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.

Food Selectivity in Children with Autism Spectrum Disorder: A Statistical Analysis in Southern Italy.

This paper focuses on autism spectrum disorder (ASD) and food selectivity, both of which are prevalent in the pediatric population. In this context, the authors paid attention to food selectivity and its possible correlation with the atypicality of sensory processes, outlining the useful rehabilitation treatments to draw on. This research included the parents or caregivers of pediatric patients diagnosed with autism spectrum disorder and placed within a therapeutic clinic. The sample is composed of 111 children, males and females, aged between 2 and 10 years, and includes 60 children diagnosed with autism and 51 children with normotypical development, similar in characteristics but without the disorder. The standardized questionnaire, "Brief Autism Mealtime Behavior Inventory", was developed to examine behavior during meals, especially in children with ASD. The "Brief Sensory Profile", and the "Child Oral and Motor Proficiency Scale", were also administered. The results obtained from the analysis lead to evidence of eating and food selectivity difficulty. Additionally, our study demonstrates that food selectivity can be caused by extreme sensory modulation and sensory problems related to the smell, texture, color, and temperature of food. In fact, the results obtained emphasize the correlation between food selectivity and the sensory domains of taste and smell. Furthermore, this research highlights a correlation between motor skills and eating skills, particularly regarding food selectivity, which is closely associated with atypical and disruptive behaviors during meals.

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-parametric combination of multimodal MRI for lesion detection in focal epilepsy.

One third of patients with medically refractory focal epilepsy have normal-appearing MRI scans. This poses a problem as identification of the epileptogenic region is required for surgical treatment. This study performs a multimodal voxel-based analysis (VBA) to identify brain abnormalities in MRI-negative focal epilepsy. Data was collected from 69 focal epilepsy patients (42 with discrete lesions on MRI scans, 27 with no visible findings on scans), and 62 healthy controls. MR images comprised T1-weighted, fluid-attenuated inversion recovery (FLAIR), fractional anisotropy (FA) and mean diffusivity (MD) from diffusion tensor imaging, and neurite density index (NDI) from neurite orientation dispersion and density imaging. These multimodal images were coregistered to T1-weighted scans, normalized to a standard space, and smoothed with 8 mm FWHM. Initial analysis performed voxel-wise one-tailed t-tests separately on grey matter concentration (GMC), FLAIR, FA, MD, and NDI, comparing patients with epilepsy to controls. A multimodal non-parametric combination (NPC) analysis was also performed simultaneously on FLAIR, FA, MD, and NDI. Resulting p-maps were family-wise error rate corrected, threshold-free cluster enhanced, and thresholded at p < 0.05. Sensitivity was established through visual comparison of results to manually drawn lesion masks or seizure onset zone (SOZ) from stereoelectroencephalography. A leave-one-out cross-validation with the same analysis protocols was performed on controls to determine specificity. NDI was the best performing individual modality, detecting focal abnormalities in 38% of patients with normal MRI and conclusive SOZ. GMC demonstrated the lowest sensitivity at 19%. NPC provided superior performance to univariate analyses with 50% sensitivity. Specificity in controls ranged between 96 and 100% for all analyses. This study demonstrated the utility of a multimodal VBA utilizing NPC for detecting epileptogenic lesions in MRI-negative focal epilepsy. Future work will apply this approach to datasets from other centres and will experiment with different combinations of MR sequences.

STATegra: Multi-Omics Data Integration - A Conceptual Scheme With a Bioinformatics Pipeline.

