Testing multiple gene interactions by the ordered combinatorial partitioning method in case–control studies

Abstract

The multifactor-dimensionality reduction (MDR) method has been widely used in multi-locus interaction analysis. It reduces dimensionality by partitioning the multi-locus genotypes into a high-risk group and a low-risk group according to whether the genotype-specific risk ratio exceeds a fixed threshold or not. Alternatively, one can maximize the chi(2) value exhaustively over all possible ways of partitioning the multi-locus genotypes into two groups, and we aim to show that this is computationally feasible. We advocate finding the optimal MDR (OMDR) that would have resulted from an exhaustive search over all possible ways of partitioning the multi-locus genotypes into two groups. It is shown that this optimal MDR can be obtained efficiently using an ordered combinatorial partitioning (OCP) method, which differs from the existing MDR method in the use of a data-driven rather than fixed threshold. The generalized extreme value distribution (GEVD) theory is applied to find the optimal order of gene combination and assess statistical significance of interactions. The computational complexity of OCP strategy is linear in the number of multi-locus genotypes in contrast with an exponential order for the naive exhaustive search strategy. Simulation studies show that OMDR can be more powerful than MDR with substantial power gain possible when the partitioning of OMDR is different from that of MDR. The analysis results of a breast cancer dataset show that the use of GEVD accelerates the determination of interaction order and reduces the time cost for P-value calculation by more than 10-fold. C++ program is available at http://home.ustc.edu.cn/~zhanghan/ocp/ocp.html