Weighting improves the "new Haseman-Elston" method

Elston et al. [Genet Epidemiol, in press] apply the results of Wright [Am J Hum Genet 1997;60:740-742] and Drigalenko [Am J Hum Genet 1998;63:1242-1245] to extend the traditional Haseman-Elston regression scheme [Haseman and Elston, Behav Genet 1972;2:3-19] to include not only linkage information contained in the sib pair's squared difference, but also information in their mean-corrected squared sum. The new algorithm detects linkage to a quantitative trait locus by modelling sib pair trait covariance as a function of identity-by-descent status. We demonstrate why this new estimator is suboptimal and can in some cases be inferior to the original Haseman-Elston method. We also describe a simple approach to estimation which improves on this new Haseman-Elston method by incorporating variance-based weights into the test statistic while staying within the linear modelling framework. In support of our theoretical claim, we conduct both a sib pair simulation and an application to GAW 10 sib pair data showing that our new estimator is superior to both the old and new Haseman-Elston schemes currently implemented in the analysis package S.A.G.E. 4.0.