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Motivation: For genetic studies, statistically significant variants explain far less trait variance than ‘sub-threshold’ association signals. To dimension follow-up studies, researchers need to accurately estimate ‘true’ effect sizes at each SNP, e.g. the true mean of odds ratios (ORs)/regression coefficients (RRs) or Z -score noncentralities. Naïve estimates of effect sizes incur winner’s curse biases, which are reduced only by laborious winner’s curse adjustments (WCAs). Given that Z -scores estimates can be theoretically translated on other scales, we propose a simple method to compute WCA for Z -scores, i.e. their true means/noncentralities. Results: WCA of Z -scores shrinks these towards zero while, on P -value scale, multiple testing adjustment (MTA) shrinks P -values toward one, which corresponds to the zero Z -score value. Thus, WCA on Z -scores scale is a proxy for MTA on P -value scale. Therefore, to estimate Z -score noncentralities for all SNPs in genome scans, we propose F DR I nverse Q uantile T ransformation (FIQT). It (i) performs the simpler MTA of P -values using FDR and (ii) obtains noncentralities by back-transforming MTA P -values on Z -score scale. When compared to competitors, realistic simulations suggest that FIQT is more (i) accurate and (ii) computationally efficient by orders of magnitude. Practical application of FIQT to Psychiatric Genetic Consortium schizophrenia cohort predicts a non-trivial fraction of sub-threshold signals which become significant in much larger supersamples. Conclusions : FIQT is a simple, yet accurate, WCA method for Z -scores (and ORs/RRs, via simple transformations). Availability and Implementation: A 10 lines R function implementation is available at https://github.com/bacanusa/FIQT . Contact: sabacanu@vcu.edu Supplementary information: Supplementary data are available at Bioinformatics online.

Motivation To increase detection power, researchers use gene level analysis methods to aggregate weak marker signals. Due to gene expression controlling biological processes, researchers proposed aggregating signals for expression Quantitative Trait Loci (eQTL). Most gene-level eQTL methods make statistical inferences based on (i) summary statistics from genome-wide association studies (GWAS) and (ii) linkage disequilibrium patterns from a relevant reference panel. While most such tools assume homogeneous cohorts, our Gene-level Joint Analysis of functional SNPs in Cosmopolitan Cohorts (JEPEGMIX) method accommodates cosmopolitan cohorts by using heterogeneous panels. However, JEPGMIX relies on brain eQTLs from older gene expression studies and does not adjust for background enrichment in GWAS signals. Results We propose JEPEGMIX2, an extension of JEPEGMIX. When compared to JPEGMIX, it uses (i) cis-eQTL SNPs from the latest expression studies and (ii) brains specific (sub)tissues and tissues other than brain. JEPEGMIX2 also (i) avoids accumulating averagely enriched polygenic information by adjusting for background enrichment and (ii) to avoid an increase in false positive rates for studies with numerous highly enriched (above the background) genes, it outputs gene q-values based on Holm adjustment of P-values. Availability and implementation https://github.com/Chatzinakos/JEPEGMIX2. Supplementary information Supplementary data are available at Bioinformatics online.

Motivation: To increase the signal resolution for large-scale meta-analyses of genome-wide association studies, genotypes at unmeasured single nucleotide polymorphisms (SNPs) are commonly imputed using large multi-ethnic reference panels. However, the ever increasing size and ethnic diversity of both reference panels and cohorts makes genotype imputation computationally challenging for moderately sized computer clusters. Moreover, genotype imputation requires subject-level genetic data, which unlike summary statistics provided by virtually all studies, is not publicly available. While there are much less demanding methods which avoid the genotype imputation step by directly imputing SNP statistics, e.g. Directly Imputing summary STatistics (DIST) proposed by our group, their implicit assumptions make them applicable only to ethnically homogeneous cohorts. Results: To decrease computational and access requirements for the analysis of cosmopolitan cohorts, we propose DISTMIX, which extends DIST capabilities to the analysis of mixed ethnicity cohorts. The method uses a relevant reference panel to directly impute unmeasured SNP statistics based only on statistics at measured SNPs and estimated/user-specified ethnic proportions. Simulations show that the proposed method adequately controls the Type I error rates. The 1000 Genomes panel imputation of summary statistics from the ethnically diverse Psychiatric Genetic Consortium Schizophrenia Phase 2 suggests that, when compared to genotype imputation methods, DISTMIX offers comparable imputation accuracy for only a fraction of computational resources. Availability and implementation: DISTMIX software, its reference population data, and usage examples are publicly available at http://code.google.com/p/distmix. Contact: dlee4@vcu.edu Supplementary information: Supplementary Data are available at Bioinformatics online.

