Abstract

Background

Genome-wide association (GWA) studies of hundreds of thousands of single nucleotide polymorphisms (SNPs), genotyped in samples of thousands of individuals, such as those undertaken by the Wellcome Trust Case Control Consortium [1], have proved successful in identifying novel common variants contributing moderate effects to a wide range of complex human traits (odds ratios greater than 1.2 for dichotomous traits or heritability of at least 1% for quantitative phenotypes). However, much of the genetic variation underpinning variation in these traits remains, as yet, unexplained. One natural way to increase power to detect rarer variants of more modest effect is to increase sample size. This can most readily be achieved through meta-analysis of multiple studies from the same or closely related populations, increasing the sample size to the order of tens of thousands. Such analyses have led to the identification of multiple, now established associations that would not otherwise have been identified in any individual study [2-4].

Meta-analysis of GWA studies has been greatly assisted by the development of imputation techniques [5,6] which predict genotypes not directly typed on available GWA genotyping products, but which are present on a dense reference panel of haplotypes, such as those available as part of the International HapMap Project [7] or the 1,000 Genomes Project [8]. With this approach, the results of GWA studies can be combined through meta-analysis of millions of SNPs, even if samples are interrogated with different GWA genotyping products.

The statistical methodology underlying meta-analysis is already well established [9], and freely available software packages provide routines for its implementation [10]. However, in the context of GWA studies, we face a number of unique challenges that make these existing tools impractical: (i) results are often combined for many studies for millions of SNPs, thus requiring memory efficient data manipulation; (ii) there may be over-dispersion of GWA test-statistics due to population structure, and between study variation, both of which must be accounted for in the meta-analysis; and (iii) computational difficulties in combining results obtained using different GWA genotyping products which may be aligned to different strands.

To address these challenges, we have developed the GWAMA (Genome-Wide Association Meta-Analysis) software to perform meta-analysis of summary statistics generated from GWA studies of dichotomous phenotypes or quantitative traits. The software incorporates tools to align studies to the same reference strand, irrespective of the GWA genotyping product, where possible, and optionally performs genomic control [11] of summary statistics to correct for population structure within each study, and potential variation between studies. The software also incorporates scripts for the generation of summaries of genome-wide meta-analyses including Manhattan and quantile-quantile (QQ) plots. Here, we demonstrate application of the GWAMA software to meta-analysis of 5 GWA studies, typed using different GWA genotyping products, but imputed at more than 2.3 million SNPs present on the International HapMap Project reference panels [7]. There are already several software packages available for meta-analysis and therefore comparison with some of the most widely used programs is part of current study.

Implementation

Consider a meta-analysis of N GWA studies, not necessarily typed using the same genotyping product or imputed to the same reference panel. We assume that studies have been filtered for appropriate quality control metrics to exclude poorly genotyped or imputed SNPs [12]. For each study, the following information is required for each good quality SNP: (i) the marker identifier; (ii) the allelic effect estimate and corresponding standard error (or an allelic odds ratio and 95% confidence interval in the case of a dichotomous trait); and (iii) the allele for which the effect has been estimated and the complimentary non-reference allele. Optionally, users may provide: (i) the frequency of the reference allele and the strand to which it has been aligned, which may aid alignment of AT/GC SNPs; (ii) the sample size contributing to the effect estimate; and (iii) an indicator to identify if the SNP has been directly genotyped in the study or imputed from a reference panel.

GWAMA begins by aligning all studies to the same reference allele at each SNP. If strand information is provided, a log file records potential misalignments and any corrections made based on the provision of reference alleles. Fixed effects meta-analysis is then performed for each SNP by combining allelic effects weighted by the inverse of their variance. The software performs tests of heterogeneity of effects across studies, and reports simple summaries of the direction of their effect in each to highlight potential inconsistencies in results. In the presence of heterogeneity of effects between studies, GWAMA can perform random-effects meta-analysis for each SNP by calculating the random-effects variance component. Graphical summaries of the results of the meta-analysis can be generated using the output of GWAMA, in conjunction with accompanying R scripts [10], provided that a map file containing SNP identifiers, chromosome and location are specified. A dense map file is provided with the GWAMA software which includes SNPs incorporated on a wide range of GWA genotyping products and variants present on the Phase 2 HapMap reference panel [7].

