A fast collapsed data method for estimating haplotype frequencies from pooled genotype data with applications to the...

Haplotype information could lead to more powerful tests of genetic association than single-locus analyses but it is not easy to estimate haplotype frequencies from genotype data due to phase ambiguity. The challenge is compounded when individuals are pooled together to save costs or to increase sample size, which is crucial in the study of rare variants. Existing expectation-maximization type algorithms are slow and cannot cope with large pool size or long haplotypes. We show that by collapsing the total allele frequencies of each pool suitably, the maximum likelihood estimates of haplotype frequencies based on the collapsed data can be calculated very quickly regardless of pool size and haplotype length. We provide a running time analysis to demonstrate the considerable savings in time that the collapsed data method can bring. The method is particularly well suited to estimating certain union probabilities useful in the study of rare variants. We provide theoretical and empirical evidence to suggest that the proposed estimation method will not suffer much loss in efficiency if the variants are rare. We use the method to analyze re-sequencing data collected from a case control study involving 148 obese persons and 150 controls. Focusing on a region containing 25 rare variants around the MGLL gene, our method selects three rare variants as potentially causal. This is more parsimonious than the 12 variants selected by a recently proposed covering method. From another set of 32 rare variants around the FAAH gene, we discover an interesting potential interaction between two of them.