NonParametric Combination Methodology Research Articles

The Influence of Food Regimes on Oxidative Stress: A Permutation-Based Approach Using the NPC Test.

(1) Background: This paper aims to assess the existence of significant differences between two dietary regimes (omnivorous vs. semi-vegetarian) with reference to some oxidative stress markers (SOD, GPx, TRxR, GR, AGEs, and AOPPs) using non-parametric combination methodology based on a permutation test. (2) Methods: At the endocrinology unit of Messina University Hospital, two hundred subjects were asked to fill out a questionnaire about their dietary habits. None were under any pharmacological treatment. Using the NPC test, all comparisons were performed stratifying patients according to gender, age (≤40 or >40 years), BMI (normal weight vs. overweight), physical activity (sedentary vs. active lifestyle), TSH, FT4 levels in quartiles, and diagnosis of Hashimoto's thyroiditis. We evaluated differences in oxidative stress parameters in relation to two examined dietary regimes (omnivorous vs. semi-vegetarian). (3) Results: The antioxidant parameters GPx and TRxR were significantly lower in subjects with an omnivorous diet than in semi-vegetarians, particularly in females, both age groups, subjects with normal weight, those not affected by Hashimoto's thyroiditis, and both the sedentary and active lifestyle groups. Finally, the AGE and AOPP markers were significantly lower in semi-vegetarians. (4) Conclusion: Thanks to the NPC methodology, we can state that dietary patterns exert a significant influence on some oxidative stress parameters.

Testing exchangeability of multivariate distributions

Although there have been a number of available tests of bivariate exchangeability, i.e. bivariate symmetry for bivariate distributions, the literature is void of tests whether a multivariate distribution with more than two dimensions is exchangeable or not. In this paper, multivariate permutation tests of exchangeability of multivariate distributions are proposed, which are based on the non-parametric combination methodology, i.e. on combining non-parametric bivariate exchangeability tests. Numerical experiments on real as well as simulated multivariate data with more than two dimensions are presented here. The multivariate permutation test turns out to be typically more powerful than a bivariate exchangeability test performed only over a single pair of variables, and also more suitable compared to tests exploiting the approaches of Benjamini–Yekutieli or Bonferroni.

Non-parametric combination analysis of multiple data types enables detection of novel regulatory mechanisms in T cells of multiple sclerosis patients

Multiple Sclerosis (MS) is an autoimmune disease of the central nervous system with prominent neurodegenerative components. The triggering and progression of MS is associated with transcriptional and epigenetic alterations in several tissues, including peripheral blood. The combined influence of transcriptional and epigenetic changes associated with MS has not been assessed in the same individuals. Here we generated paired transcriptomic (RNA-seq) and DNA methylation (Illumina 450 K array) profiles of CD4+ and CD8+ T cells (CD4, CD8), using clinically accessible blood from healthy donors and MS patients in the initial relapsing-remitting and subsequent secondary-progressive stage. By integrating the output of a differential expression test with a permutation-based non-parametric combination methodology, we identified 149 differentially expressed (DE) genes in both CD4 and CD8 cells collected from MS patients. Moreover, by leveraging the methylation-dependent regulation of gene expression, we identified the gene SH3YL1, which displayed significant correlated expression and methylation changes in MS patients. Importantly, silencing of SH3YL1 in primary human CD4 cells demonstrated its influence on T cell activation. Collectively, our strategy based on paired sampling of several cell-types provides a novel approach to increase sensitivity for identifying shared mechanisms altered in CD4 and CD8 cells of relevance in MS in small sized clinical materials.

Common multivariate estimators of location and scatter capture the symmetry of the underlying distribution

The article discusses how various multivariate location and scatter estimators capture the symmetry of the underlying distribution. Very general sufficient conditions are formulated, which ensure various symmetry properties of functionals corresponding to location or scatter. Examples of robust multivariate estimators, which fulfill these conditions, are discussed in detail. The obtained symmetry of the estimators is applicable to hypothesis tests of symmetry of the underlying distribution of the multivariate data. For this task, we propose to perform permutation tests exploiting the nonparametric combination methodology. The performance of the newly proposed tests is illustrated on simulated as well as real data. The tests are suitable for small sample sizes and represent the first available symmetry tests suitable also for non-elliptical distributions and for more than just two variables.

Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology

In this paper, we generalize the metric-based permutation test for the equality of covariance operators proposed by Pigoli et al. (2014) to the case of multiple samples of functional data. To this end, the non-parametric combination methodology of Pesarin and Salmaso (2010) is used to combine all the pairwise comparisons between samples into a global test. Different combining functions and permutation strategies are reviewed and analyzed in detail. The resulting test allows to make inference on the equality of the covariance operators of multiple groups and, if there is evidence to reject the null hypothesis, to identify the pairs of groups having different covariances. It is shown that, for some combining functions, step-down adjusting procedures are available to control for the multiple testing problem in this setting. The empirical power of this new test is then explored via simulations and compared with those of existing alternative approaches in different scenarios. Finally, the proposed methodology is applied to data from wheel running activity experiments, that used selective breeding to study the evolution of locomotor behavior in mice.

OmicsNPC: Applying the Non-Parametric Combination Methodology to the Integrative Analysis of Heterogeneous Omics Data.

BackgroundThe advance of omics technologies has made possible to measure several data modalities on a system of interest. In this work, we illustrate how the Non-Parametric Combination methodology, namely NPC, can be used for simultaneously assessing the association of different molecular quantities with an outcome of interest. We argue that NPC methods have several potential applications in integrating heterogeneous omics technologies, as for example identifying genes whose methylation and transcriptional levels are jointly deregulated, or finding proteins whose abundance shows the same trends of the expression of their encoding genes.ResultsWe implemented the NPC methodology within “omicsNPC”, an R function specifically tailored for the characteristics of omics data. We compare omicsNPC against a range of alternative methods on simulated as well as on real data. Comparisons on simulated data point out that omicsNPC produces unbiased / calibrated p-values and performs equally or significantly better than the other methods included in the study; furthermore, the analysis of real data show that omicsNPC (a) exhibits higher statistical power than other methods, (b) it is easily applicable in a number of different scenarios, and (c) its results have improved biological interpretability.ConclusionsThe omicsNPC function competitively behaves in all comparisons conducted in this study. Taking into account that the method (i) requires minimal assumptions, (ii) it can be used on different studies designs and (iii) it captures the dependences among heterogeneous data modalities, omicsNPC provides a flexible and statistically powerful solution for the integrative analysis of different omics data.

Nonparametric combination-based tests in dynamic shape analysis

Landmark-based geometric morphometric methods are probably the most widely used approaches for shape analysis. Much work has been done for static or cross-sectional shape analysis while considerably less research has focused on dynamic or longitudinal shapes. The question of analysing shape changes over time is a fundamental issue in many research fields. In this paper, as a motivating example, we consider the problem of describing the dynamics of facial expressions for which medical and sociological studies call for a proper differential analysis to distinguish their different characteristics. We address the problem from an inferential point of view testing whether landmark positions change over time, within each facial expression, and whether these changes are different between different expressions. As the shape changes over time completely depend on geometrical landmarks, part of the problem becomes finding the subset of landmarks which best describes the dynamics of the expressions. In this paper, we show by means of a motivating example related to the analysis of the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions and emotions from the Technical University Munich [Wallhoff, F. (2006), ‘Database with Facial Expressions and Emotions from Technical University of Munich (FEEDTUM)’], that NonParametric Combination (NPC) tests can be effective tools when testing whether there is a difference between dynamics of facial expressions or testing which of the landmarks are more informative in explaining their dynamics. In particular, we start analysing data by means of bivariate linear mixed-effects models and then we improve inferential results using the NPC methodology.

OVERVIEW OF NONPARAMETRIC COMBINATION-BASED PERMUTATION TESTS FOR MULTIVARIATE MULTI-SAMPLE PROBLEMS

In this work we present a review on nonparametric combination-based permutation tests along with SAS macros allowing to deal with two-sample and one-way MANOVA design problems, within NonParametric Combination methodology framework. Applications to real case studies are also presented.