Fixed-effects meta-analysis

Let β_ij denote the strand-aligned effect (log-odds ratio for a dichotomous phenotype) of the reference allele at the jth SNP in the ith study. The combined allelic effect across all studies at the jth SNP is then given by

where w_ij = [Var(β_ij)]^-1 is the inverse of the variance of the estimated allelic effect in the ith study, obtained from the standard error (or 95% confidence interval of the odds ratio for a dichotomous phenotype). Note that if the jth SNP has not been directly genotyped or imputed as part of the ith study, w_ij = 0. The variance of the combined allelic effect across studies is given by . Furthermore, the statistic has an approximate χ² distribution with one degree of freedom, and this provides the basis of a test of association of the trait with the jth SNP over all studies.

Random effects meta-analysis

In the presence of heterogeneity of allelic effects between studies, it is common to perform random-effects meta-analysis in order to correct the deflation in the variance of the fixed-effects estimate [19]. The random-effects variance component at the jth SNP is given by

and is used to inflate the variance of the estimated allelic effect in each study. The combined allelic effect across all studies at the SNP is then given by

where . The variance of the combined allelic effect across studies is given by . As in the fixed-effects meta-analysis, the statistic has an approximate χ² distribution with one degree of freedom, and this provides the basis of a test of association of the trait with the jth SNP, allowing for heterogeneity of allelic effects between studies.

Results

To demonstrate the utility of GWAMA, we present the results of an example meta-analysis of 5 GWA studies of a simulated quantitative trait with directly typed and imputed genotypes at almost 2.4 million SNPs. Association summary statistics for each individual had previously been corrected for population structure, prior to meta-analysis. Statistical tests of association from the fixed-effects meta-analysis at each SNP were corrected for potential between-study variation on output using genomic control. The analysis was completed in just 3.5 minutes using a dedicated processor with 2.4 Gb memory. The data set used in this example is made available with GWAMA to test individual processor capabilities and potential limitations. To evaluate the memory capacity and program running time, we made additional testing with 20, 50, 100 and 200 genome wide datasets (each containing 2.4 million markers). The GWAMA program peaked with memory usage 4.8 GB, 8.2 GB, 14.6 GB, and 26.2 GB accordingly taking 10 min, 24 min, 53 min, and 1 hour 52 min to run.

Figure ​Figure11 presents QQ and Manhattan plots generated from GWAMA output using the summary R scripts released with the software. The QQ plot indicates that there is no evidence of population structure or between-study variation that has not been accounted in the analysis through genomic control. The Manhattan plot highlights two regions of association, on chromosomes 13 and 17, meeting genome-wide significance (SNPs in green have meta-analysis p-value less than 10^-8).

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Figure 1

QQ and Manhattan plots generated from GWAMA output using the summary R scripts released with the software.

Discussion

There are currently several software packages designed for genome-wide meta-analysis of association test statistics including METAL [20], MetABEL [21] and META [22]. Table ​Table22 presents a comparison of the key features of these software packages and GWAMA. The most important advantages of GWAMA over the existing packages are: (i) the distribution of supplementary scripts with the software to allow pre-processing of study summary statistic files generated by widely-used GWA analysis tools and production of graphical summaries to visualise the results of the meta-analysis; (ii) the calculation of two measures of heterogeneity of allelic effects between studies; (iii) the option to perform random-effects meta-analysis is the presence of heterogeneity; and (iv) genomic control correction of the association results of each study, and the meta-analysis overall, to allow for population structure.

Conclusions

In the coming months, we expect many more meta-analyses to be undertaken of increasing numbers of GWA studies of a wide range of phenotypes. With the imminent release of data from the 1000 Genomes project [8], we expect imputation to be performed at many millions of SNPs, generating ever larger sets of association summary statistics for analysis. GWAMA is designed to efficiently address the computational challenges of working with such large data-sets by filtering the necessary summary statistics from standard output files from GWA analysis software, as described above. Therefore, we expect that GWAMA will contribute to the identification of novel loci contributing effects to complex human traits in this exciting period of genetic research.

Availability and requirements

Project name: GWAMA

Project home page: http://www.well.ox.ac.uk/GWAMA

Operating system: UNIX (source code can be compiled with other platforms), Windows XP and newer

Programming language: C++, R, PERL

Other requirements: C++ compiler, optionally R version 2.9.0 or later with PNG support to generate graphics and PERL to run file formatting scripts

Licence: BSD

Any restrictions to use by non-academics: none

Authors' contributions

RM scripted and tested the software. APM provided statistical support and participated in error checking. Both authors wrote and approved the final manuscript.

References