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 coeffcients, 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.