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Multivariate meta-analysis of genetic association studies and genome-wide association studies has received a remarkable attention as it improves the precision of the analysis. Here, we review, summarize and present in a unified framework methods for multivariate meta-analysis of genetic association studies and genome-wide association studies. Starting with the statistical methods used for robust analysis and genetic model selection, we present in brief univariate methods for meta-analysis and we then scrutinize multivariate methodologies. Multivariate models of meta-analysis for a single gene-disease association studies, including models for haplotype association studies, multiple linked polymorphisms and multiple outcomes are discussed. The popular Mendelian randomization approach and special cases of meta-analysis addressing issues such as the assumption of the mode of inheritance, deviation from Hardy-Weinberg Equilibrium and gene-environment interactions are also presented. All available methods are enriched with practical applications and methodologies that could be developed in the future are discussed. Links for all available software implementing multivariate meta-analysis methods are also provided.

Bone mineral density is known to be a heritable, polygenic trait whereas genetic variants contributing to lean mass variation remain largely unknown. We estimated the shared SNP heritability and performed a bivariate GWAS meta-analysis of total-body lean mass (TB-LM) and total-body less head bone mineral density (TBLH-BMD) regions in 10,414 children. The estimated SNP heritability is 43% (95% CI: 34-52%) for TBLH-BMD, and 39% (95% CI: 30-48%) for TB-LM, with a shared genetic component of 43% (95% CI: 29-56%). We identify variants with pleiotropic effects in eight loci, including seven established bone mineral density loci: WNT4, GALNT3, MEPE, CPED1/WNT16, TNFSF11, RIN3, and PPP6R3/LRP5. Variants in the TOM1L2/SREBF1 locus exert opposing effects TB-LM and TBLH-BMD, and have a stronger association with the former trait. We show that SREBF1 is expressed in murine and human osteoblasts, as well as in human muscle tissue. This is the first bivariate GWAS meta-analysis to demonstrate genetic factors with pleiotropic effects on bone mineral density and lean mass.Bone mineral density and lean skeletal mass are heritable traits. Here, Medina-Gomez and colleagues perform bivariate GWAS analyses of total body lean mass and bone mass density in children, and show genetic loci with pleiotropic effects on both traits.

Motivation: In the context of genome-wide association studies (GWAS), there is a variety of statistical techniques in order to conduct the analysis, but, in most cases, the underlying genetic model is usually unknown. Under these circumstances, the classical Cochran-Armitage trend test (CATT) is suboptimal. Robust procedures that maximize the power and preserve the nominal type I error rate are preferable. Moreover, performing a meta-analysis using robust procedures is of great interest and has never been addressed in the past. The primary goal of this work is to implement several robust methods for analysis and meta-analysis in the statistical package Stata and subsequently to make the software available to the scientific community., Results: The CATT under a recessive, additive and dominant model of inheritance as well as robust methods based on the Maximum Efficiency Robust Test statistic, the MAX statistic and the MIN2 were implemented in Stata. Concerning MAX and MIN2, we calculated their asymptotic null distributions relying on numerical integration resulting in a great gain in computational time without losing accuracy. All the aforementioned approaches were employed in a fixed or a random effects meta-analysis setting using summary data with weights equal to the reciprocal of the combined cases and controls. Overall, this is the first complete effort to implement procedures for analysis and meta-analysis in GWAS using Stata., Availability and Implementation: A Stata program and a web-server are freely available for academic users at http://www.compgen.org/tools/GWAR., Contact: pbagos@compgen.org., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com)

We present here an extension of the classic bivariate random effects meta-analysis for the log-transformed sensitivity and specificity that can be applied for two or more diagnostic tests. The advantage of this method is that a closed-form expression is derived for the calculation of the within-studies covariances. The method allows the direct calculation of sensitivity and specificity, as well as, the diagnostic odds ratio, the area under curve and the parameters of the summary receiver operator's characteristic curve, along with the means for a formal comparison of these quantities for different tests. There is no need for individual patient data or the simultaneous evaluation of both diagnostic tests in all studies. The method is simple and fast; it can be extended for several diagnostic tests and can be fitted in nearly all statistical packages. The method was evaluated in simulations and applied in a meta-analysis for the comparison of anti-cyclic citrullinated peptide antibody and rheumatoid factor for discriminating patients with rheumatoid arthritis, with encouraging results. Simulations suggest that the method is robust and more powerful compared with the standard bivariate approach that ignores the correlation between tests. Copyright © 2016 John Wiley & Sons, Ltd., (Copyright © 2016 John Wiley & Sons, Ltd.)