Technologies for profiling samples using different omics platforms have been at the forefront since the human genome project. Large-scale multi-omics data hold the promise of deciphering different regulatory layers. Yet, while there is a myriad of bioinformatics tools, each multi-omics analysis appears to start from scratch with an arbitrary decision over which tools to use and how to combine them. Therefore, it is an unmet need to conceptualize how to integrate such data and implement and validate pipelines in different cases. We have designed a conceptual framework (STATegra), aiming it to be as generic as possible for multi-omics analysis, combining available multi-omic anlaysis tools (machine learning component analysis, non-parametric data combination, and a multi-omics exploratory analysis) in a step-wise manner. While in several studies, we have previously combined those integrative tools, here, we provide a systematic description of the STATegra framework and its validation using two The Cancer Genome Atlas (TCGA) case studies. For both, the Glioblastoma and the Skin Cutaneous Melanoma (SKCM) cases, we demonstrate an enhanced capacity of the framework (and beyond the individual tools) to identify features and pathways compared to single-omics analysis. Such an integrative multi-omics analysis framework for identifying features and components facilitates the discovery of new biology. Finally, we provide several options for applying the STATegra framework when parametric assumptions are fulfilled and for the case when not all the samples are profiled for all omics. The STATegra framework is built using several tools, which are being integrated step-by-step as OpenSource in the STATegRa Bioconductor package.

Accuracy of Edentulous Computer-Aided Implant Surgery as Compared to Virtual Planning: A Retrospective Multicenter Study.

PURPOSE: To evaluate the accuracy of computer-aided dental implant positions obtained with mucosal-supported templates as compared to Three-Dimensional (3D) planning. MATERIALS AND METHODS: One-hundred implants were inserted into 14 edentulous patients using the All-on-4/6 protocol after surgical virtual planning with RealGUIDE, 3DIEMME, and Geomagic software. After 6 months, three-dimensional neck (V) and apex (S) spatial coordinates of implants and angle inclination displacements as compared to virtual plans were evaluated. RESULTS: The S maxilla coordinates revealed a significant discrepancy between clinical and virtual implant positions (p-value = 0.091). The V coordinates showed no significant differences (p-value = 0.71). The S (p-value = 0.017) and V (p-value = 0.038) mandible coordinates showed significant discrepancies between the clinical and virtual positions of the screws. Implant evaluation showed a 1-mm of the horizontal deviation in the V point and a 1.6-mm deviation in the S point. A mean 5° angular global deviation was detected. The multivariate permutation test of the S (p-value = 0.02) confirmed the difference. Greater errors in the mandible were detected as compared to the maxilla, and a higher S discrepancy was found in the posterior jaw compared to the anterior section of both the mandible and maxilla. CONCLUSIONS: Computer-aided surgery with mucosal-supported templates is a predictable procedure for implant placement. Data showed a discrepancy between the actual dental implant position as compared to the virtual plan, but this was not statistically significant. However, the horizontal and angle deviations detected indicated that flap surgery should be used to prevent implant positioning errors due to poor sensitivity and accuracy in cases of severe jaw atrophy.

Non-parametric combination and related permutation tests for neuroimaging.

In this work, we show how permutation methods can be applied to combination analyses such as those that include multiple imaging modalities, multiple data acquisitions of the same modality, or simply multiple hypotheses on the same data. Using the well-known definition of union-intersection tests and closed testing procedures, we use synchronized permutations to correct for such multiplicity of tests, allowing flexibility to integrate imaging data with different spatial resolutions, surface and/or volume-based representations of the brain, including non-imaging data. For the problem of joint inference, we propose and evaluate a modification of the recently introduced non-parametric combination (NPC) methodology, such that instead of a two-phase algorithm and large data storage requirements, the inference can be performed in a single phase, with reasonable computational demands. The method compares favorably to classical multivariate tests (such as MANCOVA), even when the latter is assessed using permutations. We also evaluate, in the context of permutation tests, various combining methods that have been proposed in the past decades, and identify those that provide the best control over error rate and power across a range of situations. We show that one of these, the method of Tippett, provides a link between correction for the multiplicity of tests and their combination. Finally, we discuss how the correction can solve certain problems of multiple comparisons in one-way ANOVA designs, and how the combination is distinguished from conjunctions, even though both can be assessed using permutation tests. We also provide a common algorithm that accommodates combination and correction.