Testing linkage disequilibrium from pooled DNA: a contingency table perspective

Pooling DNA samples of multiple individuals has been advocated as a method to reduce genotyping costs. Under such a scheme, only the allele counts at each locus, not the haplotype information, 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 the margins and the haplotype counts correspond to the unobserved cell counts. We show that the cell frequencies can be uniquely determined from the marginal frequencies under the usual Hardy-Weinberg equilibrium (HWE) assumption and that the maximum likelihood estimates of haplotype frequencies are consistent and asymptotically normal as the number of pools increases. The limiting covariance matrix is shown to be closely related to the extended hypergeometric distribution. Our results are used to derive Wald-type tests for linkage disequilibrium (LD) coefficient using pooled data. It is discovered that pooling is not efficient in testing weak LD despite its efficiency in estimating haplotype frequencies. We also show by simulations that the proposed LD tests are robust to slight deviation from HWE and to minor genotype error. Applications to two real angiotensinogen gene data sets are also provided.