Clinical trials demand a comprehensive evaluation of multiple endpoints to provide a thorough understanding of intervention efficacy and safety. In response to a discerned gap in existing literature, this study introduces an innovative global nonparametric testing procedure, grounded in multivariate ranks, for the holistic analysis of these diverse endpoints. Unlike conventional approaches that heavily rely on pairwise comparisons for individual endpoints, our method takes a novel approach by directly incorporating multivariate ranks. This methodology builds on the strengths of previous models while addressing their limitations, ensuring a more nuanced and robust assessment. By considering the joint ranking of all endpoints, our approach exhibits heightened resilience against diverse data distributions and common censoring mechanisms commonly encountered in clinical trials. The proposed method emerges from a thoughtful integration of existing models, contributing to the methodological evolution in the field. To illustrate its superiority, extensive simulations have been conducted. The results unequivocally demonstrate the superior performance of our multivariate rank-based approach, showcasing its ability to effectively control type I error and achieve higher power compared to conventional rank-based methods. This empirical validation not only underscores the method's efficacy but also highlights its versatility and robustness across a spectrum of clinical trial settings.

Lung adenocarcinoma (LUAD) is characterized by substantial genetic heterogeneity, making it challenging to identify reliable biomarkers for diagnosis and treatment. Tumor mutational burden (TMB) is widely recognized as a predictive biomarker due to its association with immune response and treatment efficacy. In this study, we take a different approach by treating TMB as a response variable to uncover its genetic drivers using multiomics data. We conducted a thorough evaluation of recent feature selection methods through extensive simulations and identified three top-performing approaches: projection correlation screening (PC-Screen), distance correlation sure independence screening (DC-SIS), and Wasserstein distance-based screening (WD-Screen). Unlike traditional approaches that rely on simple statistical tests or dataset splitting for validation, we adopt a method-based validation strategy, selecting top-ranked features from each method and identifying consistently selected genes across all three. Using The Cancer Genome Atlas (TCGA) dataset, we integrated copy number alteration (CNA), mRNA expression, and DNA methylation data as predictors and applied our selected methods. In the two-platform analysis (mRNA + CNA), we identified 13 key genes, including both previously reported LUAD-associated genes (CCNG1, CKAP2L, HSD17B4, SHROOM1, TIGD6, and TMEM173) and novel candidates (DTWD2, FLJ33630, NME5, NUDT12, PCBD2, REEP5, and SLC22A5). Expanding to a three-platform analysis (mRNA + CNA + methylation) further refined our findings, with PCBD2 and TMEM173 emerging as the robust candidates. These results highlight the complexity of multiomics integration and the need for advanced feature selection techniques to uncover biologically meaningful patterns. Our multiomics strategy and robust selection approach provide insights into the genetic determinants of TMB, offering potential biomarkers for targeted LUAD therapies and demonstrating the power of Wasserstein distance-based feature selection in complex genomic analysis.

Genome-Wide Association Studies (GWAS) face unique challenges in the era of big genomics data, particularly when dealing with ultra-high-dimensional datasets where the number of genetic features significantly exceeds the available samples. This paper introduces an extension to the feature selection methodology proposed by Mirzaei et al. (2020), specifically tailored to tackle the intricacies associated with ultra-high-dimensional GWAS data. Our extended approach enhances the original method by introducing a Frobenius norm penalty into the student network, augmenting its capacity to adapt to scenarios characterized by a multitude of features and limited samples. Operating seamlessly in both supervised and unsupervised settings, our method employs two key neural networks. The first leverages an autoencoder or supervised autoencoder for dimension reduction, extracting salient features from the ultra-high-dimensional genomic data. The second network, a regularized feed-forward model with a single hidden layer, is designed for precise feature selection. The introduction of the Frobenius norm penalty in the student network significantly boosts the method's resilience to the challenges posed by ultra-high-dimensional GWAS datasets. Experimental results showcase the efficacy of our approach in feature selection for GWAS data. The method not only handles the inherent complexities of ultra-high-dimensional settings but also demonstrates superior adaptability to the nuanced structures present in genomics data. The flexibility and versatility of our proposed methodology are underscored by its successful performance across a spectrum of experiments.

A bioequivalence study is a type of clinical trial designed to compare the biological equivalence of two different formulations of a drug. Such studies are typically conducted in controlled clinical settings with human subjects, who are randomly assigned to receive two formulations. The two formulations are then compared with respect to their pharmacokinetic profiles, which encompass the absorption, distribution, metabolism, and elimination of the drug. Under the guidance from Food and Drug Administration (FDA), for a size-\(\alpha\) bioequivalence test, the standard approach is to construct a 100(1 - 2\(\alpha\))% confidence interval and verify if the confidence interval falls with the critical region. In this work, we clarify that 100(1-2\(\alpha\))% confidence interval approach for bioequivalence testing yields a size-\(\alpha\) test only when the two one-sided tests in TOST are "equal-tailed". Furthermore, a 100(1 - \(\alpha\))% confidence interval approach is also discussed in the bioequivalence study.

In this work, we propose a deep learning-based method to perform semiparametric regression analysis for spatially dependent data. To be specific, we use a sparsely connected deep neural network with rectified linear unit (ReLU) activation function to estimate the unknown regression function that describes the relationship between response and covariates in the presence of spatial dependence. Under some mild conditions, the estimator is proven to be consistent, and the rate of convergence is determined by three factors: (1) the architecture of neural network class, (2) the smoothness and (intrinsic) dimension of true mean function, and (3) the magnitude of spatial dependence. Our method can handle well large data set owing to the stochastic gradient descent optimization algorithm. Simulation studies on synthetic data are conducted to assess the finite sample performance, the results of which indicate that the proposed method is capable of picking up the intricate relationship between response and covariates. Finally, a real data analysis is provided to demonstrate the validity and effectiveness of the proposed method.

Statistical inference based on lossy or incomplete samples is often needed in research areas such as signal/image processing, medical image storage, remote sensing, signal transmission. In this paper, we propose a nonparametric testing procedure based on samples quantized to $B$ bits through a computationally efficient algorithm. Under mild technical conditions, we establish the asymptotic properties of the proposed test statistic and investigate how the testing power changes as $B$ increases. In particular, we show that if $B$ exceeds a certain threshold, the proposed nonparametric testing procedure achieves the classical minimax rate of testing (Shang and Cheng, 2015) for spline models. We further extend our theoretical investigations to a nonparametric linearity test and an adaptive nonparametric test, expanding the applicability of the proposed methods. Extensive simulation studies {together with a real-data analysis} are used to demonstrate the validity and effectiveness of the proposed tests.