The genetic basis of complex diseases often involves multiple causative loci. Under such a disease etiology, assuming one disease locus in linkage disequilibrium mapping is likely to induce bias and lead to efficiency loss in disease locus estimation. An approach is needed for simultaneously localizing multiple functional loci within the same region. However, due to the increasing number of parameters accompanying disease loci, these estimates can be computationally infeasible. To circumvent this problem, we propose to estimate the main and two-adjacent-locus joint effects and a nuisance parameter at the disease loci separately through a linear approximation. Estimates of the genetic effects are entered into a generalized estimating equation to estimate disease loci, and the procedure is conducted iteratively until convergence. The proposed method provides estimates and confidence intervals (CIs) for the disease loci, the genetic main effects, and the joint effects of two adjacent disease loci, with the CIs for the disease loci providing useful regions for further fine-mapping. We apply the proposed approach to a data example of case-control studies. Results of the simulations and data example suggest that the developed method performs well in terms of bias, variance, and coverage probability under scenarios with up to three disease loci.
