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Complex diseases will have multiple functional sites, and it will be invaluable to understand the cross-locus interaction in terms of linkage disequilibrium (LD) between those sites (epistasis) in addition to the haplotype-LD effects.  We investigated the statistical properties of a class of matrix-based statistics to assess this epistasis.  These statistical methods include two LD contrast tests (Zaykin et al., 2006) and partial least squares regression (Wang et al., 2008).  To estimate Type 1 error rates and power, we simulated multiple two-variant disease models using the SIMLA software package.  SIMLA allows for the joint action of up to two disease genes in the simulated data with all possible multiplicative interaction effects between them.  Our goal was to detect an interaction between multiple disease-causing variants by means of their linkage disequilibrium (LD) patterns with other markers.  We measured the effects of marginal disease effect size, haplotype LD, disease prevalence and minor allele frequency have on cross-locus interaction (epistasis).In the setting of strong allele effects and strong interaction, the correlation between the two disease genes was weak (r = 0.2).  In a complex system with multiple correlations (both marginal and interaction), it was difficult to determine the source of a significant result.  Despite these complications, the partial least squares and modified LD contrast methods maintained adequate power to detect the epistatic effects; however, for many of the analyses we often could not separate interaction from a strong marginal effect.  While we did not exhaust the entire parameter space of possible models, we do provide guidance on the effects that population parameters have on cross-locus interaction.

Assessment of LD Matrix Measures for the Analysis of Biological Pathway Association