Improving power of multivariate combination-based permutation tests

Developing powerful hypothesis testing procedures devoted at comparing multivariate populations is quite a common and relevant topic either from the methodological and the practical point of view and in this connection the NonParametric Combination (NPC) permutation methodology provides a more flexible and effective background for many multivariate testing problems (Pesarin and Salmaso in Permutation tests for complex data: theory, applications and software, 2010a). The goal of this paper is to propose some specific procedures aimed at possibly improving power of NPC Tests in the context of the additive linear model. It will be shown by an extensive simulation study, the improved-in-power NPC Tests are certainly good alternatives with respect to the traditional multivariate tests such as Hotelling T 2 and multivariate rank-based tests, especially in cases of heavy-tailed distributions. Moreover, the NPC methodology offers several advantages since it provides robust solutions with respect to the true underlying random error distribution and it is not affected by the problem of the loss of degrees of freedom when keeping fixed the number of observations. Indeed, unlike traditional methods, when the number of informative variables increases its power monotonically increases as well (leading to the so-called finite-sample consistency property of NPC Test, Pesarin and Salmaso in J. Nonparametr. Stat. 22(5):669---684, 2010b).

Iterated combination-based paired permutation tests to determine shape effects of chemotherapy in patients with esophageal cancer

The nonparametric combination of dependent permutation tests method is a useful general tool when a testing problem can be broken down into a set of different k > 1 partial tests. These partial tests, after adjustment of p-values to control for multiplicity, can be marginally analyzed, but jointly considered they can provide information on an overall hypothesis, which might represent the true goal of the testing problem. On the one hand, independence among the partial tests is usually an unrealistic assumption; on the other, even when the underlying dependence relations are known quite often they are difficult to cope with properly. Therefore this combination must be achieved nonparametrically, by implicitly taking into account the dependence structure of tests without explicitly describing it. An important property of the tests based on nonparametric combination methodology, when the number of response variables is high compared to the sample sizes, consists in the finite sample consistency. A practical problem involves choosing the most suitable combining function for each specific testing problem given that the final result can be affected by this crucial choice. The purpose of this article is to present an nonparametric combination solution based on the iterated combination of partial tests, evaluate its power behavior using a Monte Carlo simulation study and apply it to a real medical problem, namely the evaluation of the effects of chemotherapy on the shape of esophageal tumors. R code has been implemented to carry out the analyses.

Evaluating treatment effect within a multivariate stochastic ordering framework: Nonparametric combination methodology applied to a study on multiple sclerosis

Multiple sclerosis is an autoimmune complex disease that affects the central nervous system. It has a multitude of symptoms that are observed in different people in many different ways. At this time, there is no definite cure for multiple sclerosis. However, therapies that slow the progression of disability, controlling symptoms and helping patients to maintain a normal quality of life, are available. We will focus on relapsing-remitting multiple sclerosis patients treated with interferons or glatiramer acetate. These treatments have been shown to be effective, but their relative effectiveness has not been well established yet. To assess the superiority of a treatment, instead of classical parametric methods, we propose a statistical approach within the permutation setting and the nonparametric combination of dependent permutation tests. In this framework, we may easily handle with hypothesis testing problems for multivariate monotonic stochastic ordering. This approach has been motivated by the analysis of a large observational Italian multicentre study on multiple sclerosis, with several continuous and categorical outcomes measured at multiple time points.

Robust non-parametric tests for complex-repeated measures problems in ophthalmology

The NonParametric Combination methodology (NPC) of dependent permutation tests allows the experimenter to face many complex multivariate testing problems and represents a convincing and powerful alternative to standard parametric methods. The main advantage of this approach lies in its flexibility in handling any type of variable (categorical and quantitative, with or without missing values) while at the same time taking dependencies among those variables into account without the need of modelling them. NPC methodology enables to deal with repeated measures, paired data, restricted alternative hypotheses, missing data (completely at random or not), high-dimensional and small sample size data. Hence, NPC methodology can offer a significant contribution to successful research in biomedical studies with several endpoints, since it provides reasonably efficient solutions and clear interpretations of inferential results. Pesarin F. Multivariate permutation tests: with application in biostatistics. Chichester-New York: John Wiley &Sons, 2001; Pesarin F, Salmaso L. Permutation tests for complex data: theory, applications and software. Chichester, UK: John Wiley &Sons, 2010. We focus on non-parametric permutation solutions to two real-case studies in ophthalmology, concerning complex-repeated measures problems. For each data set, different analyses are presented, thus highlighting characteristic aspects of the data structure itself. Our goal is to present different solutions to multivariate complex case studies, guiding researchers/readers to choose, from various possible interpretations of a problem, the one that has the highest flexibility and statistical power under a set of less stringent assumptions. MATLAB code has been implemented to carry out the analyses.

