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Recently-developed genotype imputation methods are a powerful tool fordetecting untyped genetic variants that affect disease susceptibility ingenetic association studies. However, existing imputation methods requireindividual-level genotype data, whereas, in practice, it is often the case thatonly summary data are available. For example, this may occur because, forreasons of privacy or politics, only summary data are made available to theresearch community at large; or because only summary data are collected, as inDNA pooling experiments. In this article we introduce a new statistical methodthat can accurately infer the frequencies of untyped genetic variants in thesesettings, and indeed substantially improve frequency estimates at typedvariants in pooling experiments where observations are noisy. Our approach,which predicts each allele frequency using a linear combination of observedfrequencies, is statistically straightforward, and related to a long history ofthe use of linear methods for estimating missing values (e.g., Kriging). Themain statistical novelty is our approach to regularizing the covariance matrixestimates, and the resulting linear predictors, which is based on methods frompopulation genetics. We find that, besides being both fast andflexible---allowing new problems to be tackled that cannot be handled byexisting imputation approaches purpose-built for the genetic context---theselinear methods are also very accurate. Indeed, imputation accuracy using thisapproach is similar to that obtained by state-of-the-art imputation methodsthat use individual-level data, but at a fraction of the computational cost.

Using linear predictors to impute allele frequencies from summary or pooled genotype data