Multi-aspect permutation tests in shape analysis with small sample size

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.

Non-Motherhood between Obligation and Choice: Statistical Analysis Based on Permutation Tests of Spontaneous and Induced Abortion Rates in the Italian Context

(1) Background: This paper aims to examine two relevant phenomena in the context of public health: spontaneous abortion (SA) and induced abortion (IA). SA is one of the most common complications of pregnancies; IA is a conscious choice that is made by the mother/couple. (2) Methods: Permutation tests were applied to SA and IA standardized rates detected by ISTAT (2016–2020). The NPC test, chosen for its optimal properties, was applied to compare different Italian territorial divisions (stratifying for year and age classes of women) and analyze the trend of years by stochastic ordering. (3) Results: Only for SA, there are significant differences among the three territorial divisions: the South records higher SA standardized rates than the North and the Center; the rates of IA are similar. Relating to distinct women age classes, the SA standardized rates do not show significant differences among the three analyzed geographical areas; different results are highlighted for IA. Stochastic ordering shows that only the IA standardized rates are characterized by a significant monotonous decreasing trend over the years. (4) Conclusion: The SA phenomenon has shown a decreasing trend that could be justified by the progress of science. For IA, we can certainly say that the general decrease in the phenomenon is due to the greater use of contraceptive methods that help to prevent unwanted pregnancies.

A Multi-Aspect Permutation Test for Goodness-of-Fit Problems

Parametric techniques commonly rely on specific distributional assumptions. It is therefore fundamental to preliminarily identify the eventual violations of such assumptions. Therefore, appropriate testing procedures are required for this purpose to deal with a the goodness-of-fit (GoF) problem. This task can be quite challenging, especially with small sample sizes and multivariate data. Previous studiesshowed how a GoF problem can be easily represented through a traditional two-sample system of hypotheses. Following this idea, in this paper, we propose a multi-aspect permutation-based test to deal with the multivariate goodness-of-fit, taking advantage of the nonparametric combination (NPC) methodology. A simulation study is then conducted to evaluate the performance of our proposal and to identify the eventual critical scenarios. Finally, a real data application is considered.

Landmark-free, parametric hypothesis tests regarding two-dimensional contour shapes using coherent point drift registration and statistical parametric mapping

This paper proposes a computational framework for automated, landmark-free hypothesis testing of 2D contour shapes (i.e., shape outlines), and implements one realization of that framework. The proposed framework consists of point set registration, point correspondence determination, and parametric full-shape hypothesis testing. The results are calculated quickly (<2 s), yield morphologically rich detail in an easy-to-understand visualization, and are complimented by parametrically (or nonparametrically) calculated probability values. These probability values represent the likelihood that, in the absence of a true shape effect, smooth, random Gaussian shape changes would yield an effect as large as the observed one. This proposed framework nevertheless possesses a number of limitations, including sensitivity to algorithm parameters. As a number of algorithms and algorithm parameters could be substituted at each stage in the proposed data processing chain, sensitivity analysis would be necessary for robust statistical conclusions. In this paper, the proposed technique is applied to nine public datasets using a two-sample design, and an ANCOVA design is then applied to a synthetic dataset to demonstrate how the proposed method generalizes to the family of classical hypothesis tests. Extension to the analysis of 3D shapes is discussed.

Bonferroni-Holm and permutation tests to compare health data: methodological and applicative issues

BACKGROUND

Statistical methodology is a powerful tool in the health research; however, there is wide accord that statistical methodologies are not usually used properly. In particular when multiple comparisons are needed, it is necessary to check the rate of false positive results and the potential inflation of type I errors. In this case, permutation testing methods are useful to check the simultaneous significance level and identify the most significant factors.

METHODS

In this paper an application of permutation tests, in the medical context of Inflammatory Bowel Diseases, is performed. The main goal is to assess the existence of significant differences between Crohn's Disease (CD) and Ulcerative Colitis (UC). The Sequentially Rejective Multiple Test (Bonferroni-Holm procedure) is used to find which of the partial tests are effectively significant and solve the problem of the multiplicity control.

