Haplotype Estimation and Linkage Disequilibrium Tests from Pooled DNA:a Contingency Table Perspectiv

Abstract

Pooling DNA samples of multiple individuals has been advocated as a method to reduce genotyping costs. Under such a scheme, only allele counts at each locus, not haplotype counts which are of primary interests, are observed. We develop a systematic way for handling such data by formulating the problem in terms of contingency tables, where pooled allele counts are expressed as margins and haplotype counts correspond to (unobserved) cell counts. We show that the cell frequencies can be uniquely determined from the marginal frequencies under the usual Hardy-Weinberg equilibrium assumption and that the maximum likelihood estimates of haplotype frequencies are consistent and asymptotically normal as number of tables increases. An explicit formula for the limiting covariance matrix is obtained and shown to be closely related to the extended hypergeometric distribution. Efficiency of pooling in estimating haplotype frequencies has been studied by several authors. However, in most association studies, estimation of haplotype frequencies is the first step in analysis of linkage disequilibrium and the more important aspect - efficiency of pooling in testing linkage disequilibrium remains much unknown. Our results are used to derive estimate and novel Wald-type test for linkage disequilibrium coefficient.Efficiency of pooling in testing linkage disequilibrium is studied. The application to a DNA pooling study of the angiotensinogen gene is also provided.