii errors , contrast (vision) , homogeneous , negative control , statistics , focus (optics) , computer science , control (management) , multiple comparisons problem , econometrics , mathematics , mathematical optimization , medicine , artificial intelligence , combinatorics , physics , optics , traditional medicine
This paper addresses multiple comparisons in the presence of both a negative and a positive control. The methodology of the three‐arm trial is extended to the case of many experimental treatment arms or different doses of a compound. In contrast to the classic three‐arm trial, the focus is on the family‐wise error type I. Normally distributed data with either homogeneous or heterogeneous group variances are considered. Explicit criteria for an optimal allocation are proposed. Depending on the pattern of heterogeneity, remarkably unbalanced designs are power‐optimal. As an example, the method will be applied to a toxicological experiment. Copyright © 2012 John Wiley & Sons, Ltd.