Materials
Data from a total of 1096 affected sib pairs from 757 multiplex families in the North American Arthritis Consortium study (NARAC) were included. Only 615 or 627 sib pairs (depending on the chromosomal regions) had genotype information, and thus these were used for our analysis. The NARAC multiplex families contain 8017 individuals, about 90.6% of whom are Caucasian, the rest are Hispanic (5.42%), African-American (2.92%), Native American (0.57%), and Asian (0.51%). When we performed the analyses using the subset of Caucasians and the whole data set, the results were quite similar; hence, we report only the results from whole data set here.
A total of 375 microsatellite markers were used in the analyses. The genotype data for 12 affected sib pairs on chromosomes 1 to 11, 13 to 16, and 19 to 22 were missing; therefore, 615 affected sib pairs were available for those chromosomes and 627 affected sib pairs were available for chromosomes 12, 17, and 18. Due to the missingness of the incorporated quantitative variables, the total number of affected sib pairs being included in the analysis varied from 588 to 622, depending on the quantitative variable and on the genotype data on the chromosomal regions.
Linkage approaches
The GeneHunter program was used to calculate identity by descent (IBD) sharing of affected sib pairs. The GeneFinder program was used to perform the linkage mapping with estimates of C and τ based on the phenotype of disease status only. It provides estimates of τ and its 95% confidence interval as well as the p-value of testing whether C = 0 (namely, if the linkage is present). A Fortran program developed by Chiou et al. [5] was applied to estimate τ and its 95% confidence interval where C was a non-linear function of the quantitative variable and was estimated nonparametrically. C as a function of a quantitative covariate was estimated by such that was the minimizer of the following kernel weighted least squares function with respect to , where was the imputed IBD sharing at (), an estimate of τ. gi1 = g1(xi1, xi2) = (xi1 + xi2)/2, (xi1, xi2) were the values of the quantitative variable for the ith affected sib pair. K2 was a kernel function, and H was a non-singular square bandwidth matrix.
Because this method is an extension to the approach proposed by Liang et al. [4], it is also a robust approach in that no assumption about the genetic mechanism is required other than that the region contains no more than one susceptibility locus for the qualitative trait. No assumption about the underlying genetic mechanism of an incorporated quantitative trait is required.
We compared the results from incorporating the quantitative variable with those obtained from the GeneFinder search to evaluate the efficiency gained by the additional information from a given quantitative variable.