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Combining dependent tests of significance has broad applications but the related p‐value calculation is challenging. For Fisher's combination test, current p‐value calculation methods (eg, Brown's approximation) tend to inflate the type I error rate when the desired significance level is substantially less than 0.05. The problem could lead to significant false discoveries in big data analyses. This paper provides two main contributions. First, it presents a general family of Fisher type statistics, referred to as the GFisher, which covers many classic statistics, such as Fisher's combination, Good's statistic, Lancaster's statistic, weighted Z‐score combination, and so forth. The GFisher allows a flexible weighting scheme, as well as an omnibus procedure that automatically adapts proper weights and the statistic‐defining parameters to a given data. Second, the paper presents several new p‐value calculation methods based on two novel ideas: moment‐ratio matching and joint‐distribution surrogating. Systematic simulations show that the new calculation methods are more accurate under multivariate Gaussian, and more robust under the generalized linear model and the multivariate t‐distribution. The applications of the GFisher and the new p‐value calculation methods are demonstrated by a gene‐based single nucleotide polymorphism (SNP)‐set association study. Relevant computation has been implemented to an R package GFisher available on the Comprehensive R Archive Network. [ABSTRACT FROM AUTHOR]

If it turns out that more proportion of responders is observed from the test drug group than the control group, then the test drug can be approved for general patient population. In the clinical development of new drugs, research pharmaceutical industry and biotech companies (known as sponsors) design and execute clinical trials in order to evaluate the efficacy and safety of the study drug. When comparing the drug efficacy of two groups (e.g., test treatment vs. control), development teams often study the differences in the proportion of responders between these two treatments. In other words, the Phase III clinical trial is designed to compare a test drug against another drug for the same indication, and this other drug has already been approved by regulatory agencies. [Extracted from the article]

Cluster analysis is an unsupervised learning strategy that is exceptionally useful for identifying homogeneous subgroups of observations in data sets of unknown structure. However, it is challenging to determine if the identified clusters represent truly distinct subgroups rather than noise. Existing approaches for addressing this problem tend to define clusters based on distributional assumptions, ignore the inherent correlation structure in the data, or are not suited for high‐dimension low‐sample size (HDLSS) settings. In this paper, we propose a novel method to evaluate the significance of identified clusters by comparing the explained variation due to the clustering from the original data to that produced by clustering a unimodal reference distribution that preserves the covariance structure in the data. The reference distribution is generated using kernel density estimation, and thus, does not require that the data follow a particular distribution. By utilizing sparse covariance estimation, the method is adapted for the HDLSS setting. The approach can be used to test the null hypothesis that the data cannot be partitioned into clusters and to determine the optimal number of clusters. Simulation examples, theoretical evaluations, and applications to temporomandibular disorder research and cancer microarray data illustrate the utility of the proposed method. [ABSTRACT FROM AUTHOR]