Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.

Many studies aim to assess whether a therapy has a beneficial effect on multiple outcomes simultaneously relative to a control. Often the joint null hypothesis of no difference for the set of outcomes is tested using separate tests with a correction for multiple tests, or using a multivariate T2-lik...

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Autor principal:	John M Lachin
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2014
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3446667ce5d14f028310fdae7ce191aa
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spelling	oai:doaj.org-article:3446667ce5d14f028310fdae7ce191aa2021-11-25T05:56:09ZApplications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.1932-620310.1371/journal.pone.0108784https://doaj.org/article/3446667ce5d14f028310fdae7ce191aa2014-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0108784https://doaj.org/toc/1932-6203Many studies aim to assess whether a therapy has a beneficial effect on multiple outcomes simultaneously relative to a control. Often the joint null hypothesis of no difference for the set of outcomes is tested using separate tests with a correction for multiple tests, or using a multivariate T2-like MANOVA or global test. However, a more powerful test in this case is a multivariate one-sided or one-directional test directed at detecting a simultaneous beneficial treatment effect on each outcome, though not necessarily of the same magnitude. The Wei-Lachin test is a simple 1 df test obtained from a simple sum of the component statistics that was originally described in the context of a multivariate rank analysis. Under mild conditions this test provides a maximin efficient test of the null hypothesis of no difference between treatment groups for all outcomes versus the alternative hypothesis that the experimental treatment is better than control for some or all of the component outcomes, and not worse for any. Herein applications are described to a simultaneous test for multiple differences in means, proportions or life-times, and combinations thereof, all on potentially different scales. The evaluation of sample size and power for such analyses is also described. For a test of means of two outcomes with a common unit variance and correlation 0.5, the sample size needed to provide 90% power for two separate one-sided tests at the 0.025 level is 64% greater than that needed for the single Wei-Lachin multivariate one-directional test at the 0.05 level. Thus, a Wei-Lachin test with these operating characteristics is 39% more efficient than two separate tests. Likewise, compared to a T2-like omnibus test on 2 df, the Wei-Lachin test is 32% more efficient. An example is provided in which the Wei-Lachin test of multiple components has superior power to a test of a composite outcome.John M LachinPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 9, Iss 10, p e108784 (2014)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q John M Lachin Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.
description	Many studies aim to assess whether a therapy has a beneficial effect on multiple outcomes simultaneously relative to a control. Often the joint null hypothesis of no difference for the set of outcomes is tested using separate tests with a correction for multiple tests, or using a multivariate T2-like MANOVA or global test. However, a more powerful test in this case is a multivariate one-sided or one-directional test directed at detecting a simultaneous beneficial treatment effect on each outcome, though not necessarily of the same magnitude. The Wei-Lachin test is a simple 1 df test obtained from a simple sum of the component statistics that was originally described in the context of a multivariate rank analysis. Under mild conditions this test provides a maximin efficient test of the null hypothesis of no difference between treatment groups for all outcomes versus the alternative hypothesis that the experimental treatment is better than control for some or all of the component outcomes, and not worse for any. Herein applications are described to a simultaneous test for multiple differences in means, proportions or life-times, and combinations thereof, all on potentially different scales. The evaluation of sample size and power for such analyses is also described. For a test of means of two outcomes with a common unit variance and correlation 0.5, the sample size needed to provide 90% power for two separate one-sided tests at the 0.025 level is 64% greater than that needed for the single Wei-Lachin multivariate one-directional test at the 0.05 level. Thus, a Wei-Lachin test with these operating characteristics is 39% more efficient than two separate tests. Likewise, compared to a T2-like omnibus test on 2 df, the Wei-Lachin test is 32% more efficient. An example is provided in which the Wei-Lachin test of multiple components has superior power to a test of a composite outcome.
format	article
author	John M Lachin
author_facet	John M Lachin
author_sort	John M Lachin
title	Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.
title_short	Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.
title_full	Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.
title_fullStr	Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.
title_full_unstemmed	Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.
title_sort	applications of the wei-lachin multivariate one-sided test for multiple outcomes on possibly different scales.
publisher	Public Library of Science (PLoS)
publishDate	2014
url	https://doaj.org/article/3446667ce5d14f028310fdae7ce191aa
work_keys_str_mv	AT johnmlachin applicationsoftheweilachinmultivariateonesidedtestformultipleoutcomesonpossiblydifferentscales
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Applications of the Wei-Lachin multivariate one-sided test for multiple outcomes on possibly different scales.

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