  Interactions among multiple genes across the genome may contribute to the
risks of many complex human diseases. Whole-genome single nucleotide
polymorphisms (SNPs) data collected for many thousands of SNP markers from
thousands of individuals under the case--control design promise to shed light
on our understanding of such interactions. However, nearby SNPs are highly
correlated due to linkage disequilibrium (LD) and the number of possible
interactions is too large for exhaustive evaluation. We propose a novel
Bayesian method for simultaneously partitioning SNPs into LD-blocks and
selecting SNPs within blocks that are associated with the disease, either
individually or interactively with other SNPs. When applied to homogeneous
population data, the method gives posterior probabilities for LD-block
boundaries, which not only result in accurate block partitions of SNPs, but
also provide measures of partition uncertainty. When applied to case--control
data for association mapping, the method implicitly filters out SNP
associations created merely by LD with disease loci within the same blocks.
Simulation study showed that this approach is more powerful in detecting
multi-locus associations than other methods we tested, including one of ours.
When applied to the WTCCC type 1 diabetes data, the method identified many
previously known T1D associated genes, including PTPN22, CTLA4, MHC, and IL2RA.
