Memory and other properties of multiple test procedures generated by entangled graphs.

Abstract:

:Methods for addressing multiplicity in clinical trials have attracted much attention during the past 20 years. They include the investigation of new classes of multiple test procedures, such as fixed sequence, fallback and gatekeeping procedures. More recently, sequentially rejective graphical test procedures have been introduced to construct and visualize complex multiple test strategies. These methods propagate the local significance level of a rejected null hypothesis to not-yet rejected hypotheses. In the graph defining the test procedure, hypotheses together with their local significance levels are represented by weighted vertices and the propagation rule by weighted directed edges. An algorithm provides the rules for updating the local significance levels and the transition weights after rejecting an individual hypothesis. These graphical procedures have no memory in the sense that the origin of the propagated significance level is ignored in subsequent iterations. However, in some clinical trial applications, memory is desirable to reflect the underlying dependence structure of the study objectives. In such cases, it would allow the further propagation of significance levels to be dependent on their origin and thus reflect the grouped parent-descendant structures of the hypotheses. We will give examples of such situations and show how to induce memory and other properties by convex combination of several individual graphs. The resulting entangled graphs provide an intuitive way to represent the underlying relative importance relationships between the hypotheses, are as easy to perform as the original individual graphs, remain sequentially rejective and control the familywise error rate in the strong sense.

journal_name

Stat Med

journal_title

Statistics in medicine

authors

Maurer W,Bretz F

doi

10.1002/sim.5711

subject

Has Abstract

pub_date

2013-05-10 00:00:00

pages

1739-53

issue

10

eissn

0277-6715

issn

1097-0258

journal_volume

32

pub_type

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