Rationale for the update algorithm of the graphical approach to sequentially rejective multiple test procedures. (12th July 2022)

• Record Type: Journal Article
• Authors: Maurer, Willi; Bretz, Frank; Posch, Martin
• Other Names: Senn Stephen guestEditor.; Smith Mike K. guestEditor.
• Is Part Of: Pharmaceutical statistics. Volume 21:Number 4(2022)
• Page Start: 757
• Page End: 763
• Publication Date: 2022-07-12
• Subjects: clinical trials -- Markov chain -- multiple endpoints -- multiple testing; Pharmacy -- Statistical methods -- Periodicals; Pharmacy -- Statistics -- Periodicals; 615.10727
• DOI: 10.1002/pst.2227
• Languages: English
• ISSNs: 1539-1604

Abstract

Abstract: The graphical approach by Bretz et al. is a convenient tool to construct, visualize and perform multiple test procedures that are tailored to structured families of hypotheses while controlling the familywise error rate. A critical step is to update the transition weights following a pre‐specified algorithm. In their original publication, however, the authors did not provide a detailed rationale for the update formula. This paper closes the gap and provides three alternative arguments for the update of the transition weights of the graphical approach. It is a legacy of the first author, based on an unpublished technical report from 2014, and after his untimely death reconstructed by the other two authors as a tribute to Willi Maurer's collaboration with Andy Grieve and contributions to biostatistics over many years.