Statistical Framework for Association Analysis
We used the following analyses to test associations between HLA variants and risk of four binary phenotypes: (1) overall analysis of PsV susceptibility (PsV-affected versus control individuals), (2) stratified analysis of PsA susceptibility (PsA-affected versus control individuals), (3) stratified analysis of PsC susceptibility (PsC-affected versus control individuals), and (4) intra-PsV analysis directly comparing PsA to PsC (PsA-affected versus PsC-affected individuals). For each phenotype, we assessed variant risk with a logistic-regression model assuming additive effects of the allele dosages in the log-odds scale and their fixed effects among the data-set collections. We defined HLA variants to include biallelic SNPs in the MHC region, two- and four-digit biallelic classical HLA or MICA alleles, biallelic HLA or MICA amino acid polymorphisms for respective residues, and multiallelic HLA or MICA amino acid polymorphisms for respective positions. To account for potential population-based and data-set-specific confounding factors, we included the top ten PCs and an indicator variable for each data set as covariates. For HLA variants with m alleles (m = 2 for biallelic variants and m > 2 for multiallelic variants), we included m − 1 alleles, excluding the most frequent allele as a reference, as independent variables in the regression model. This resulted in the following logistic-regression model:log(odds)=β0+∑j=1m−1β1,jxj+∑k=1K(∑l=1Lβ2,k,lyk,l+β3,kzk)+ε,where β0 is the logistic-regression intercept and β1,j is the additive effect of the dosage of allele j for the variant xj. K and L are numbers of the collections and PCs enrolled in the analysis. yk,l is the lth PC for the kth collection, and zk is the indicator variable for the collection-specific intercept. β2,k,l and β3,k parameters are the effects of yk,l and zk, respectively. An omnibus p value of the variant (pomnibus) was obtained by a log-likelihood ratio test comparing the likelihood of the null model against the likelihood of the fitted model. We assessed the significance of the improvement in fit by calculating the deviance (−2 × the log likelihood ratio), which follows a χ2 distribution with m − 1 degree(s) of freedom.