Institute of Mathematical Statistics Lecture Notes - Monograph Series

Compatible confidence intervals for intersection union tests involving two hypotheses

Klaus Strassburger, Frank Bretz, and Yosef Hochberg

Full-text: Open access

Abstract

The intersection union test is a standard test in situations where the rejection of all elements of a set of $k$ hypotheses is required. In particular, the intersection union test is known to be uniformly most powerful within a certain class of monotone level$-\alpha$ tests. In this article we consider the special case of $k=2$. We consider the problem of deriving simultaneous confidence intervals which are compatible with the associated test decisions. We apply the general partitioning principle of Finner and Strassburger (2002) to derive a general method to construct confidence intervals which are compatible to a given test. Several examples of partitioning the two-dimensional parameter space are given and their characteristics are discussed in detail. The methods in this paper are illustrated by two gold standard clinical trials, where a new treatment under investigation is compared to both a placebo group and a standard therapy.

Chapter information

Source
Y. Benjamini, F. Bretz and S. Sarkar, eds., Recent Developments in Multiple Comparison Procedures (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 129-142

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285631

Digital Object Identifier
doi:10.1214/lnms/1196285631

Mathematical Reviews number (MathSciNet)
MR2118597

Zentralblatt MATH identifier
1268.62027

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62J15: Paired and multiple comparisons

Keywords
multiple hypotheses testing min-test partitioning principle gold standard clinical trials stepwise testing

Rights
Copyright © 2004, Institute of Mathematical Statistics

Citation

Strassburger, Klaus; Bretz, Frank; Hochberg, Yosef. Compatible confidence intervals for intersection union tests involving two hypotheses. Recent Developments in Multiple Comparison Procedures, 129--142, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2004. doi:10.1214/lnms/1196285631. https://projecteuclid.org/euclid.lnms/1196285631


Export citation