title: Multiple hypotheses testing based on ordered p values--a historical survey with applications to medical research.
abstract: Global tests and multiple test procedures are often based on ordered p values. Such procedures are available for arbitrary dependence structures as well as for specific dependence assumptions of the test statistics. Most of these procedures have been considered as global tests. Multiple test procedures can be obtained by applying the closure principle in order to control the familywise error rate, or by using the false discovery rate as a criterion for type I error rate control. We provide an overview and present examples showing the importance of these procedures in medical research. Finally, we discuss modifications when different weights for the hypotheses of interest are chosen.
authors.affiliation: Institut fur Medizinische Biometrie, Epidemiologie und Informatik, Universitatsmedizin Mainz, Germany. Gerhard.Hommel@unimedizin-mainz.de
authors.forename: Gerhard
authors.initials: G
authors.lastname: Hommel
authors.forename: Frank
authors.initials: F
authors.lastname: Bretz
authors.forename: Willi
authors.initials: W
authors.lastname: Maurer
mesh_terms: D035843:Biomedical Research / Q000706:statistics & numerical data*; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D023381:Endpoint Determination; D015233:Models, Statistical; D011336:Probability