Modeling linkage disequilibrium in exact linkage computations: a comparison of first-order Markov approaches and the clustered-markers approach

Abstract

Recent studies have shown that linkage disequilibrium (LD) between single-nucleotide polymorphism (SNP) markers is widespread. Assuming linkage equilibrium has been shown to cause false positives in linkage studies where parental genotypes are not available. Therefore, linkage analysis methods that can deal with LD are required to accurately analyze SNP marker data sets. We compared three approaches to deal with LD between markers: 1) The clustered-markers approach implemented in the computer program MERLIN; 2) The standard hidden Markov model (HMM) multipoint model augmented with a first-order Markov model for the allele frequencies of the founders, in which we considered both a Bayesian and a maximum-likelihood implementation of this approach; 3) The 'independent' SNPs approach, i.e., removing SNPs from the data set until the remaining SNPs have low levels of LD.We evaluated these approaches on the Illumina 6K SNP data set of affected sib-pairs of Problem 2. We found that the first-order Markov model was able to account for most of the strong LD in this data set. The difference between the Bayesian and maximum- likelihood implementation was small. An advantage of the first-order Markov model is that it does not require the user to specify parameters.

Figure 1

Assessment of LD between markers. r² was estimated for adjacent markers, every second marker, every third marker, and every tenth marker (denoted by respectively, Δ = 1, Δ = 2, Δ = 3, and Δ = 10). The left panel shows histogram of r² over marker pairs for different Δ, the middle panel shows mean value of r² as a function of Δ, and the right panel shows scatter plot of r² as modeled by the FOMM vs. r² as estimated from the data for Δ = 2.

Figure 2

Comparison of approaches in the region on chromosome 6 with the highest score. Top panel show nonparametric linkage statistic Z_pairs and bottom panel shows estimated pair-wise LD correlation coefficient (r²) (black) and standard deviation (gray) as estimated from the posterior distribution over the LD parameters computed with the Bayesian FOMM approach.