The use of imputed values in the meta-analysis of genome-wide association studies

In genome-wide association studies (GWAS), it is a common practice to impute the genotypes of untyped single nucleotide polymorphism (SNP) by exploiting the linkage disequilibrium structure among SNPs. The use of imputed genotypes improves genome coverage and makes it possible to perform meta-analysis combining results from studies genotyped on different platforms. A popular way of using imputed data is the "expectation-substitution" method, which treats the imputed dosage as if it were the true genotype. In current practice, the estimates given by the expectation-substitution method are usually combined using inverse variance weighting (IVM) scheme in meta-analysis. However, the IVM is not optimal as the estimates given by the expectation-substitution method are generally biased. The optimal weight is, in fact, proportional to the inverse variance and the expected value of the effect size estimates. We show both theoretically and numerically that the bias of the estimates is very small under practical conditions of low effect sizes in GWAS. This finding validates the use of the expectation-substitution method, and shows the inverse variance is a good approximation of the optimal weight. Through simulation, we compared the power of the IVM method with several methods including the optimal weight, the regular z-score meta-analysis and a recently proposed "imputation aware" meta-analysis method (Zaitlen and Eskin [2010] Genet Epidemiol 34:537-542). Our results show that the performance of the inverse variance weight is always indistinguishable from the optimal weight and similar to or better than the other two methods.