A Wilcoxon-Mann-Whitney Test for Latent Variables.
Ontology highlight
ABSTRACT:
SUBMITTER: Dehaene H
PROVIDER: S-EPMC8634887 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:For the two-sample problem, the Wilcoxon-Mann-Whitney (WMW) test is used frequently: it is simple to explain (a permutation test on the difference in mean ranks), it handles continuous or ordinal responses, it can be implemented for large or small samples, it is robust to outliers, it requires few assumptions, and it is efficient in many cases. Unfortunately, the WMW test is rarely presented with an effect estimate and confidence interval. A natural effect parameter associated with this test is the Mann-Whitney parameter, ??=?Pr[?X<Y?]?+?0.5 Pr[X?=?Y?]. Ideally, we desire confidence intervals on ? that are compatible with the WMW test, meaning the test rejects at level ? if and only if the 100(1?-??)% confidence interval on the Mann-Whitney parameter excludes 1/2. Existing confidence interval procedures on ? are not compatible with the usual asymptotic implementation of the WMW test that uses a continuity correction nor are they compatible with exact WMW tests. We develop compatible confidence interval procedures for the asymptotic WMW tests and confidence interval procedures for some exact WMW tests that appear to be compatible. We discuss assumptions and interpretation of the resulting tests and confidence intervals. We provide the wmwTest function of the asht R package to calculate all of the developed confidence intervals.
| S-EPMC6377068 | biostudies-literature
Project description:The Wilcoxon-Mann-Whitney (WMW) test is a popular rank-based two-sample testing procedure for the strong null hypothesis that the two samples come from the same distribution. A modified WMW test, the Fligner-Policello (FP) test, has been proposed for comparing the medians of two populations. A fact that may be underappreciated among some practitioners is that the FP test can also be used to test the strong null like the WMW. In this paper we compare the power of the WMW and FP tests for testing the strong null. Our results show that neither test is uniformly better than the other and that there can be substantial differences in power between the two choices. We propose a new, modified WMW test that combines the WMW and FP tests. Monte Carlo studies show that the combined test has good power compared to either the WMW and FP test. We provide a fast implementation of the proposed test in an open-source software. Supplementary materials are available online.
| S-EPMC6422344 | biostudies-literature
Project description:There are many different proposed procedures for sample size planning for the Wilcoxon-Mann-Whitney test at given type-I and type-II error rates α and β, respectively. Most methods assume very specific models or types of data to simplify calculations (eg, ordered categorical or metric data, location shift alternatives, etc). We present a unified approach that covers metric data with and without ties, count data, ordered categorical data, and even dichotomous data. For that, we calculate the unknown theoretical quantities such as the variances under the null and relevant alternative hypothesis by considering the following "synthetic data" approach. We evaluate data whose empirical distribution functions match the theoretical distribution functions involved in the computations of the unknown theoretical quantities. Then, well-known relations for the ranks of the data are used for the calculations. In addition to computing the necessary sample size N for a fixed allocation proportion t = n1 /N, where n1 is the sample size in the first group and N = n1 + n2 is the total sample size, we provide an interval for the optimal allocation rate t, which minimizes the total sample size N. It turns out that, for certain distributions, a balanced design is optimal. We give a characterization of such distributions. Furthermore, we show that the optimal choice of t depends on the ratio of the two variances, which determine the variance of the Wilcoxon-Mann-Whitney statistic under the alternative. This is different from an optimal sample size allocation in case of the normal distribution model.
