The examples in Table 2 show that imputation accuracy may sometimes decrease when using the most likely haplotype pair for each GWAS individual rather than integrating over the phase uncertainty. We also note that, over the span of entire chromosomes and in the datasets examined here, haplotype estimates will almost never match the true underlying haplotypes. These considerations led us to assess whether we could improve accuracy for a reasonable increment in computing time by saving multiple sampled haplotype configurations at the pre-phasing stage and then imputing into each of these (see Supplementary Notes for details). Supplementary Fig. 2 and Supplementary Fig. 3 show that imputing into 4–10 sampled haplotypes per individual provide a small increase in accuracy while increasing computational costs by 4–10x. At the same time, Supplementary Fig. 2 shows that using a much larger number of sampled haplotypes (up to 500 per individual, for a 500x increase in computing time) provides only a modest additional increase in accuracy, which confirms that a single pre-phased configuration provides nearly as much accuracy as much more compute intensive methods for
