A coalescent model for genotype imputation

The potential for imputed genotypes to enhance an analysis of genetic data depends largely on the accuracy of imputation, which in turn depends on properties of the reference panel of template haplotypes used to perform the imputation. To provide a basis for exploring how properties of the reference panel affect imputation accuracy theoretically rather than with computationally intensive imputation experiments, we introduce a coalescent model that considers imputation accuracy in terms of population-genetic parameters. Our model allows us to investigate sampling designs in the frequently occurring scenario in which imputation targets and templates are sampled from different populations. In particular, we derive expressions for expected imputation accuracy as a function of reference panel size and divergence time between the reference and target populations. We find that a modestly sized "internal" reference panel from the same population as a target haplotype yields, on average, greater imputation accuracy than a larger "external" panel from a different population, even if the divergence time between the two populations is small. The improvement in accuracy for the internal panel increases with increasing divergence time between the target and reference populations. Thus, in humans, our model predicts that imputation accuracy can be improved by generating small population-specific custom reference panels to augment existing collections such as those of the HapMap or 1000 Genomes Projects. Our approach can be extended to understand additional factors that affect imputation accuracy in complex population-genetic settings, and the results can ultimately facilitate improvements in imputation study designs.