Assessing Evidence in Multiple Hypotheses

Goutis, C.E.; Casella, George; Wells, Martin T.

doi:10.2307/2291745

Cited by 16 publications

(13 citation statements)

References 13 publications

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“…Similar properties of combining functions have been discussed by Goutis et al (1996) and Pesarin (2001), among others. We first prove that CT(k 1 , k 2 ) is asymptotically unbiased.…”

Section: Unbiasedness and Consistencysupporting

confidence: 75%

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

Lim

Kim

et al. 2011

Metrika

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We study a permutation procedure to test the equality of mean vectors, homogeneity of covariance matrices, or simultaneous equality of both mean vectors and covariance matrices in multivariate paired data. We propose to use two test statistics for the equality of mean vectors and the homogeneity of covariance matrices, respectively, and combine them to test the simultaneous equality of both mean vectors and covariance matrices. Since the combined test has composite null hypothesis, we control its type I error probability and theoretically prove the asymptotic unbiasedness and consistency of the combined test. The new procedure requires no structural assumption on the covariances. No distributional assumption is imposed on the data, except that the permutation test for mean vector equality assumes symmetric joint distribution of the paired data. We illustrate the good performance of the proposed approach with comparison to competing methods via simulations. We apply the proposed method to testing the symmetry of tooth size in a dental study and to finding differentially expressed gene sets with dependent structures in a microarray study of prostate cancer.123 834 E. Li et al.

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“…Similar properties of combining functions have been discussed by Goutis et al (1996) and Pesarin (2001), among others. We first prove that CT(k 1 , k 2 ) is asymptotically unbiased.…”

Section: Unbiasedness and Consistencysupporting

confidence: 75%

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

Lim

Kim

et al. 2011

Metrika

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“…Let P k be the P-value from stage k and Z k = −1 1 − P k the associated Z-value. Becker (1994) and Goutis et al (1996) review the many different methods that have been proposed for combining P-values. The two most popular methods are 1.…”

Section: Interpreting Rejection Of the Combination Hypothesismentioning

confidence: 99%

Adaptive Seamless Designs: Selection and Prospective Testing of Hypotheses

Jennison

Turnbull

2007

Journal of Biopharmaceutical Statistics

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There is a current trend towards clinical protocols which involve an initial "selection" phase followed by a hypothesis testing phase. The selection phase may involve a choice between competing treatments or different dose levels of a drug, between different target populations, between different endpoints, or between a superiority and a non-inferiority hypothesis. Clearly there can be benefits in elapsed time and economy in organizational effort if both phases can be designed up front as one experiment, with little downtime between phases. Adaptive designs have been proposed as a way to handle these selection/testing problems. They offer flexibility and allow final inferences to depend on data from both phases, while maintaining control of overall false positive rates. We review and critique the methods, give worked examples and discuss the efficiency of adaptive designs relative to more conventional procedures. Where gains are possible using the adaptive approach, a variety of logistical, operational, data handling and other practical difficulties remain to be overcome if adaptive, seamless designs are to be effectively implemented.

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“…Some of the points we will mention here have been discussed before (e.g. Goutis et al, 1996), but not in the closure context, which adds an additional layer of complexity.…”

Section: P-value Combination Tests: Global Vs Closurementioning

confidence: 99%

Closed Testing in Pharmaceutical Research: Historical and Recent Developments

Henning

Westfall

2015

Statistics in Biopharmaceutical Research

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In pharmaceutical research, making multiple statistical inferences is standard practice. Unless adjustments are made for multiple testing, the probability of making erroneous determinations of significance increases with the number of inferences. Closed testing is a flexible and easily explained approach to controlling the overall error rate that has seen wide use in pharmaceutical research, particularly in clinical trials settings. In this article, we first give a general review of the uses of multiple testing in pharmaceutical research, with particular emphasis on the benefits and pitfalls of closed testing procedures. We then provide a more technical examination of a class of closed tests that use additive-combination-based and minimum-based p-value statistics, both of which are commonly used in pharmaceutical research. We show that, while the additive combination tests are generally far superior to minimum p-value tests for composite hypotheses, the reverse is true for multiple comparisons using closure-based testing. The loss of power of additive combination tests is explained in terms worst-case "hurdles" that must be cleared before significance can be determined via closed testing. We prove mathematically that this problem can result in the power of a closure-based minimum p-value test approaching 1, while the power of an closure-based additive combination test approaches 0. Finally, implications of these results to pharmaceutical researchers are given.

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Assessing Evidence in Multiple Hypotheses

Cited by 16 publications

References 13 publications

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

Adaptive Seamless Designs: Selection and Prospective Testing of Hypotheses

Closed Testing in Pharmaceutical Research: Historical and Recent Developments

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