Potts model for haplotype associations

Abstract

Bayesian spatial modeling has become important in disease mapping and has also been suggested as a useful tool in genetic fine mapping. We have implemented the Potts model and applied it to the Genetic Analysis Workshop 14 (GAW14) simulated data. Because the "answers" were known we have analyzed latent phenotype P1-related observed phenotypes affection status (genetically determined) and i (random) in the Danacaa population replicate 2. Analysis of the microsatellite/ single-nucleotide polymorphism-based haplotypes at chromosomes 1 and 3 failed to identify multiple clusters of haplotype effects. However, the analysis of separately simulated data with postulated differences in the effects of the two clusters has yielded clear estimated division into the two clusters, demonstrating the correctness of the algorithm. Although we could not clearly identify the disease-related and the non-associated groups of haplotypes, results of both GAW14 and our own simulation encourage us to improve the efficiency and sensitivity of the estimation algorithm and to further compare the proposed method with more traditional methods.

Fine mapping by linkage and association in nuclear family and case-control designs

“…Two of these selected unrelated population controls [Shepard et al, 2005;Song et al, 2005], and two used family controls, including multiple cases and controls from the same family [Molitor et al, 2005;Moltchanova et al, 2005]. With one exception, association analyses were conducted within a single population, reducing the likelihood of confounding by population stratification.…”

“…The evaluation of marker associations with case-control status is then based on clusters of similar haplotypes rather than on single haplotypes. While both models considered by these groups assumed a logistic penetrance model, the Potts model implemented by Moltchanova et al [2005] assigned haplotypes to clusters probabilistically, while the Voronoi model implemented by Molitor et al [2005] assigned haplotypes deterministically at each iteration. Over the course of iterations, however, the haplotype cluster assignments changed, so a probabilistic distribution for each haplotype was effectively generated.…”

“…The remaining two groups [Molitor et al, 2005;Moltchanova et al, 2005] examined Bayesian spatial modeling of haplotype clusters. The idea underlying this approach is that haplotype clusters can act as a low-dimensional surrogate for the unobserved genealogy reflected in unphased genotype data.…”

“…Over the course of iterations, however, the haplotype cluster assignments changed, so a probabilistic distribution for each haplotype was effectively generated. Moltchanova et al [2005] adopted a two-stage approach in applying the Potts model to the Danacaa (DA) population. In the first stage, individual three-locus haplotypes were estimated from the phase-unknown genotypes for an SNP and its two flanking microsatellite markers, using a pedigree-based EM algorithm for phase determination.…”

“…In contrast, Song et al [2005] constructed composite replicates by pooling three populations with the intention of creating population structure. As in the family-based analyses, both single-marker [Shephard et al, 2005;Song et al, 2005] and haplotype-based [Molitor et al, 2005;Moltchanova et al, 2005;Shephard et al, 2005] analyses were conducted.…”