Motivation: Gene expression is influenced by variants commonly known as expression quantitative trait loci (eQTL). On the basis of this fact, researchers proposed to use eQTL/functional information univariately for prioritizing single nucleotide polymorphisms (SNPs) signals from genome-wide association studies (GWAS). However, most genes are influenced by multiple eQTLs which, thus, jointly affect any downstream phenotype. Therefore, when compared with the univariate prioritization approach, a joint modeling of eQTL action on phenotypes has the potential to substantially increase signal detection power. Nonetheless, a joint eQTL analysis is impeded by (i) not measuring all eQTLs in a gene and/or (ii) lack of access to individual genotypes. Results: We propose joint effect on phenotype of eQTL/functional SNPs associated with a gene (JEPEG), a novel software tool which uses only GWAS summary statistics to (i) impute the summary statistics at unmeasured eQTLs and (ii) test for the joint effect of all measured and imputed eQTLs in a gene. We illustrate the behavior/performance of the developed tool by analysing the GWAS meta-analysis summary statistics from the Psychiatric Genomics Consortium Stage 1 and the Genetic Consortium for Anorexia Nervosa. Conclusions: Applied analyses results suggest that JEPEG complements commonly used univariate GWAS tools by: (i) increasing signal detection power via uncovering (a) novel genes or (b) known associated genes in smaller cohorts and (ii) assisting in fine-mapping of challenging regions, e.g. major histocompatibility complex for schizophrenia. Availability and implementation: JEPEG, its associated database of eQTL SNPs and usage examples are publicly available at http://code.google.com/p/jepeg/. Contact: dlee4@vcu.edu Supplementary information: Supplementary data are available at Bioinformatics online.

Motivation: To increase detection power, gene level analysis methods are used to aggregate weak signals. To greatly increase computational efficiency, most methods use as input summary statistics from genome-wide association studies (GWAS). Subsequently, gene statistics are constructed using linkage disequilibrium (LD) patterns from a relevant reference panel. However, all methods, including our own Joint Effect on Phenotype of eQTL/functional single nucleotide polymorphisms (SNPs) associated with a Gene (JEPEG), assume homogeneous panels, e.g. European. However, this renders these tools unsuitable for the analysis of large cosmopolitan cohorts. Results: We propose a JEPEG extension, JEPEGMIX, which similar to one of our software tools, Direct Imputation of summary STatistics of unmeasured SNPs from MIXed ethnicity cohorts, is capable of estimating accurate LD patterns for cosmopolitan cohorts. JEPEGMIX uses this accurate LD estimates to (i) impute the summary statistics at unmeasured functional variants and (ii) test for the joint effect of all measured and imputed functional variants which are associated with a gene. We illustrate the performance of our tool by analyzing the GWAS meta-analysis summary statistics from the multi-ethnic Psychiatric Genomics Consortium Schizophrenia stage 2 cohort. This practical application supports the immune system being one of the main drivers of the process leading to schizophrenia. Availability and implementation: Software, annotation database and examples are available at http://dleelab.github.io/jepegmix/. Contact: donghyung.lee@vcuhealth.org Supplementary information: Supplementary material is available at Bioinformatics online.

Motivation: Genotype imputation methods are used to enhance the resolution of genome-wide association studies, and thus increase the detection rate for genetic signals. Although most studies report all univariate summary statistics, many of them limit the access to subject-level genotypes. Because such an access is required by all genotype imputation methods, it is helpful to develop methods that impute summary statistics without going through the interim step of imputing genotypes. Even when subject-level genotypes are available, due to the substantial computational cost of the typical genotype imputation, there is a need for faster imputation methods. Results: Direct Imputation of summary STatistics (DIST) imputes the summary statistics of untyped variants without first imputing their subject-level genotypes. This is achieved by (i) using the conditional expectation formula for multivariate normal variates and (ii) using the correlation structure from a relevant reference population. When compared with genotype imputation methods, DIST (i) requires only a fraction of their computational resources, (ii) has comparable imputation accuracy for independent subjects and (iii) is readily applicable to the imputation of association statistics coming from large pedigree data. Thus, the proposed application is useful for a fast imputation of summary results for (i) studies of unrelated subjects, which (a) do not provide subject-level genotypes or (b) have a large size and (ii) family association studies. Availability and implementation: Pre-compiled executables built under commonly used operating systems are publicly available at http://code.google.com/p/dist/. Contact: dlee4@vcu.edu Supplementary information: Supplementary data are available at Bioinformatics online.