title: Simultaneous confidence intervals that are compatible with closed testing in adaptive designs.
abstract: We describe a general method for finding a confidence region for a parameter vector that is compatible with the decisions of a two-stage closed test procedure in an adaptive experiment. The closed test procedure is characterized by the fact that rejection or nonrejection of a null hypothesis may depend on the decisions for other hypotheses and the compatible confidence region will, in general, have a complex, nonrectangular shape. We find the smallest cross-product of simultaneous confidence intervals containing the region and provide computational shortcuts for calculating the lower bounds on parameters corresponding to the rejected null hypotheses. We illustrate the method with an adaptive phase II/III clinical trial.
authors.affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, U.K.
authors.forename: D
authors.initials: D
authors.lastname: Magirr
authors.affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, U.K.
authors.forename: T
authors.initials: T
authors.lastname: Jaki
authors.affiliation: Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, 1090 Wien, Austria.
authors.forename: M
authors.initials: M
authors.lastname: Posch
authors.affiliation: Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, 1090 Wien, Austria.
authors.forename: F
authors.initials: F
authors.lastname: Klinglmueller
keywords: Closed testing principle; Combination test; Conditional error; Multiple comparisons; Simultaneous inference