Genotype imputation in a coalescent model with infinitely-many-sites mutation

Empirical studies have identified population-genetic factors as important determinants of the properties of genotype-imputation accuracy in imputation-based disease association studies. Here, we develop a simple coalescent model of three sequences that we use to explore the theoretical basis for the influence of these factors on genotype-imputation accuracy, under the assumption of infinitely-many-sites mutation. Employing a demographic model in which two populations diverged at a given time in the past, we derive the approximate expectation and variance of imputation accuracy in a study sequence sampled from one of the two populations, choosing between two reference sequences, one sampled from the same population as the study sequence and the other sampled from the other population. We show that, under this model, imputation accuracy—as measured by the proportion of polymorphic sites that are imputed correctly in the study sequence—increases in expectation with the mutation rate, the proportion of the markers in a chromosomal region that are genotyped, and the time to divergence between the study and reference populations. Each of these effects derives largely from an increase in information available for determining the reference sequence that is genetically most similar to the sequence targeted for imputation. We analyze as a function of divergence time the expected gain in imputation accuracy in the target using a reference sequence from the same population as the target rather than from the other population. Together with a growing body of empirical investigations of genotype imputation in diverse human populations, our modeling framework lays a foundation for extending imputation techniques to novel populations that have not yet been extensively examined.