Abstract:
Unlike qualitative or binary traits which can be characterized completely by allele frequencies and genotypic penetrances, quantitative traits require an additional level of modeling: the probability distribution of the underlying trait. Hence, likelihood based methods like variance components, which requires assumptions like multivariate normality of trait values within a family, may yield misleading linkage inferences when underlying model assumptions are violated. The Haseman-Elston regression method (1972) and its extensions do not assume any specific probability distribution for the trait values, but assume a linear relationship between the squared sib-pair trait differences (or mean-corrected cross products of sib-pair trait values) and the estimated identity-by-descent scores at a marker locus. Since it is often difficult to test the validity of these assumptions, it is of interest to explore for non-parametric alternatives. Ghosh and Majumder (2000) have therefore proposed that it may be strategically more judicious to empirically estimate the nature of dependence of the two above mentioned variables using non-parametric diagnostics like rank correlation or kernel-smoothing regression.
In this study, we extend our earlier methodologies to multipoint mapping and compare their performances to the linear regression procedures of Elston et al. (2000). We find that while the non-parametric regression method is marginally less powerful than the linear regression methods in the absence of dominance, it performs increasingly better as dominance increases. The non-parametric method also outperforms the linear regression procedures with increasing deviation of the distribution of trait values from normality.
We have used the non-parametric regression method to analyze data on Slow Beta EEG waves collected by the Collaborative Study on the Genetics of Alcoholism project. We have obtained statistically significant signals of linkage on Chromosomes 1, 4, 5 and 15. We have also investigated the presence of epistatic interactions between regions exhibiting significant linkage. Evidence of epistasis was found between regions on Chromosomes 1 and 4 with those on Chromosome 15.