Simultaneous confidence sets and confidence intervals for multiple ratios

Dilba, Gemechis; Bretz, Frank; Guiard, V.

doi:10.1016/j.jspi.2004.11.009

Cited by 38 publications

(52 citation statements)

References 30 publications

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“…The method to plug in the estimated ratios instead is a simple solution that can be shown to have good properties. See Dilba et al (2006) for the homoscedastic case, and Hasler (2008) for the heteroscedastic case. Simulation results can be obtained on request from the first author.…”

Section: A-simulationsmentioning

confidence: 99%

Multiple Contrast Tests in the Presence of Heteroscedasticity

Hasler

Hothorn

2008

Biometrical J

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This paper proposes a general approach for handling multiple contrast tests for normally distributed data in the presence of heteroscedasticity. Three candidate procedures are described and compared by simulations. Only the procedure with both comparison‐specific degrees of freedom and a correlation matrix depending on sample variances maintains the α‐level over all situations. Other approaches may fail notably as the variances differ more. Furthermore, related approximate simultaneous confidence intervals are given. The approach will be applied to a toxicological experiment. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Section: A-simulationsmentioning

confidence: 99%

Multiple Contrast Tests in the Presence of Heteroscedasticity

Hasler

Hothorn

2008

Biometrical J

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“…A formulation based on ratios -instead of differences -of means following Dilba et al [17] might also be possible. The aim is to simultaneously test the hypotheses H 0l : η l δ l ðl ¼ 1; .…”

Section: Testing Problemmentioning

confidence: 99%

Multiple Contrasts for Repeated Measures

Hasler

2013

The International Journal of Biostatistics

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This article addresses the problem of multiple contrast tests for repeated measures. Three procedures are described and compared by simulations concerning the familywise error type I. The procedure based on sandwich estimators seems to be most robust, except for all-pair comparisons.Keywords: repeated measures, multiple contrasts, sandwich estimator, multivariate t-distribution, familywise error type I *Corresponding author: Mario Hasler, Christian-Albrechts-University, Kiel, Germany, E-mail: hasler@email.uni-kiel.de IntroductionMultiple contrast tests (MCTs) and related simultaneous confidence intervals (SCIs) are well-known methods for testing and estimating linear functions of means called contrasts. A broad class of testing problems can be handled in specifying suitable contrast coefficients. The many-to-one comparison of Dunnett [1] is one of the most frequently applied and cited testing procedures today and it represents a simple example. Several treatments are compared with one control and tested for deviation. The all-pair comparison of Tukey [2], comparing all treatments against each other, is another very well-known example. Bretz [3] has formulated the trend test of Williams [4] as an approximate MCT. Here, the contrast coefficients depend in addition on the sample sizes of the treatment groups. Moreover, other problem-specific contrasts can be defined (see Nelson [5], Westfall [6] or Bretz et al. [7] for example). Furthermore, MCTs and SCIs can also be formulated for ratios of means (see Dilba et al. [8]) if conclusions about ratios -rather than differencesof means are of interest. This applies when relative changes are to be analyzed. Because correlations between the contrasts are involved by a joint distribution, MCTs exactly maintain the familywise error type I (FWE) over all contrasts. No further multiplicity adjustment is needed. SCIs (and adjusted p-values) are obtained for all hypotheses to be tested, complying with the guideline of the ICH [9]. Stepwise or gatekeeping procedures, for example, do not allow informative SCIs; see Strassburger and Bretz [10] and Guilbaud [11].MCTs and related SCIs are usually confined to normally distributed, homoscedastic and independent data with one primary endpoint. For the heteroscedastic case, Hasler and Hothorn [12] described a solution based on Games and Howell [13]. Konietschke et al. [14] presented a non-parametric version. Hasler and Hothorn [15,16] gave extensions for the case of multiple correlated endpoints. Unlike conventional MCTs, these approaches represent approximate solutions. They focus on situations where the usual assumptions are not fulfilled. Repeated measures also represent a situation where such an assumption is not met. For example, the means of several groups have to be compared simultaneously but the measurement values for these groups come from the same measurement objects (patients, plants, etc.), respectively. The groups are mostly according to time points but they can also represent different parts of the body, for ...

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“…Fieller's confidence intervals are computed by using the R function sci.ratio in the contributed package mratios. Dilba et al [21] and the help files in R detail the method used. Consider the case J = 2, a 1 = 1, a 2 = −1.…”

Section: Simulation Studymentioning

confidence: 99%

“…This problem has been studied by many authors over the past 50 years. We mention Fieller [13], Bennett [14], Chakravarti [1], Steffens [15], James et al [16], Sevin [2], Mendoza and Gutierrez-Pena [7], Tsao and Hwang [17], Li and Zhang [9], Diaz-Frances and Sprott [10], Lee and Lin [18], Kim [19], Mendoza [20], Dilba et al [21], and Shi et al [22].…”

Section: Introductionmentioning

confidence: 99%