A nonparametric regression-based linkage scan of rheumatoid factor-IgM using sib-pair squared sums and differences

Parametric linkage methods for quantitative trait locus mapping require explicit specification of the probability model of the quantitative trait and hence can lead to misleading linkage inferences when the model assumptions are not valid. Ghosh and Majumder developed a nonparametric regression method based on kernel-smoothing for linkage mapping of quantitative trait locus using squared differences in trait values of independent sib pairs, which is relatively more robust than parametric methods with respect to violations in distributional assumptions. In this study, we modify the above mentioned nonparametric regression method by considering local linear polynomials instead of the Nadaraya-Watson estimator and squared sums of sib-pair trait values in addition to squared differences to perform a genome-wide scan of rheumatoid factor-IgM levels on sib pairs in the Genetic Analysis Workshop 15 simulated data set. We obtain significant evidence of linkage very close to the quantitative trait locus controlling for RF-IgM. We find that the simultaneous use of squared differences and squared sums increases the power to detect linkage compared to using only squared differences. However, because of all the sib pairs are selected for rheumatoid arthritis, there is reduced variance of RF-IgM values, and empirical power to detect linkage is not very high. We also compare the performance of our method with two linear regression approaches: the classical Haseman-Elston method using squared sib-pair trait differences and its extension proposed by Elston et al. using mean-corrected sib-pair cross-products. We find that the proposed nonparametric method yields more power than the linear regression approaches.