Heteroscedasticity: multiple degrees of freedom vs. sandwich estimation

Hasler, Mario

doi:10.1007/s00362-014-0640-4

Cited by 9 publications

(4 citation statements)

References 35 publications

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“…Especially for this latter type of comparisons, but also when the data are notably unbalanced, we recommend using separate DFs per elementary comparison and thereby also making the critical values comparison‐specific. This was shown to work well in our simulations and also by Hasler and Hothorn and Hasler but is admittedly somewhat ad hoc. As an alternative, a joint multivariate reference distribution with comparison‐specific marginal DFs can be constructed using a normal or t copula; this ensured FWER control even for very small‐sample sizes ( n k ≤5) in our simulations.…”

Section: Discussionmentioning

confidence: 99%

“…One possible corrective that circumvents these issues is to use a vector of comparison‐specific DFs

ν = (ν_{1}, ⋯, ν_{z})

and compare every test statistic against a quantile from its own multivariate t reference distribution . This approach—although an approximation only—has been shown in simulations to work reasonably well for heteroscedastic data . As an alternative, we can use a z ‐dimensional reference distribution whose marginals are univariate t distributions with DFs ν 1 ,…, ν z , linked by a normal or t copula with the estimated correlation matrix

\overset{Σ}{true}

.…”

Section: Methodsmentioning

confidence: 99%

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Simultaneous small‐sample comparisons in longitudinal or multi‐endpoint trials using multiple marginal models

Pallmann

Ritz

Hothorn

2018

Statistics in Medicine

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Simultaneous inference in longitudinal, repeated-measures, and multi-endpoint designs can be onerous, especially when trying to find a reasonable joint model from which the interesting effects and covariances are estimated. A novel statistical approach known as multiple marginal models greatly simplifies the modelling process: the core idea is to "marginalise" the problem and fit multiple small models to different portions of the data, and then estimate the overall covariance matrix in a subsequent, separate step. Using these estimates guarantees strong control of the family-wise error rate, however only asymptotically. In this paper, we show how to make the approach also applicable to small-sample data problems. Specifically, we discuss the computation of adjusted P values and simultaneous confidence bounds for comparisons of randomised treatment groups as well as for levels of a nonrandomised factor such as multiple endpoints, repeated measures, or a series of points in time or space. We illustrate the practical use of the method with a data example.

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Section: Discussionmentioning

confidence: 99%

“…One possible corrective that circumvents these issues is to use a vector of comparison‐specific DFs

ν = (ν_{1}, ⋯, ν_{z})

\overset{Σ}{true}

.…”

Section: Methodsmentioning

confidence: 99%

Simultaneous small‐sample comparisons in longitudinal or multi‐endpoint trials using multiple marginal models

Pallmann

Ritz

Hothorn

2018

Statistics in Medicine

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“…Additionally, a random imputation method (RIM) has been considered, where the missing values are replaced by randomly chosen values (sampling with replacement) from corresponding group and endpoint. The simulation results have been obtained from 10 000 simulation runs each, using a program code in the statistical software R , packages mvtnorm ,() multcomp ,() and SimComp . The first simulation study represents a more or less normal situation.…”

Section: Comparison Of the Methodsmentioning

confidence: 99%

Multi‐arm trials with multiple primary endpoints and missing values

Hasler

Hothorn

2017

Statistics in Medicine

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We present an extension of multiple contrast tests for multiple endpoints to the case of missing values. The endpoints are assumed to be normally distributed and correlated and to have equal covariance matrices for the different treatments. Different multivariate t distributions will be applied, differing in endpoint-specific degrees of freedom. In contrast to competing methods, the familywise error type I is maintained in the strong sense in an admissible range, and the problem of different marginal errors type I is avoided. The information of all observations is exploited, thereby enabling a gain in power compared with a complete case analysis.

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“…We propose a novel simulation-based method for this purpose. Some other references that have considered the Dunnett procedure as applied to nonnormal and/or heteroskedastic data include Dunnett (1980), Hasler (2016), Hasler andHothorn (2011), Herberich et al (2010), Hothorn and Kluxen (2019), and Wen et al (2022).…”

Section: Also We Usementioning

confidence: 99%

Multiplicity adjustments for the Dunnett procedure under heterokcedasticity

Tamhane,

2023

Biometrical J

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We give a simulation‐based method for computing the multiplicity adjusted p‐values and critical constants for the Dunnett procedure for comparing treatments with a control under heteroskedasticity. The Welch–Satterthwaite test statistics used in this procedure do not have a simple multivariate t‐distribution because their denominators are mixtures of chi‐squares and are correlated because of the common control treatment sample variance present in all denominators. The joint distribution of the denominators of the test statistics is approximated by correlated chi‐square variables and is generated using a novel algorithm proposed in this paper. This approximation is used to derive critical constants or adjusted p‐values. The familywise error rate (FWER) of the proposed method is compared with some existing methods via simulation under different heteroskedastic scenarios. The results show that our proposed method controls the FWER most accurately, whereas other methods are either too conservative or liberal or control the FWER less accurately. The different methods considered are illustrated on a real data set.

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Heteroscedasticity: multiple degrees of freedom vs. sandwich estimation

Cited by 9 publications

References 35 publications

Simultaneous small‐sample comparisons in longitudinal or multi‐endpoint trials using multiple marginal models

Simultaneous small‐sample comparisons in longitudinal or multi‐endpoint trials using multiple marginal models

Multi‐arm trials with multiple primary endpoints and missing values

Multiplicity adjustments for the Dunnett procedure under heterokcedasticity

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