We propose a method to construct simultaneous confidence intervals for a parameter vector from inverting a series of randomization tests (RT). The randomization tests are facilitated by an efficient multivariate Robbins-Monro procedure that takes the correlation information of all components into account. The estimation method does not require any distributional assumption of the population other than the existence of the second moments. The resulting simultaneous confidence intervals are not necessarily symmetric about the point estimate of the parameter vector but possess the property of equal tails in all dimensions. In particular, we present the constructing the mean vector of one population and the difference between two mean vectors of two populations. Extensive simulation is conducted to show numerical comparison with four methods. We illustrate the application of the proposed method to test bioequivalence with multiple endpoints on some real data.

The dysbiosis of the gut microbiome associated with ulcerative colitis (UC) has been extensively studied in recent years. However, the question of whether UC influences the spatial heterogeneity of the human gut mucosal microbiome has not been addressed. Spatial heterogeneity (specifically, the inter-individual heterogeneity in microbial species abundances) is one of the most important characterizations at both population and community scales, and can be assessed and interpreted by Taylor\'s power law (TPL) and its community-scale extensions (TPLEs). Due to the high mobility of microbes, it is difficult to investigate their spatial heterogeneity explicitly; however, TPLE offers an effective approach to implicitly analyze the microbial communities. Here, we investigated the influence of UC on the spatial heterogeneity of the gut microbiome with intestinal mucosal microbiome samples collected from 28 UC patients and healthy controls. Specifically, we applied Type-I TPLE for measuring community spatial heterogeneity and Type-III TPLE for measuring mixed-species population heterogeneity to evaluate the heterogeneity changes of the mucosal microbiome induced by UC at both the community and species scales. We further used permutation test to determine the possible differences between UC patients and healthy controls in heterogeneity scaling parameters. Results showed that UC did not significantly influence gut mucosal microbiome heterogeneity at either the community or mixed-species levels. These findings demonstrated significant resilience of the human gut microbiome and confirmed a prediction of TPLE: that the inter-subject heterogeneity scaling parameter of the gut microbiome is an intrinsic property to humans, invariant with UC disease.

BACKGROUND: Gastrointestinal disorders cause morbidity and can lead to mortality, especially in the developing world where sanitation is deficient. A large part of the human population relies on medicinal plants for treating various diseases, including gastrointestinal disorders. The present review summarizes the traditional uses of medicinal plants of Nepal used to treat gastrointestinal disorders, and evaluates their bio-efficacy based on a review of the available phytochemical and pharmacological literature.
METHODS: We searched different electronic databases and libraries for the literature on medicinal plants used in Nepal to treat gastrointestinal disorders. For each species, we also searched the literature for information on conservation status, as well as for phytochemical and pharmacological studies in support of the ethnobotanical information. We used principal component analysis to explore the relation among disorders and plant families, plant life forms, plant parts and preparation modes. We also performed permutation tests to determine if botanical families were used more often than expected considering their availability in the Nepali flora.
RESULTS: We documented a total of 947 species belonging to 158 families and 586 genera used to treat gastrointestinal disorders in Nepal. Diarrhea was the disorder treated by the highest number of species (348), followed by stomachache (340) and dysentery (307). Among the reported species, five were endemic to Nepal, whereas 16 orchid species were protected under CITES Appendices II and III. The randomization test showed that species belonging to 14 families were used less often than expected, whereas plants belonging to 25 families were used more often than expected. The PCA scatter plot showed distinct groups of gastrointestinal disorders treated with similar plant life forms, plant parts, and/or preparation modes. We found 763 phytochemical studies on 324 species and 654 pharmacological studies on 269 species.
CONCLUSIONS: We showed the diversity and importance of medicinal plants used to treat gastrointestinal disorders in the traditional health care system of Nepal. As such disorders are still causing several deaths each year, it is of the utmost importance to conduct phytochemical and pharmacological studies on the most promising species. It is also crucial to increase access to traditional medicine, especially in rural areas. Threatened species need special attention for traditional herbal medicine to be exploited sustainably.

Gene selection is an important task in bioinformatics studies, because the accuracy of cancer classification generally depends upon the genes that have biological relevance to the classifying problems. In this work, randomization test (RT) is used as a gene selection method for dealing with gene expression data. In the method, a statistic derived from the statistics of the regression coefficients in a series of partial least squares discriminant analysis (PLSDA) models is used to evaluate the significance of the genes. Informative genes are selected for classifying the four gene expression datasets of prostate cancer, lung cancer, leukemia and non-small cell lung cancer (NSCLC) and the rationality of the results is validated by multiple linear regression (MLR) modeling and principal component analysis (PCA). With the selected genes, satisfactory results can be obtained.