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

Motivation: 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. Methods: Rather than carrying out constrained maximization as in PoooL, we revert to the usual EM algorithm but make it computationally feasible by using normal approximations. The resulting algorithm is much simpler to implement than PoooL because there is no need to invoke sophisticated iterative scaling methods as in PoooL. We also develop an estimating equation analogue of the EM algorithm for the case of Hardy-Weinberg disequilibrium (HWD) by conditioning on the haplotypes of both chromosomes of the same individual. Incorporated into the method is a way of estimating the inbreeding coefficient by relating it to overdispersion. Results: Simulation study assuming HWE shows that our simplified implementation of the EM algorithm leads to estimates with substantially smaller SDs than PoooL estimates. Further simulations show that ignoring HWD will induce biases in the estimates. Our extended method with estimation of inbreeding coefficient incorporated is able to reduce the bias leading to estimates with substantially smaller mean square errors. We also present results to suggest that our method can cope with a certain degree of locus-specific inbreeding as well as additional overdispersion not caused by inbreeding.