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Open Access Methodology article

An EM algorithm based on an internal list for estimating haplotype distributions of rare variants from pooled genotype data

Anthony YC Kuk1, Xiang Li1* and Jinfeng Xu2

Author Affiliations

1 Department of Statistics and Applied Probability, National University of Singapore, Singapore, 117546, Singapore

2 Division of Biostatistics, Department of Population Health, New York University School of Medicine, New York, NY 10016, USA

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BMC Genetics 2013, 14:82  doi:10.1186/1471-2156-14-82

Published: 13 September 2013



Pooling is a cost effective way to collect data for genetic association studies, particularly for rare genetic variants. It is of interest to estimate the haplotype frequencies, which contain more information than single locus statistics. By viewing the pooled genotype data as incomplete data, the expectation-maximization (EM) algorithm is the natural algorithm to use, but it is computationally intensive. A recent proposal to reduce the computational burden is to make use of database information to form a list of frequently occurring haplotypes, and to restrict the haplotypes to come from this list only in implementing the EM algorithm. There is, however, the danger of using an incorrect list, and there may not be enough database information to form a list externally in some applications.


We investigate the possibility of creating an internal list from the data at hand. One way to form such a list is to collapse the observed total minor allele frequencies to “zero” or “at least one”, which is shown to have the desirable effect of amplifying the haplotype frequencies. To improve coverage, we propose ways to add and remove haplotypes from the list, and a benchmarking method to determine the frequency threshold for removing haplotypes. Simulation results show that the EM estimates based on a suitably augmented and trimmed collapsed data list (ATCDL) perform satisfactorily. In two scenarios involving 25 and 32 loci respectively, the EM-ATCDL estimates outperform the EM estimates based on other lists as well as the collapsed data maximum likelihood estimates.


The proposed augmented and trimmed CD list is a useful list for the EM algorithm to base upon in estimating the haplotype distributions of rare variants. It can handle more markers and larger pool size than existing methods, and the resulting EM-ATCDL estimates are more efficient than the EM estimates based on other lists.

Collapsed data; EM algorithm; Haplotype frequency estimation; Haplotype list; Pooled genotype data; Rare variants