Sequential and Multiple Testing for Dose-Response Analysis
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SEQUENTIAL AND MULTIPLE TESTING FOR DOSE-RESPONSE ANALYSIS WALTERLEHMACHER, PHD Professor, Institute for Medical Statistics, Informatics and Epidemiology, University of Cologne, Germany
MEINHARD KIESER,PHD Head, Department of Biometry, Dr. Willmar Schwabe Pharmaceuticals, Karlsruhe, Germany
LUDWIGHOTHORN, PHD Professor, Department of Bioinformatics, University of Hannover, Germany
For the analysis of dose-response relationship under the assumption of ordered alternatives several global trend tests are available. Furthermore. there are multiple test procedures which can identify doses as effective or even as minimally effective. In this paper it is shown that the principles of multiple comparisons and interim analyses can be combined inflexible and adaptive strategies for dose-responseanalyses; these procedures control the experimentwise error rate. Key Words: Dose-response; Interim analysis; Multiple testing
INTRODUCTION
rate in a strong sense) are necessary. The global and multiplicity aspects are also reTHE FIRST QUESTION in dose-response flected by the actual International Conferanalysis is whether a monotone trend across ence for Harmonization Guidelines (1) for dose groups exists. This leads to global trend dose-response analysis. Appropriate order tests, where the global level (familywise errestricted tests can be confirmatory for demror rate in a weak sense) is controlled. In onstrating a global trend and suitable multiclinical research, one is additionally interple procedures can identify a recommended ested in which doses are effective, which dose. minimal dose is effective, or which dose For the global hypothesis, there are sevsteps are effective, in order to substantiate eral suitable trend tests. For multiple comparthe choice of a dose. Dose differences are isons, there are several approaches for multiconsidered effective if they are clinically relple test procedures, some of which are evant and statistically significant. Therefore, described in the following. It is easy to permultiple comparisons which control the exform global tests in group sequential or adapperimentwise level (familywise type-I error tive interim versions, but it seems that there are only a few methods which combine multiple test procedures with interim analyses. Reprint address: Prof. Dr. Walter Lehmacher, lnstitut In this paper, some new approaches are profur Medizinische Statistik, Informatik und Epidemiologie der UniversiM zu Koln, Joseph-Stelzmann-Str.9, D- posed for the combination of these multiple 50931, Koln. Germany. E-mail: Walter.Lehmacher@ and sequential dose-response analyses, medizin.uni-koeln.de. which can link proof of global trend with 591
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Walter Lehmacher, Meinhard Kieser, and Ludwig Hothorn
proof of efficacy of a chosen dose. Sequential procedures can be especially useful in this area because the multiplicity of this problem makes a reasonable sample
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