Searching for epistasis and linkage heterogeneity by correlations of pedigree-specific linkage scores

Abstract

Recognizing that multiple genes are likely responsible for common complex traits, statistical methods are needed to rapidly screen for either interacting genes or locus heterogeneity in genetic linkage data. To achieve this, some investigators have proposed examining the correlation of pedigree linkage scores between pairs of chromosomal regions, because large positive correlations suggest interacting loci and large negative correlations suggest locus heterogeneity (Cox et al. [1999]; Maclean et al. [1993]). However, the statistical significance of these extreme correlations has been difficult to determine due to the autocorrelation of linkage scores along chromosomes. In this study, we provide novel solutions to this problem by using results from random field theory, combined with simulations to determine the null correlation for syntenic loci. Simulations illustrate that our new methods control the Type-I error rates, so that one can avoid the extremely conservative Bonferroni correction, as well as the extremely time-consuming permutational method to compute P-values for non-syntenic loci. Application of these methods to prostate cancer linkage studies illustrates interpretation of results and provides insights into the impact of marker information content on the resulting statistical correlations, and ultimately the asymptotic P-values.

Fig. 1

Autocorrelation of fraction of alleles shared identical-by-descent for an affected sib pair [Cor(π(s), π(t))] as a function of marker spacing (gap = |t−s|) and their sliding distance to a trait locus at 50cM with genetic effect size λ (assuming a single locus with no dominance effect).

Fig. 2

Pedigree structure for simulations.

Fig. 3

P-values for z- and t-statistics over all simulations (transformed to −log₁₀).

Fig. 4

Contours of within-chromosome correlations for all 1,000 simulated pedigrees for chromosome-1 (253 cM; panel A) and chromosome-2 (42 cM; panel B).

Fig. 5

Area scale (|Λ|^1/2) within chromosomes (upper left panel) and between pairs of different chromosomes (remaining panels) for Mayo observed data.