title: A unified framework for weighted parametric multiple test procedures.
abstract: We describe a general framework for weighted parametric multiple test procedures based on the closure principle. We utilize general weighting strategies that can reflect complex study objectives and include many procedures in the literature as special cases. The proposed weighted parametric tests bridge the gap between rejection rules using either adjusted significance levels or adjusted p-values. This connection is made by allowing intersection hypotheses of the underlying closed test procedure to be tested at level smaller than α. This may be also necessary to take certain study situations into account. For such cases we introduce a subclass of exact α-level parametric tests that satisfy the consonance property. When the correlation is known only for certain subsets of the test statistics, a new procedure is proposed to fully utilize this knowledge within each subset. We illustrate the proposed weighted parametric tests using a clinical trial example and conduct a simulation study to investigate its operating characteristics.
authors.affiliation: Novartis Pharmaceuticals Corporation, East Hanover, NJ, 07936, USA.
authors.forename: Dong
authors.identifier: http://orcid.org/0000-0003-1482-234X
authors.initials: D
authors.lastname: Xi
authors.affiliation: Novartis Pharma AG, 4002, Basel, Switzerland.|Otto-von-Guericke-University Magdeburg, Medical Faculty, Institute for Biometrics and Medical Informatics, Germany.
authors.forename: Ekkehard
authors.initials: E
authors.lastname: Glimm
authors.affiliation: Novartis Pharma AG, 4002, Basel, Switzerland.
authors.forename: Willi
authors.initials: W
authors.lastname: Maurer
authors.affiliation: Novartis Pharma AG, 4002, Basel, Switzerland.|School of Statistics and Management, Shanghai University of Finance and Economics, People's Republic of China.
authors.forename: Frank
authors.initials: F
authors.lastname: Bretz
mesh_terms: D001699:Biometry / Q000379:methods*; D002986:Clinical Trials as Topic; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans
keywords: Adjusted p-value; Closure principle; Consonance; Multiple test procedure; Non-exhaustiveness