Bayesian estimates of linkage disequilibrium

Background: The maximum likelihood estimator of D ' - a standard measure of linkage disequilibrium - is biased toward disequilibrium, and the bias is particularly evident in small samples and rare haplotypes. Results: This paper proposes a Bayesian estimation of D ' to address this problem. The reduction of the bias is achieved by using a prior distribution on the pair-wise associations between single nucleotide polymorphisms (SNP)s that increases the likelihood of equilibrium with increasing physical distances between pairs of SNPs. We show how to compute the Bayesian estimate using a stochastic estimation based on MCMC methods, and also propose a numerical approximation to the Bayesian estimates that can be used to estimate patterns of LD in large datasets of SNPs. Conclusion: Our Bayesian estimator of D ' corrects the bias toward disequilibrium that affects the maximum likelihood estimator. A consequence of this feature is a more objective view about the extent of linkage disequilibrium in the human genome, and a more realistic number of tagging SNPs to fully exploit the power of genome wide association studies.