The genome-wide association study (GWAS) has proven to be a successful method for identifying loci contributing to the genetic basis of complex human diseases. While the list of single nucleotide polymorphisms (SNPs) and genes correlated with phenotypes continues to grow, many of the discovered variants exhibit only a weak-to-moderate effect and account for just a small fraction of the total phenotypic variance. Over 75% of the associations identified by case-control GWAS had reported odds ratios (OR) of less than 1.4 with 39% having less than 1.2. In order to achieve 90% power to capture a SNP with an OR = 1.2, minor allele frequency (MAF) of 0.2, and genome-wide cutoff of 10−6
under a multiplicative model, 15,248 individuals must be collected in a balanced study. Over 82% of discovered loci from completed case-control GWAS are from studies with significantly fewer individuals and are therefore underpowered to reliably discover these associations [Hindorff et al., 2009
Given this observation, GWAS must be designed with larger numbers of individuals to have sufficient power to identify weaker variants. This requires a large-scale effort to collect potentially tens of thousands of individuals, who are then genotyped at hundreds of thousands of SNPs. Although the cost of genotyping is dropping, it remains difficult to find, screen, and approve individuals suited for a study. For many diseases, especially those with significant impact on global health, multiple groups are performing association studies, each collecting their own case and control cohorts. A natural approach to address the lack of power of each of the individual studies is to combine the cohorts using meta-analysis.
Meta-analysis is a well-studied problem and is currently widely used in the genetics community in the planning and analysis of GWAS. For a review of meta-analysis techniques and pitfalls, see Kavvoura and Ioannidis 
. Traditional approaches to meta-analysis combine the statistics at each marker from both studies. This approach requires individuals to be genotyped on the same set of SNPs. Since studies often employ different genotyping platforms and different SNPs pass quality control filters in each study, many markers are not shared between studies and cannot be combined using traditional meta-analysis methods.
Recently, several “imputation” methods have been proposed which use a reference set such as the HapMap [International-HapMap-Consortium, 2005
] to estimate the frequency of ungenotyped SNPs in a study [Guan and Stephens, 2008
; Li and Abecasis, 2006
; Marchini et al., 2007
]. Provided that the study population is similar to one of the HapMap populations, these imputation
methods are highly accurate for many of the HapMap SNPs. A straightforward approach to combining studies with different marker sets is to impute the ungenotyped SNPs in each study so that all HapMap SNPs are either genotyped or imputed in both studies. A standard meta-analysis method may then be applied to the genotyped and imputed SNPs. Indeed, several recent meta-analyses have adopted this approach [Soranzo et al., 2009
; Willer et al., 2009
; Zeggini et al., 2008
] Unfortunately, not all SNPs are imputed with perfect accuracy. In fact, this accuracy may vary greatly from SNP to SNP. Most meta-analyses do not take this into account and this uncertainty leads to a loss of power.
Recently, de Bakker et al. 
have analyzed issues relating to conducting meta-analysis in the context of GWAS. In particular, they suggested incorporating estimates of imputation accuracy into the meta-analysis statistic by using an imputed SNP information measure. While this heuristic is intuitive, the exact statistic that maximizes meta-analysis study power remains unknown. In this work, we develop a new statistic, which takes this approach, correcting for potential inaccuracies of imputation by weighting results from each association study based on the accuracy of the imputation at each marker. In brief, results with large studies and accurate imputation are given more weight than smaller studies with inaccurate imputation. Furthermore, we analytically derive an optimal set of weights for combining results from each study in order to maximize power. We show that it can result in a significant increase in power compared to the standard weighted sum of Z-scores (WSoZ) approach used, for example, in three recent meta-analyses [Soranzo et al., 2009
; Willer et al., 2009
; Zeggini et al., 2008
]. Unfortunately, the optimal weights cannot be computed directly from the data since they require knowledge about the true accuracy of the imputation. There are several methods for estimating the accuracy and we examine the application of one developed by Li and Abecasis 
in the context of our imputation aware meta-analysis statistic. We conduct several experiments showing that our new method for handling imputed genotypes from distinct SNP sets improves the power of meta-analysis.