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The SNP-set analysis is a powerful tool for dissecting the genetics of complex human diseases. There are three fundamental genetic association approaches to SNR-set analysis: the marginal model fitting approach, the joint model fitting approach, and the decorrelation approach. A problem of primary interest is how these approaches compare with each other. To address this problem, we develop a theoretical platform to compare the signal-to-noise ratio (SNR) of these approaches under the generalized linear model. We elaborate on how causal genetic effects give rise to statistically detectable association signals, and show that when causal effects spread over blocks of strong linkage disequilibrium (LD), the SNR of the marginal model fitting is usually higher than that of the decorrelation approach, which in turn is higher than that of the unbiased joint model fitting approach. We also scrutinize dense effects and LDs by a bivariate model and extensive simulations using the 1000 Genome Project data. Last, we compare the statistical power of two generic types of SNP-set tests (summation-based and supremum-based) by simulations and an osteoporosis study using large data from UK Biobank. Our results help develop powerful tools for SNP-set analysis and understand the signal detection problem in the presence of colored noise. 

Combining SNP p -values from GWAS summary data is a promising strategy for detecting novel genetic factors. Existing statistical methods for the p -value-based SNP-set testing confront two challenges. First, the statistical power of different methods depends on unknown patterns of genetic effects that could drastically vary over different SNP sets. Second, they do not identify which SNPs primarily contribute to the global association of the whole set. We propose a new signal-adaptive analysis pipeline to address these challenges using the omnibus thresholding Fisher’s method (oTFisher). The oTFisher remains robustly powerful over various patterns of genetic effects. Its adaptive thresholding can be applied to estimate important SNPs contributing to the overall significance of the given SNP set. We develop efficient calculation algorithms to control the type I error rate, which accounts for the linkage disequilibrium among SNPs. Extensive simulations show that the oTFisher has robustly high power and provides a higher balanced accuracy in screening SNPs than the traditional Bonferroni and FDR procedures. We applied the oTFisher to study the genetic association of genes and haplotype blocks of the bone density-related traits using the summary data of the Genetic Factors for Osteoporosis Consortium. The oTFisher identified more novel and literature-reported genetic factors than existing p -value combination methods. Relevant computation has been implemented into the R package TFisher to support similar data analysis. 

Abstract 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.