Multiple Regression Approach to Mapping of Quantitative Trait Loci (qtl) Based on Sib-pair Data: a Theoretical Analysis

The interval mapping method has been shown to be a powerful tool for mapping QTL. However, it is still a challenge to perform a simultaneous analysis of several linked QTLs, and to isolate multiple linked QTLs. To circumvent these problems, multiple regression analysis has been suggested for experimental species. In this paper, the multiple regression approach is extended to human sib-pair data through multiple regression of the squared difference in trait values between two sibs on the proportions of alleles shared identical by descent by sib pairs at marker loci. We conduct an asymptotic analysis of the partial regression coefficients, which provide a basis for the estimation of the additive genetic variance and of locations of the QTLs. We demonstrate how the magnitude of the regression coefficients can be used to separate multiple linked QTLs. Further, we shall show that the multiple regression model using sib pairs is identifiable, and our proposed procedure for locating QTLs is robust in the sense that it can detect the number of QTLs and their locations in the presence of several linked (QTLs) in an interval, unlike a simple regression model which may find a “ghost” QTL with no effect on the trait in the interval with several linked QTLs. Moreover, we give procedures for computing the threshold values for prespecified significance levels and for computing the power for detecting (QTLs). Finally, we investigate the consistency of the estimator for QTL locations. Using the concept of epi-convergence and variation analysis theory, we shall prove the consistency of the estimator of map location in the framework of the multiple regression approach. Since the true IBD status is not always known, the multiple regression of the squared sib difference on the estimated IBD sharing is also considered.