Computationally feasible estimation of haplotype frequencies from pooled DNA with and without Hardy–Weinberg equilibrium

Pooling large number of DNA samples is a common practice in association study, especially for initial screening. However, the use of expectation-maximization (EM)-type algorithms in estimating haplotype distributions for even moderate pool sizes is hampered by the computational complexity involved. A novel constrained EM algorithm called PoooL has been proposed recently to bypass the difficulty via the use of asymptotic normality of the pooled allele frequencies. The resulting estimates are, however, not maximum likelihood estimates and hence not optimal. Furthermore, the assumption of Hardy-Weinberg equilibrium (HWE) made may not be realistic in practice.