title: A note on testing families of hypotheses using graphical procedures.
abstract: Regulatory guidelines for drug development suggest a strong control of the familywise error rate, when multiple hypotheses are simultaneously tested in confirmatory clinical trials. Accordingly, a variety of multiple test procedures exist for pharmaceutical trial applications, which are typically defined on a single structured family of null hypotheses. For some confirmatory clinical trials with multiple objectives, however, it is advantageous to address the arising multiplicity problems via grouped families of hypotheses. Graphical test procedures have been developed to construct, visualize, and perform multiple test procedures that are tailored to either a single or multiple families of structured hypotheses of interest. This note complements the existing literature by introducing a general algorithm to calculate adjusted p-values for any sequentially rejective graphical test procedure where the test procedures within the individual families of hypotheses are not necessarily graphical.
authors.affiliation: Novartis Pharma AG, CH-4002, Basel, Switzerland.
authors.forename: Willi
authors.initials: W
authors.lastname: Maurer
authors.forename: Frank
authors.initials: F
authors.lastname: Bretz
mesh_terms: D000465:Algorithms; D000577:Amides / Q000494:pharmacology; D000959:Antihypertensive Agents / Q000494:pharmacology; D002986:Clinical Trials as Topic / Q000379:methods*; D003196:Computer Graphics; D003627:Data Interpretation, Statistical; D004338:Drug Combinations; D004656:Enalapril / Q000494:pharmacology; D023381:Endpoint Determination / Q000379:methods*; D005650:Fumarates / Q000494:pharmacology; D006333:Heart Failure / Q000188:drug therapy; D006801:Humans
chemical_list: D000577:Amides; D000959:Antihypertensive Agents; D004338:Drug Combinations; D005650:Fumarates; C446481:aliskiren; D004656:Enalapril
keywords: adjusted p-value; graphical approach; group sequential design; multiple testing