| In previous work, we have developed a Bayesian approach to linkage analysis based on the posterior probability of linkage (PPL). To date, however, the method has assumed linkage equilibrium in the population from which the families are sampled. We have now generalized the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model including the locus heterogeneity (admixture) parameter and other trait model parameters, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. In the case of SNPs, the likelihood can be parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. We have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples. We have applied the method to a previously published schizophrenia dataset, where strong LD has been detected between the region of CAPON on chromosome 1q22 and schizophrenia. Stronger linkage signals have been obtained using the LD-PPL than using the PPL, suggesting the LD-PPL method may be more powerful for gene identification even in complex disorders. In addition, the estimates of LD differ from previously published results, indicating even stronger LD with schizophrenia and a different pattern of LD across the gene. |