| S-EPMC6491996 | biostudies-literature
Project description:When the distributional assumptions for a t-test are not met, the default position of many analysts is to resort to a rank-based test, such as the Wilcoxon-Mann-Whitney Test to compare the difference in means between two samples. The Wilcoxon-Mann-Whitney Test presents no danger of tied observations when the observations in the data are continuous. However, in practice, observations are discretized due various logical reasons, or the data are ordinal in nature. When ranks are tied, most textbooks recommend using mid-ranks to replace the tied ranks, a practice that affects the distribution of the Wilcoxon-Mann-Whitney Test under the null hypothesis. Other methods for breaking ties have also been proposed. In this study, we examine four tie-breaking methods-average-scores, mid-ranks, jittering, and omission-for their effects on Type I and Type II error of the Wilcoxon-Mann-Whitney Test and the two-sample t-test for various combinations of sample sizes, underlying population distributions, and percentages of tied observations. We use the results to determine the maximum percentage of ties for which the power and size are seriously affected, and for which method of tie-breaking results in the best Type I and Type II error properties. Not surprisingly, the underlying population distribution of the data has less of an effect on the Wilcoxon-Mann-Whitney Test than on the t-test. Surprisingly, we find that the jittering and omission methods tend to hold Type I error at the nominal level, even for small sample sizes, with no substantial sacrifice in terms of Type II error. Furthermore, the t-test and the Wilcoxon-Mann-Whitney Test are equally effected by ties in terms of Type I and Type II error; therefore, we recommend omitting tied observations when they occur for both the two-sample t-test and the Wilcoxon-Mann-Whitney due to the bias in Type I error that is created when tied observations are left in the data, in the case of the t-test, or adjusted using mid-ranks or average-scores, in the case of the Wilcoxon-Mann-Whitney.
| S-EPMC6057651 | biostudies-literature
Project description:We consider a two-group randomized clinical trial, where mortality affects the assessment of a follow-up continuous outcome. Using the worst-rank composite endpoint, we develop a weighted Wilcoxon-Mann-Whitney test statistic to analyze the data. We determine the optimal weights for the Wilcoxon-Mann-Whitney test statistic that maximize its power. We derive a formula for its power and demonstrate its accuracy in simulations. Finally, we apply the method to data from an acute ischemic stroke clinical trial of normobaric oxygen therapy.
| S-EPMC5393279 | biostudies-other
Project description:We consider a clinical trial of a potentially lethal disease in which patients are randomly assigned to two treatment groups and are followed for a fixed period of time; a continuous endpoint is measured at the end of follow-up. For some patients; however, death (or severe disease progression) may preclude measurement of the endpoint. A statistical analysis that includes only patients with endpoint measurements may be biased. An alternative analysis includes all randomized patients, with rank scores assigned to the patients who are available for the endpoint measurement on the basis of the magnitude of their responses and with 'worst-rank' scores assigned to those patients whose death precluded the measurement of the continuous endpoint. The worst-rank scores are worse than all observed rank scores. The treatment effect is then evaluated using the Wilcoxon-Mann-Whitney test. In this paper, we derive closed-form formulae for the power and sample size of the Wilcoxon-Mann-Whitney test when missing measurements of the continuous endpoints because of death are replaced by worst-rank scores. We distinguish two approaches for assigning the worst-rank scores. In the tied worst-rank approach, all deaths are weighted equally, and the worst-rank scores are set to a single value that is worse than all measured responses. In the untied worst-rank approach, the worst-rank scores further rank patients according to their time of death, so that an earlier death is considered worse than a later death, which in turn is worse than all measured responses. In addition, we propose four methods for the implementation of the sample size formulae for a trial with expected early death. We conduct Monte Carlo simulation studies to evaluate the accuracy of our power and sample size formulae and to compare the four sample size estimation methods.
| S-EPMC4289456 | biostudies-other
Project description:Minimal sufficient balance (MSB) is a recently suggested method for adaptively controlling covariate imbalance in randomized controlled trials in a manner which reduces the impact on randomness of allocation over other approaches by only intervening when the imbalance is sufficiently significant. Despite its improvements, the approach is unable to consider the relative clinical importance or magnitude of imbalance in each covariate weight, and ignores any imbalance which is not statistically significant, even when these imbalances may collectively justify intervention. We propose the common scale MSB (CS-MSB) method which addresses these limitations, and present simulation studies comparing our proposed method to MSB. We demonstrate that CS-MSB requires less intervention than MSB to achieve the same level of covariate balance, and does not adversely impact either statistical power or Type-I error.
