Supplementary Material for: A New Strategy for Linkage Analysis under Epistasis Taking into Account Genetic Heterogeneity

<i>Background/Aims:</i> Epistasis, the biological interaction of multiple genes modulating their individual effects, is likely omnipresent in complex diseases, and modelling epistasis in linkage studies can help detect loci with little marginal effect and detect epistatic effects themselves. We propose a complete three-step strategy for parametric linkage analysis under epistasis and heterogeneity in extended pedigrees. <i>Methods:</i> (1) Loci most likely involved in epistatic interactions are pre-screened using two-locus one-marker analyses. (2) Among selected loci, linkage to each locus is evaluated conditionally on linkage information at another locus under two-locus epistatic models. Linkage statistics are maximized over a space of epistatic models to avoid misspecification of model parameters. (3) Families linked to the conditioning locus are selected to deal with heterogeneity between pairs of epistatically interacting loci and other unlinked loci. Properties of conditional linkage statistics prevent the introduction of bias. <i>Results:</i> Simulations reveal important gains in power to detect a locus with weak marginal effect involved in epistatic interaction. Application of our methods to schizophrenia and bipolar disorder in Eastern Quebec kindreds suggests epistasis between three locus pairs for bipolar disorder: 8p11-16p13, 15q11-16p13 and 18q12-15q11. <i>Conclusion:</i> These results suggest that the proposed strategy is powerful for tackling complex phenotypes involving epistasis and heterogeneity.