1,721,050 research outputs found
An unbiased rank-based estimator of the Mann–Whitney variance including the case of ties
No full textMany estimators of the variance of the well-known unbiased and uniform most powerful estimator of the Mann–Whitney effect, are considered in the literature. Some of these estimators are only valid in cases of no ties or are biased in small sample sizes where the amount of bias is not discussed. Here, we derive an unbiased estimator based on different rankings, the so-called ’placements’ (Orban and Wolfe in Commun Stat Theory Methods 9:883–904, 1980), which is therefore easy to compute. This estimator does not require the assumption of continuous distribution functions and is also valid in the case of ties. Moreover, it is shown that this estimator is non-negative and has a sharp upper bound, which may be considered an empirical version of the well-known Birnbaum–Klose inequality. The derivation of this estimator provides an option to compute the biases of some commonly used estimators in the literature. Simulations demonstrate that, for small sample sizes, the biases of these estimators depend on the underlying distribution functions and thus are not under control. This means that in the case of a biased estimator, simulation results for the type-I error of a test or the coverage probability of a confidence interval do not only depend on the quality of the approximation of by a normal distribution but also an additional unknown bias caused by the variance estimator. Finally, it is shown that this estimator is L2-consistent
A studentized permutation test for the non-parametric Behrens-Fisher problem
No full textFor the non-parametric Behrens-Fisher problem a pen-nutation test based on the studentized rank statistic of Brunner and Munzel is proposed. This procedure is applicable to count or ordered categorical data. By applying the central limit theorem of Janssen, it is shown that the asymptotic permutational distribution of this test statistic is a standard normal distribution. For very small and very different sample sizes, frequently occurring in medical and biological applications, an extensive simulation study suggests that this permutation test works well for data from several underlying distributions. The proposed test is applied to data from a clinical trial. (c) 2006 Elsevier B.V. All rights reserved
Rank methods for the analysis of clustered data in diagnostic trials
No full textMethods for comparing areas under receiver operating characteristic curves usually depend on the assumption of independence between diseased and nondiseased units in the trial. However, if several parts of the same subject have to be classified as diseased or nondiseased, such observations are no longer independent. This situation is referred to as clustered data. First ideas for the analysis of such data are based on the theory of U-statistics. The idea of the multivariate nonparametric Behrens-Fisher problem is extended to clustered data and to factorial designs. ANOVA-type statistics are suggested for both small and moderate sample sizes. They are evaluated in a simulation study and applied to a real-data example. (c) 2006 Elsevier B.V. All rights reserved
Nonparametric analysis of clustered data in diagnostic trials: Estimation problems in small sample sizes
No full textIn diagnostic trials, clustered data are obtained when several subunits ( e. g., organs or vessels) of the same patient are observed where no, several, or all subunits may be diseased or non-diseased as classified by a gold standard. In such a design, repeated measures appear in a natural way since the same patient is observed under different conditions by several readers and the repeated measures may have a quite involved correlation structure. A nonparametric method for clustered data in multiple reader studies to estimate the area under the ROC curve has been previously considered. The disadvantage of this procedure is that the test statistic ( a quadratic form) can become negative in case of small samples. Therefore, a slightly different approach by weighting the estimators of the areas under the curves (AUC) is proposed. It is shown that the proposed new estimator of the covariance matrix of the weighted AUC estimators is always positive semidefinite. Simulation studies show that the new statistic maintains the pre-assigned type-I error level quite well even in case of small sample sizes. The method is motivated by a real data example where the previously suggested statistic becomes negative. This example demonstrates the advantage of the new method. (C) 2008 Elsevier B. V. All rights reserved
Wilcoxon-Mann-Whitney test for stratified samples and Efron's paradox dice
No full textTwo-treatment multi-center clinical trials are the most common type of clinical trials in practice. The aim of this paper is to discuss a curious property of certain standard nonparametric procedures used in the analysis of such clinical trials. Different analyses of a simulated data example are presented, which lead to contrasting and surprising results. The source of the potentially misleading outcome is then explored while relating the simulated data with the concept of Efron's paradox dice and the notion of nontransitivity. With the root of the problem established, an alternate nonparametric method from the literature is shown to address the problem. Finally, pointing out an interpretational concern of using the alternate procedure, a modification to this procedure is also suggested and corresponding theoretical results are presented. (c) 2006 Elsevier B.V. All rights reserved
A New Approach to the Nonparametric Behrens–Fisher Problem With Compatible Confidence Intervals
No full textABSTRACT We propose a new method to address the nonparametric Behrens–Fisher problem, allowing for unequal distribution functions across the two samples. The procedure tests the null hypothesis , where denotes the Mann–Whitney effect. Apart from the trivial case of one‐point distributions, no restrictions are imposed on the underlying data distribution. The test is derived by evaluating the ratio of the true variance of the Mann–Whitney effect estimator to its theoretical maximum, as derived from the Birnbaum–Klose inequality. Through simulations, we demonstrate that the proposed test effectively controls the type‐I error rate under various conditions, including small and unbalanced sample sizes, and different data‐generating mechanisms. Notably, it provides better control of the type‐I error rate than the widely used Brunner–Munzel test, particularly at small significance levels such as . We further construct range‐preserving compatible confidence intervals and show that they exhibit improved coverage compared to the confidence intervals compatible to the Brunner–Munzel test. Finally, we illustrate the application of the method in a clinical trial example.Deutsche Forschungsgemeinschaft https://doi.org/10.13039/50110000165
Sensitivity, specificity and ROC-curves in multiple reader diagnostic trials—A unified, nonparametric approach
No full textIn diagnostic trials, the performance of a product is most frequently measured in terms such as sensitivity, specificity and the area under the ROC-curve (AUC). In multiple-reader trials, correlated data appear in a natural way since the same patient is observed under different conditions by several readers. The repeated measures may have quite an involved correlation structure. Even though sensitivity, specificity and the AUC are all assessments of diagnostic ability, a unified approach to analyze all such measurements allowing for an arbitrary correlation structure does not exist. Thus, a unified approach for these three effect measures of diagnostic ability will be presented in this paper. The fact that sensitivity and specificity are particular AUCs will serve as a basis for our method of analysis. As the presented theory can also be used in set-ups with correlated binomial random-variables, it may have a more extensive application than only in diagnostic trials. (c) 2012 Elsevier B.V. All rights reserved
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