Composite measure of linkage disequilibrium for testing interaction between unlinked loci

Widely used statistical interaction models essentially treated the interaction effect as a residual term and hence are likely to limit the power to detect interaction. Alternatively, interactions between two loci can be understood as irreducible dependencies between loci causing disease or viewed as the linkage disequilibrium (LD) between them. This motivated the development of LD-based statistics for the detection of interaction between two loci. Although LD-based statistics have demonstrated high power to detect interaction between two loci, in general, linkage phase information of marker loci for unrelated individuals is unknown. To overcome this limitation, we classify the interaction between two loci into intragametic interaction that characterizes interaction of two alleles from different loci on the same haplotype and intergametic interaction that characterizes the interaction of two alleles from different loci on different haplotypes. Then we show that intragametic and intergametic interaction will lead to the corresponding intragametic and intergametic LD. This stimulates the use of composite measure of LD for developing statistics to detect interaction between two unlinked loci. To study the validity of the composite LD-based statistic for testing interaction, we estimate its type 1 error rates by simulation. To evaluate the performance of the composite LD-based statistic for detection of interaction between two loci, we compare its power with logistic regression and apply it to two real examples. The preliminary results demonstrate that the composite LD-based statistic is a strong alternative to the logistic regressions and the intragametic LD-based statistic for the detection of interaction between two unlinked loci.