Statistical modelling of inter-locus interactions in a complex disease: rejection of the multiplicative model of epistasis in type 1 diabetes

In general, common diseases do not follow a Mendelian inheritance pattern. To identify disease mechanisms and etiology, their genetic dissection may be assisted by evaluation of linkage in mouse models of human disease. Statistical modeling of multiple-locus linkage data from the nonobese diabetic (NOD) mouse model of type 1 diabetes has previously provided evidence for epistasis between alleles of several Idd (insulin-dependent diabetes) loci. The construction of NOD congenic strains containing selected segments of the diabetes-resistant strain genome allows analysis of the joint effects of alleles of different loci in isolation, without the complication of other segregating Idd loci. In this article, we analyze data from congenic strains carrying two chromosome intervals (a double congenic strain) for two pairs of loci: Idd3 and Idd10 and Idd3 and Idd5. The joint action of both pairs is consistent with models of additivity on either the log odds of the penetrance, or the liability scale, rather than with the previously proposed multiplicative model of epistasis. For Idd3 and Idd5 we would also not reject a model of additivity on the penetrance scale, which might indicate a disease model mediated by more than one pathway leading to beta-cell destruction and development of diabetes. However, there has been confusion between different definitions of interaction or epistasis as used in the biological, statistical, epidemiological, and quantitative and human genetics fields. The degree to which statistical analyses can elucidate underlying biologic mechanisms may be limited and may require prior knowledge of the underlying etiology.