Uniformly More Powerful Tests for Hypotheses concerning Linear Inequalities and Normal Means

Berger, Roger L.

doi:10.1080/01621459.1989.10478755

Cited by 49 publications

(11 citation statements)

References 15 publications

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“…, 0) and the results in GS are not applicable. Berger (1989) pointed out that the likelihood ratio test has lower power than the level of significance for alternatives closer to the origin. To overcome this undesirable feature, the likelihood ratio statistic has been modified by Zelterman (1990) for the special case of two groups.…”

Section: Discussionmentioning

confidence: 99%

Tests Against Qualitative Interaction: Exact Critical Values and Robust Tests

Silvapulle¹

2001

Biometrics

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Consider a study to evaluate treatment A with a placebo in two or more groups of patients. If treatment A is beneficial to one group of patients and harmful to another, then we say that there is qualitative interaction or crossover interaction between patient groups and the treatments. Gail and Simon (1985, Biometrics 41, 361-372) developed a large-sample procedure for this testing problem. Their test has received favorable coverage in the literature. In this article, we obtain corresponding exact finite sample results for normal error distribution and provide a table of critical values. The test statistic is similar to the familiar F-ratio, and its p-value is equal to a weighted sum of tail areas of F-distributions. The computations to implement this are simple. A simulation study shows that the exact critical values provided here for normal error distribution are preferable to the asymptotic critical values for a wide range of error distributions. We also develop tests that are power robust against long-tailed error distributions. Our robust test uses M-estimators instead of the least squares estimators. We show that the efficiency robustness of the M-estimator translates to power robustness of the corresponding test. Therefore, our robust tests are better if outliers are expected. A simulation study illustrates the substantial power advantages of our robust tests.

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Section: Discussionmentioning

confidence: 99%

Tests Against Qualitative Interaction: Exact Critical Values and Robust Tests

Silvapulle¹

2001

Biometrics

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“…The hypothesis in (5) can be formulated within the framework of the intersection-union test (IUT) ( S2 Text ) [ 46 – 50 ] with A denoting the complement of set A .…”

Section: Methodsmentioning

confidence: 99%

“…The hypothesis in (5) can be formulated within the framework of the intersection-union test (IUT) (S2 Text) [46][47][48][49][50]…”

Section: Intersection-union Survival Mixture-adjusted Mediation Test (Iusmmt)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We subsequently determined the existence of mediation effect to detect candidate genes with potentially mediating roles by adherence to the principle of intersection-union test (IUT) [ 46 – 52 ], in which the maximum of the two P -values (denoted by P max ) in the two tests above is taken as the significance measurement. Although it is conceptually straightforward, this naïve IUT-based approach is oftentimes extremely conservative especially in large scale mediation effect tests due to its composite null nature [ 43 , 53 ], which can be equivalently expressed as a combination of three disjoint component null hypotheses.…”

Section: Introductionmentioning

confidence: 99%

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IUSMMT: Survival mediation analysis of gene expression with multiple DNA methylation exposures and its application to cancers of TCGA

et al. 2021

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Effective and powerful survival mediation models are currently lacking. To partly fill such knowledge gap, we particularly focus on the mediation analysis that includes multiple DNA methylations acting as exposures, one gene expression as the mediator and one survival time as the outcome. We proposed IUSMMT (intersection-union survival mixture-adjusted mediation test) to effectively examine the existence of mediation effect by fitting an empirical three-component mixture null distribution. With extensive simulation studies, we demonstrated the advantage of IUSMMT over existing methods. We applied IUSMMT to ten TCGA cancers and identified multiple genes that exhibited mediating effects. We further revealed that most of the identified regions, in which genes behaved as active mediators, were cancer type-specific and exhibited a full mediation from DNA methylation CpG sites to the survival risk of various types of cancers. Overall, IUSMMT represents an effective and powerful alternative for survival mediation analysis; our results also provide new insights into the functional role of DNA methylation and gene expression in cancer progression/prognosis and demonstrate potential therapeutic targets for future clinical practice.

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Min Test

Laska

Meisner

2005

Encyclopedia of Statistical Sciences

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The Min test is a statistical tool used to test a null hypothesis such as H o i : ν i ≤ 0 for at least one i versus the alternative H 1 : ν i > 0 for i = 1, 2,…, K . This is sometimes called the sign‐testing problem. If every α‐level test of H o i : ν i ≤ 0 individually rejects the i ‐th null hypothesis at the α level, then the global null hypothesis is rejected according to the Min test. No adjustment for multiplicity is required. Such hypotheses arise in many clinical trials when it is desired to establish that a set of inequalities on the parameters simultaneously holds. Examples include testing whether an identified treatment is best on single or multiple endpoints; whether one treatment is equivalent to or noninferior to a control; and whether a dose of a combination is synergistic.

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Uniformly More Powerful Tests for Hypotheses concerning Linear Inequalities and Normal Means

Cited by 49 publications

References 15 publications

Tests Against Qualitative Interaction: Exact Critical Values and Robust Tests

Tests Against Qualitative Interaction: Exact Critical Values and Robust Tests

IUSMMT: Survival mediation analysis of gene expression with multiple DNA methylation exposures and its application to cancers of TCGA

Min Test

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