Testing association with interactions by partitioning chi-squares

Gene-gene interaction plays an important role in association studies for complex diseases. There have been different approaches to incorporating gene-gene interactions in candidate gene or genome-wide association studies, especially for those genes with no marginal effects but with interaction effects. However, there is no general agreement on how interaction should be tested and how main effects and interaction effects act on a significance signal. In this paper, we propose a test of the null hypothesis of no association in terms of interaction effects for two unlinked loci, which is a 4 degrees of freedom (df) chi-square for two SNPs. The test, derived by contrasting inter-locus disequilibrium measures between cases and controls, can be viewed as the interaction component of the total Pearson chi-square. The remaining portion of the total chi-square can also be used for association analysis, which emphasizes main effects. Simulation studies show that in most situations our interaction test is similar in power to the test based on a logistic regression model but has more power when the genes have no marginal effects. Results also show that single-locus marginal tests can lose much power if interaction effects dominate main effects. For some specific genetic models, the interaction test may be further partitioned into four 1-df chi-squares for individual interaction effect. The interaction pattern can best be demonstrated by the 1-df chi-square components. Simulation results show that there is substantial power gain if interaction patterns are properly incorporated in association analysis.