Academic Journal
Closed testing using surrogate hypotheses with restricted alternatives.
| Title: | Closed testing using surrogate hypotheses with restricted alternatives. |
|---|---|
| Authors: | John M Lachin, Ionut Bebu, Michael D Larsen, Naji Younes |
| Source: | PLoS ONE, Vol 14, Iss 7, p e0219520 (2019) |
| Publisher Information: | Public Library of Science (PLoS), 2019. |
| Publication Year: | 2019 |
| Collection: | LCC:Medicine LCC:Science |
| Subject Terms: | Medicine, Science |
| More Details: | IntroductionThe closed testing principle provides strong control of the type I error probabilities of tests of a set of hypotheses that are closed under intersection such that a given hypothesis H can only be tested and rejected at level α if all intersection hypotheses containing that hypothesis are also tested and rejected at level α. For the higher order hypotheses, multivariate tests (> 1df) are generally employed. However, such tests are directed to an omnibus alternative hypothesis of a difference in any direction for any component that may be less meaningful than a test directed against a restricted alternative hypothesis of interest.MethodsHerein we describe applications of this principle using an α-level test of a surrogate hypothesis [Formula: see text] such that the type I error probability is preserved if [Formula: see text] such that rejection of [Formula: see text] implies rejection of H. Applications include the analysis of multiple event times in a Wei-Lachin test against a one-directional alternative, a test of the treatment group difference in the means of K repeated measures using a 1 df test of the difference in the longitudinal LSMEANS, and analyses within subgroups when a test of treatment by subgroup interaction is significant. In such cases the successive higher order surrogate tests can be aimed at detecting parameter values that fall within a more desirable restricted subspace of the global alternative hypothesis parameter space.ConclusionClosed testing using α-level tests of surrogate hypotheses will protect the type I error probability and detect specific alternatives of interest, as opposed to the global alternative hypothesis of any difference in any direction. |
| Document Type: | article |
| File Description: | electronic resource |
| Language: | English |
| ISSN: | 1932-6203 |
| Relation: | https://doaj.org/toc/1932-6203 |
| DOI: | 10.1371/journal.pone.0219520 |
| Access URL: | https://doaj.org/article/0817a33e4bdb45b191d6827368741945 |
| Accession Number: | edsdoj.0817a33e4bdb45b191d6827368741945 |
| Database: | Directory of Open Access Journals |
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| ISSN: | 19326203 |
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| DOI: | 10.1371/journal.pone.0219520 |
| Published in: | PLoS ONE |
| Language: | English |