| S-EPMC9303921 | biostudies-literature
Project description:Late phase clinical trials are occasionally planned with one or more interim analyses to allow for early termination or adaptation of the study. While extensive theory has been developed for the analysis of ordered categorical data in terms of the Wilcoxon-Mann-Whitney test, there has been comparatively little discussion in the group sequential literature on how to provide repeated confidence intervals and simple power formulas to ease sample size determination. Dealing more broadly with the nonparametric Behrens-Fisher problem, we focus on the comparison of two parallel treatment arms and show that the Wilcoxon-Mann-Whitney test, the Brunner-Munzel test, as well as a test procedure based on the log win odds, a modification of the win ratio, asymptotically follow the canonical joint distribution. In addition to developing power formulas based on these results, simulations confirm the adequacy of the proposed methods for a range of scenarios. Lastly, we apply our methodology to the FREEDOMS clinical trial (ClinicalTrials.gov Identifier: NCT00289978) in patients with relapse-remitting multiple sclerosis.
| S-EPMC9523827 | biostudies-literature
Project description:BackgroundThe malaria risk analysis of multiple populations is crucial and of great importance whilst compressing limitations. However, the exponential growth in diversity and accumulation of genetic variation data obtained from malaria-infected patients through Genome-Wide Association Studies opens up unprecedented opportunities to explore the significant differences between genetic markers (risk factors), particularly in the resistance or susceptibility of populations to malaria risk. Thus, this study proposes using statistical tests to analyse large-scale genetic variation data, comprising 20,854 samples from 11 populations within three continents: Africa, Oceania, and Asia.MethodsEven though statistical tests have been utilized to conduct case-control studies since the 1950s to link risk factors to a particular disease, several challenges faced, including the choice of data (ordinal vs. non-ordinal) and test (parametric vs. non-parametric). This study overcomes these challenges by adopting the Mann-Whitney U test to analyse large-scale genetic variation data; to explore the statistical significance of markers between populations; and to further identify the highly differentiated markers.ResultsThe findings of this study revealed a significant difference in the genetic markers between populations (p < 0.01) in all the case groups and most control groups. However, for the highly differentiated genetic markers, a significant difference (p < 0.01) was present for most genetic markers with varying p-values between the populations in the case and control groups. Moreover, several genetic markers were observed to have very significant differences (p < 0.001) across all populations, while others exist between certain specific populations. Also, several genetic markers have no significant differences between populations.ConclusionsThese findings further support that the genetic markers contribute differently between populations towards malaria resistance or susceptibility, thus showing differences in the likelihood of malaria infection. In addition, this study demonstrated the robustness of the Mann-Whitney U test in analysing genetic markers in large-scale genetic variation data, thereby indicating an alternative method to explore genetic markers in other complex diseases. The findings hold great promise for genetic markers analysis, and the pipeline emphasized in this study can fully be reproduced to analyse new data.
| S-EPMC8905822 | biostudies-literature
Project description:This work presents a technique for fault detection and identification in centrifugal pumps (CPs) using a novel fault-specific Mann-Whitney test (FSU Test) and K-nearest neighbor (KNN) classification algorithm. Traditional fault indicators, such as the mean, peak, root mean square, and impulse factor, lack sensitivity in detecting incipient faults. Furthermore, for defect identification, supervised models rely on pre-existing knowledge about pump defects for training purposes. To address these concerns, a new centrifugal pump fault indicator (CPFI) that does not rely on previous knowledge is developed based on a novel fault-specific Mann-Whitney test. The new fault indicator is obtained by decomposing the vibration signature (VS) of the centrifugal pump hierarchically into its respective time-frequency representation using the wavelet packet transform (WPT) in the first step. The node containing the fault-specific frequency band is selected, and the Mann-Whitney test statistic is calculated from it. The combination of hierarchical decomposition of the vibration signal for fault-specific frequency band selection and the Mann-Whitney test form the new fault-specific Mann-Whitney test. The test output statistic yields the centrifugal pump fault indicator, which shows sensitivity toward the health condition of the centrifugal pump. This indicator changes according to the working conditions of the centrifugal pump. To further enhance fault detection, a new effect ratio (ER) is introduced. The KNN algorithm is employed to classify the fault type, resulting in promising improvements in fault classification accuracy, particularly under variable operating conditions.
| S-EPMC10675659 | biostudies-literature