MOTIVATION
Traditional genome wide association study (GWAS) focuses on testing one-to-one relationship between genetic variants and complex human diseases or traits. While its success in the past decade, this one-to-one paradigm lacks efficiency because it does not utilize the information of intrinsic genetic structure and pleiotropic effects. Due to privacy reasons, only summary statistics of current GWAS data are publicly available. Existing summary statistics-based association tests do not consider covariates for regression model, while adjusting for covariates including population stratification factors is a routine issue.


RESULTS
In this work, we first derive the correlation coefficients between summary Wald statistics obtained from linear regression model with covariates. Then, a new test is proposed by integrating three-level information including the intrinsic genetic structure, pleiotropy, and the potential information combinations. Extensive simulations demonstrate that the proposed test outperforms three other existing methods under most of the considered scenarios. Real data analysis of polyunsaturated fatty acids further shows that the proposed test can identify more genes than the compared existing methods.


AVAILABILITY AND IMPLEMENTATION
Code is available at https://github.com/bschilder/ThreeWayTest.


SUPPLEMENTARY INFORMATION
Supplementary data are available at Bioinformatics online.

Summary statistics-based association test for identifying the pleiotropic effects with set of genetic variants.

Genome-wide association studies (GWAS) have revolutionized our understanding of the genetic architecture of complex traits and diseases. GWAS summary statistics have become essential tools for various genetic analyses, including meta-analysis, fine-mapping, and risk prediction. However, the increasing number of GWAS summary statistics and the diversity of software tools available for their analysis can make it challenging for researchers to select the most appropriate tools for their specific needs. This systematic review aims to provide a comprehensive overview of the currently available software tools and databases for GWAS summary statistics analysis. We conducted a comprehensive literature search to identify relevant software tools and databases. We categorized the tools and databases by their functionality, including data management, quality control, single-trait analysis, and multiple-trait analysis. We also compared the tools and databases based on their features, limitations, and user-friendliness. Our review identified a total of 305 functioning software tools and databases dedicated to GWAS summary statistics, each with unique strengths and limitations. We provide descriptions of the key features of each tool and database, including their input/output formats, data types, and computational requirements. We also discuss the overall usability and applicability of each tool for different research scenarios. This comprehensive review will serve as a valuable resource for researchers who are interested in using GWAS summary statistics to investigate the genetic basis of complex traits and diseases. By providing a detailed overview of the available tools and databases, we aim to facilitate informed tool selection and maximize the effectiveness of GWAS summary statistics analysis. 

The goldmine of GWAS summary statistics: a systematic review of methods and tools

A novel method for computing exact p-values of one-sided statistics from the Kolmogorov-Smirnov family is presented. It covers the Higher Criticism statistic, one-sided weighted Kolmogorov-Smirnov statistics, and the one-sided Berk-Jones statistics. In addition to p-values, the method can also be used for power analysis, finding alpha-level thresholds, and the construction of confidence bands for the empirical distribution function. With its quadratic runtime and numerical stability, the method easily scales to sample sizes in the hundreds of thousands and takes less than a second to run on a sample size of 25,000. This allows practitioners working on large data sets to use exact finite-sample computations instead of approximation schemes. The method is based on a reduction to the boundary-crossing probability of a pure jump stochastic process. FFT convolutions of two different sizes are then used to efficiently propagate the probabilities of the non-crossing paths. This approach has applications beyond statistics, for example in financial risk modeling. 

Fast calculation of p-values for one-sided Kolmogorov-Smirnov type statistics

This letter considers detecting a multichannel Gaussian signal hidden in a small fraction of multivariate observations. We start by formulating the problem under a multivariate sparse mixture model, where the rarely occurring signal is manifested as a shift in the observation covariance matrix. A novel signal detection method is proposed by applying the higher criticism to energy statistics for each multivariate observation. Moreover, the proposed detector is shown to possess an asymptotic optimality in the sense that its false alarm rate and false detection rate vanish as the number of samples increases to infinity. Finally, numerical examples confirm superior performance of the proposed detector to some conventional ones. 

Detection of a Rare Multichannel Gaussian Signal via Higher Criticism

The eigen higher criticism and eigen Berk–Jones tests for multiple trait association studies based on GWAS summary statistics

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The eigen higher criticism and eigen Berk–Jones tests for multiple trait association studies based on GWAS summary statistics