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

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.