Data
For the 757 families in the NARAC data, genotypes of 404 single-nucleotide polymorphisms (SNPs) and 27 microsatellites on chromosome 6 were combined for the estimation of IBD. There were 1019 ARPs with genotypes, including 877 full siblings (FS), 45 HS, 13 first cousins (FC), and 84 AP. Only FS, HS, and AP were used in our analyses because each had reasonable sample size. For the Canada-Illumina data, there were 59 ASPs genotyped from 59 families with 404 SNPs on chromosome 6. The French data contained 88 families with 119 ASPs, with 64 microsatellite markers on chromosome 6. We used the first screen of the United Kingdom (UK) data, combining 18 microsatellite markers genotyped on 175 families with 667 SNPs genotyped on 157 families. There were 237 ASPs in the UK data. RA affection status was the only phenotype analyzed.
To avoid biased estimates of IBD from linkage disequilibrium (LD) among high-density SNPs, markers with pair wise r2 > 0.5 and all intervening markers were joined into clusters to estimate IBD scores, using the software Merlin (version 1.0.1) [9, 10].
GEEARP analysis
The unknown parameters in the mean function are the locations (τ1 and τ2) of two susceptibility loci, and genetic effects for each locus (C1kand C2k, the effects of genes at τ1 and τ2 for the kth type of ARP). When the two disease susceptibility loci are linked, C1kand C2kdo not represent the marginal effects of each locus, but rather they incorporate the effect of each other, and thus they change with the recombination fraction between them. When there are several kinds of ARPs, this method involves a large number of parameters (i.e., two genetic effects per ARP type), which can cause considerable variability in parameter estimates, especially when the numbers of the different types of ARPs are small. To reduce the number of parameters, we also fit a constrained model, which constrains the genetic effect of each locus across the different types of ARPs. That is, based on results from Risch [13], the risk ratio λ is a function of genetic effect C, and under no dominance and no epistasis (i.e., genetic relative risks are multiplicative), the genetic effects (Cik) can be formulated as functions of only one parameter for each locus, λ
i
, i = 1 or 2. A score test proposed by Schaid et al. [6] tests the homogeneity of risk ratios across different types of ARPs, and has an approximate chi-square distribution. Both unconstrained and constrained models were fit to the pooled data, for both one-locus and two-locus models.