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

Abstract

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.

Linkage analyses of rheumatoid arthritis and related quantitative phenotypes: the GAW15 experience

“…However, as pointed out by Yang et al [2007], analyzing quantitative traits in affected sib-pair study designs may lead to reduced evidence of linkage. Moreover, violations in probability distribution assumptions of the quantitative trait like normality or symmetry due to skewness or ascertainment bias can result in reduced power to detect linkage, and hence, nonparametric statistical methods may be more suitable under such scenarios [Ghosh et al, 2007].…”

“…In order to validate this hypothesis for a non-parametric regression method, Ghosh et al [2007] extended their earlier method using squared differences only [Ghosh and Majumder, 2000] to a combined nonparametric regression strategy incorporating both squared differences and squared sums. Based on the simulated data set, they found that there was indeed a substantial increase in power.…”

“…Using the NAR-AC data set, Yang et al [2007] and Zhou et al [2007] analyzed anti-CCP levels while Taylor et al [2007] considered both RF-IgM and anti-CCP. Ghosh et al [2007] performed a genome-wide linkage scan on RF-IgM levels using the simulated data set. The measurement of low RF-IgM values and high anti-CCP values are not very reliable (GAW15 Problem 2 notes).…”