Transformation of sib-pair values for the Haseman-Elston method

Abstract

The squared sib-pair phenotype difference (SQD) has been used as a dependent variable in the Haseman-Elston (H-E) regression quantitative-trait locus (QTL) linkage method, but it has been shown that the SQD does not make full use of linkage information. In this study, we examine the efficiency of SQD in H-E regression compared to other proposed functions of the sib-pair phenotypes. A new function of sib-pair phenotypes, the product of pair values corrected with family mean (PCF), is shown to have desirable properties in many realistic situations. Consistent results were obtained using a combination of large-sample analytic approximations, simulation, and analyses of quantitative-trait data from Genetic Analysis Workshop 10. The advantages of PCF are further improved in the presence of family-specific effects arising from environmental factors or when additional QTLs influence the trait. All of the phenotype functions are incorporated in our new, freely available linkage-mapping program MULTIGENE 1.0 for the PC environment.

Figure 1

Residual ratios calculated from the formulas. Plots A, B, C, and D were obtained under h²=1.0, .8, .5, and .2, respectively. For PRO, ψ was 0 for all of the plots. For PCG, the grand mean is assumed to be known (i.e., limit as the total number of siblings N approaches infinity). The number of siblings per family is denoted by n.

Figure 2

Replicate 19 of GAW 10 problem 2A shows the results from the four transformation schemes. The triangles show the true locations of the QTLs.

Figure 3

Results from 1,000 simulations, illustrating the influence of sibship size on the residual ratio. The sibship sizes varied, but the total sample size N was fixed at 1,000. IBD values were assumed to be known for each sib pair. The QTL phenotypic contribution was h²=.5 with two equally likely alleles, and m=0.

Figure 4

Results of 1,000 simulations, illustrating the influence of family-specific effects on residual ratios. The sibship size was n=4 in all cases, with total sample size N=2,000. IBD values were obtained unambiguously at the QTL.