In case-control studies identifying disease susceptibility loci, it has been shown that the interaction caused by multiple single nucleotide polymorphisms (SNPs) within a gene as well as by SNPs at unlinked genes plays an important role in influencing risk of a disease. A novel statistical approach is proposed to detect gene-gene interactions at the allelic level contributing to a disease trait. With a new allelic score inferred from the observed genotypes at two or more unlinked SNPs, we derive a score test from logistic regression and test for association of the allelic scores with a disease trait. Furthermore, F and likelihood ratio tests are derived from Cochran-Armitage regression. By testing for the association, the interaction can be assessed both in cases where the SNP association can be detected and cannot be detected as a main effect in single SNP approach. The analytical power and type I error rates over 6 two-way interaction models are investigated based on the non-centrality parameter approximation of the score test. Simulation studies demonstrate that (1) the power of the score test is asymptotically equivalent to that of the test statistics by the Cochran-Armitage method and (2) the allelic based method provides higher power than two genotypic based methods.
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