A Landmark Analysis‐Based Approach to Age and Sex Classification of the Skull of the Mediterranean Monk Seal (Monachus monachus) (Hermann, 1779)

This work aimed at applying geometric morphometric analysis techniques to the skull of the Mediterranean monk seal (Monachus monachus, Hermann, 1779). Inferential analyses were performed using a non-parameteric permutation framework based on a series of skulls of different age classes belonging to individuals of both sexes. Our goal was to establish whether a statistical approach based on osteometric measurements and surface analysis of photographs of the left lateral plane of the skull may lead to a different and scientifically sound method of age and sex classification in this critically endangered marine mammal. Our data indicate that non-parametric combination methodology enables the researcher to give local assessment using a combination with domains. Developing geometric morphometric techniques in a non-parametric permutation framework could be useful in solving high dimensional and small sample size problems as well as classification problems, including zoological classification of specimens within a specific population. The Mediterranean monk seal is believed to be the world's rarest pinniped and one of the most endangered mammals of the world, with fewer than 600 individuals currently surviving. The use of shape analysis would allow new insights into the biological characteristics of the monk seal by simply extracting potentially new information on age and size from museal specimens.

Metodi non parametrici per la verifica di ipotesi in indagini multicentriche

This paper deals with an application of the nonparametric combination methodology of dependent permutation tests (NPC) (Pesarin, 1990, 2001) to an epidemiological multivariate testing problem. The data analysed come from an observational multicentric study on adverse events related to two different categories of anti-depressive pharmacological treatments. The NPC methodology allows the resolution of complex multidimensional and multistrata testing problems also when the number of variables is greater than the number of observations, i.e. in cases where there are no degrees of freedom (see also Crowder & Hand, 1990; Diggle et al., 1996), and in presence of missing data. Under rather mild conditions the NPC methodology allows to obtain an exact, unbiased and consistent solution and asymptotically equivalent to the optimal parametric solution when the latter exists (Pesarin, 2001). An interesting feature of NPC is that it does not require to model the dependence structure underlying variables. A brief description of the NPC with extension to the case of both repeated measurements and stratified samples and the results of the testing problem are presented.

Multivariate And Multistrata Nonparametric Tests: The NonParametric Combination Method

Researchers and practitioners in many scientific disciplines and industrial fields are often faced with complex problems when dealing with comparisons between two or more groups using classical parametric methods. The data arising from real problems rarely are in agreement with stringent parametric assumptions. The NonParametric Combination (NPC) methodology frees the researcher from stringent assumptions of parametric methods and allows a more flexible analysis, both in terms of specification of multivariate hypotheses and in terms of the nature of the variables involved in the analysis. An outline of NPC methodology is given, along with case studies.

A discussion on multi-way ANOVA using a permutation approach

We deal with permutation testing for balanced and unbalanced repeated measures designs and we consider a replicated homoscedastic (balanced or unbalanced) factorial design with fixed effects (Milliken et al., 1984) as the basic experimental plan. The design responses are measured in L time occasions. The usual linear model for responses is: y = {y ij(l) r = so that, the null hypothesis H 0 is true if all partial sub hypotheses are true. In order to test separately the overall null hypotheses, we jointly consider the L measures, then the permutation solution is based on the nonparametric combination methodology (Pesarin, 2001). It is worth noting that the new permutation approach, presented here, is exact and, being conditional to the sufficient statistic represented by the data matrix it does not require normality of error terms in the linear model for responses.