Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data

Dobler, Dennis; Pauly, Markus

doi:10.1007/s11749-017-0565-z

Cited by 28 publications

(26 citation statements)

References 71 publications

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“…On the other hand, Akritas (1986) has verified that Efron's bootstrap for right-censored data (Efron, 1981) still works in the presence of ties. The planned future paper may also be considered an extension of the article by Dobler and Pauly (2017) to the multi-sample and multivariate case.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The second equality follows from the functional delta-method applied to the integral functionals φ i ; cf. Dobler and Pauly (2017) for the two-sample case. In this asymptotic expansion, the now proposed wild bootstrap tries to estimate each involved residual ε jk (x) = c(x − X jk ) − F j (x), k = 1, .…”

Section: Asymptotic Properties and Resampling Methodsmentioning

confidence: 99%

“…, a, under a Hadamard-differentiable mapping φ. This can be seen following the lines in the proof of Theorem 2.1 in Dobler and Pauly (2017) where the case a = 2 is discussed; in their proof, K = ∞ needs to be chosen. Hence, asymptotic normality follows from an application of the functional delta-method; cf.…”

Section: A Proofsmentioning

confidence: 99%

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Nonparametric MANOVA in meaningful effects

2019

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Multivariate analysis of variance (MANOVA) is a powerful and versatile method to infer and quantify main and interaction effects in metric multivariate multi-factor data. It is, however, neither robust against change in units nor a meaningful tool for ordinal data. Thus, we propose a novel nonparametric MANOVA. Contrary to existing rank-based procedures we infer hypotheses formulated in terms of meaningful Mann-Whitney-type effects in lieu of distribution functions. The tests are based on a quadratic form in multivariate rank effect estimators and critical values are obtained by the bootstrap. This newly developed procedure provides asymptotically exact and consistent inference for general models such as the nonparametric Behrens-Fisher problem as well as multivariate one-, two-, and higherway crossed layouts. Computer simulations in small samples confirm the reliability of the developed method for ordinal as well as metric data with covariance heterogeneity. Finally, an analysis of a real data example illustrates the applicability and correct interpretation of the results.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Asymptotic Properties and Resampling Methodsmentioning

confidence: 99%

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Nonparametric MANOVA in meaningful effects

2019

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“…Li et al 13 indicated that the conducted statistics based on the area difference between two curves are unstable with small sample sizes; thus, we proposed a permutation procedure to avoid this problem. We named this method the permutation test 14 (Perm). First, according to ABC test, we can obtain the Z ABC statistics.…”

Section: Methodsmentioning

confidence: 99%

Comparison of two treatments in the presence of competing risks

Lyu

Chen

Hou

et al. 2020

Pharmaceutical Statistics

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Summary Competing risks data arise frequently in clinical trials, and a common problem encountered is the overall homogeneity between two groups. In competing risks analysis, when the proportional subdistribution hazard assumption is violated or two cumulative incidence function (CIF) curves cross; currently, the most commonly used testing methods, for example, the Gray test and the Pepe and Mori test, may lead to a significant loss of statistical testing power. In this article, we propose a testing method based on the area between the CIF curves (ABC). The ABC test captures the difference over the whole time interval for which survival information is available for both groups and is not based on any special assumptions regarding the underlying distributions. The ABC test was also extended to test short‐term and long‐term effects. We also consider a combined test and a two‐stage procedure based on this new method, and a bootstrap resampling procedure is suggested in practice to approximate the limiting distribution of the combined test and two‐stage test. An extensive series of Monte Carlo simulations is conducted to investigate the power and the type I error rate of the methods. In addition, based on our simulations, our proposed TS, Comb, and ABC tests have a relatively high power in most situations. In addition, the methods are illustrated using two different datasets with different CIF situations.

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“…As this can be hard to verify or simply wrong, some alternatives to hazard ratios as effect sizes are desired that provide “ clinically meaningful outcomes for (…) patients ” and for “ discussing the value of clinical trials with patients ”. 7 Proposed alternatives cover average hazard ratios, 8,9 concordance and Mann–Whitney effects, 10–12 the (restricted) mean survival, 13,14 or median survival times (MSTs). 15–17…”

Section: Introductionmentioning

confidence: 99%

Inferring median survival differences in general factorial designs via permutation tests

Ditzhaus

Dobler

Pauly

2020

Stat Methods Med Res

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Factorial survival designs with right-censored observations are commonly inferred by Cox regression and explained by means of hazard ratios. However, in case of non-proportional hazards, their interpretation can become cumbersome; especially for clinicians. We therefore offer an alternative: median survival times are used to estimate treatment and interaction effects and null hypotheses are formulated in contrasts of their population versions. Permutation-based tests and confidence regions are proposed and shown to be asymptotically valid. Their type-1 error control and power behavior are investigated in extensive simulations, showing the new methods’ wide applicability. The latter is complemented by an illustrative data analysis.

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Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data

Cited by 28 publications

References 71 publications

Nonparametric MANOVA in meaningful effects

Nonparametric MANOVA in meaningful effects

Comparison of two treatments in the presence of competing risks

Inferring median survival differences in general factorial designs via permutation tests

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