RESULTS

Applying Non-Parametric Combination (NPC) Test for partial and combined tests we conclude that Crohn's Disease patients and Ulcerative Colitis patients differ between them for most examined variables. UC patients compared with the CD patients, have a higher diagnosis age, not show smoking status, proportion of patients treated with immunosuppressants or with biological drugs is lower than the CD patients, even if the duration of such therapies is longer. CD patients have a higher rate of re-hospitalization. Diabetes is more present in the sub-population of UC patients. Analyzing the Charlson score we can highlight that UC patients have a more severe clinical situation than CD patients. Finally, CD patients are more frequently subject to surgery compared to UC. Appling of the Bonferroni Holm procedure, which provided adjusted p-values, we note that only nine of the examined variables are statistically significant: Smoking habit, Immunosuppressive therapy, Surgery, Biological Drug, Diabetes, Adverse Events, Re-hospitalization, Gender and Duration of Immunosoppressive Therapy. Therefore, we can conclude that these are the specific variables that can discriminate effectively the Crohn's Disease and Ulcerative Colitis groups.

CONCLUSIONS

We identified significant variables that discriminate the two groups, satisfying the multiplicity problem, in fact we can affirm that Smoking habit, Immunosuppressive therapy, Surgery, Biological Drug, Diabetes, Adverse Events, Hospitalization, Gender and Duration of Immunosoppressive Therapy are the effectively significant variables.

Automatic statistical shape analysis of cerebral asymmetry in 3D T1-weighted magnetic resonance images at vertex-level: application to neuroleptic-naïve schizophrenia

The study of the structural asymmetries in the human brain can assist the early diagnosis and progression of various neuropsychiatric disorders, and give insights into the biological bases of several cognitive deficits. The high inter-subject variability in cortical morphology complicates the detection of abnormal asymmetries especially if only small samples are available. This work introduces a novel automatic method for the local (vertex-level) statistical shape analysis of gross cerebral hemispheric surface asymmetries which is robust to the individual cortical variations. After segmentation of the cerebral hemispheric volumes from three-dimensional (3D) T1-weighted magnetic resonance images (MRI) and their spatial normalization to a common space, the right hemispheric masks were reflected to match with the left ones. Cerebral hemispheric surfaces were extracted using a deformable model-based algorithm which extracted the salient morphological features while establishing the point correspondence between the surfaces. The interhemispheric asymmetry, quantified by customized measures of asymmetry, was evaluated in a few thousands of corresponding surface vertices and tested for statistical significance. The developed method was tested on scans obtained from a small sample of healthy volunteers and first-episode neuroleptic-naïve schizophrenics. A significant main effect of the disease on the local interhemispheric asymmetry was observed, both in females and males, at the frontal and temporal lobes, the latter being often linked to the cognitive, auditory, and memory deficits in schizophrenia. The findings of this study, although need further testing in larger samples, partially replicate previous studies supporting the hypothesis of schizophrenia as a neurodevelopmental disorder.

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.

Sexual dimorphism in multiple aspects of 3D facial symmetry and asymmetry defined by spatially dense geometric morphometrics

Accurate measurement of facial sexual dimorphism is useful to understanding facial anatomy and specifically how faces influence, and have been influenced by, sexual selection. An important facial aspect is the display of bilateral symmetry, invoking the need to investigate aspects of symmetry and asymmetry separately when examining facial shape. Previous studies typically employed landmarks that provided only a sparse facial representation, where different landmark choices could lead to contrasting outcomes. Furthermore, sexual dimorphism is only tested as a difference of sample means, which is statistically the same as a difference in population location only. Within the framework of geometric morphometrics, we partition facial shape, represented in a spatially dense way, into patterns of symmetry and asymmetry, following a two-factor anova design. Subsequently, we investigate sexual dimorphism in symmetry and asymmetry patterns separately, and on multiple aspects, by examining (i) population location differences as well as differences in population variance-covariance; (ii) scale; and (iii) orientation. One important challenge in this approach is the proportionally high number of variables to observations necessitating the implementation of permutational and computationally feasible statistics. In a sample of gender-matched young adults (18-25 years) with self-reported European ancestry, we found greater variation in male faces than in women for all measurements. Statistically significant sexual dimorphism was found for the aspect of location in both symmetry and asymmetry (directional asymmetry), for the aspect of scale only in asymmetry (magnitude of fluctuating asymmetry) and, in contrast, for the aspect of orientation only in symmetry. Interesting interplays with hypotheses in evolutionary and developmental biology were observed, such as the selective nature of the force underpinning sexual dimorphism and the genetic independence of the structural patterns of fluctuating asymmetry. Additionally, insights into growth patterns of the soft tissue envelope of the face and underlying skull structure can also be obtained from the results.

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.