Closed testing using surrogate hypotheses with restricted alternatives.
<h4>Introduction</h4>The 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 containi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2019-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0219520 |
| _version_ | 1819145969975951360 |
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| author | John M Lachin Ionut Bebu Michael D Larsen Naji Younes |
| author_facet | John M Lachin Ionut Bebu Michael D Larsen Naji Younes |
| author_sort | John M Lachin |
| collection | DOAJ |
| description | <h4>Introduction</h4>The 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.<h4>Methods</h4>Herein 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.<h4>Conclusion</h4>Closed 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. |
| first_indexed | 2024-12-22T13:06:29Z |
| format | Article |
| id | doaj.art-0817a33e4bdb45b191d6827368741945 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-22T13:06:29Z |
| publishDate | 2019-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-0817a33e4bdb45b191d68273687419452022-12-21T18:24:51ZengPublic Library of Science (PLoS)PLoS ONE1932-62032019-01-01147e021952010.1371/journal.pone.0219520Closed testing using surrogate hypotheses with restricted alternatives.John M LachinIonut BebuMichael D LarsenNaji Younes<h4>Introduction</h4>The 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.<h4>Methods</h4>Herein 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.<h4>Conclusion</h4>Closed 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.https://doi.org/10.1371/journal.pone.0219520 |
| spellingShingle | John M Lachin Ionut Bebu Michael D Larsen Naji Younes Closed testing using surrogate hypotheses with restricted alternatives. PLoS ONE |
| title | Closed testing using surrogate hypotheses with restricted alternatives. |
| title_full | Closed testing using surrogate hypotheses with restricted alternatives. |
| title_fullStr | Closed testing using surrogate hypotheses with restricted alternatives. |
| title_full_unstemmed | Closed testing using surrogate hypotheses with restricted alternatives. |
| title_short | Closed testing using surrogate hypotheses with restricted alternatives. |
| title_sort | closed testing using surrogate hypotheses with restricted alternatives |
| url | https://doi.org/10.1371/journal.pone.0219520 |
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