N arbitrary distribution with mean 0 and variance y, testing the null hypothesis, bGm = 0, is equivalent to testing y = 0 (i.e., a variance-component test score done using the corresponding mixed model). For a case-control sample with n individuals sampled and p variants genotyped, G is the n6p matrix of genotypes, and K = GGT is an n6n linear 
kernel matrix, which defines the genetic similarity between all individuals for the p SNPs. The function that links each element of the matrix K to the genotypes G is the kernel function. To test for the association 
between the disease and the SNP-set, the variance-component score statistic Q follows a mixture of chi-square distributions. y Q { K {?y where, is the predicted mean of the vector of disease status values y (y) under the null hypothesis, obtained by regressing y on the adjustment covariates only. For theses analyses, we used the linear kernel (equivalent to fitting the unconditional multivariate logistic regression) and the exact Davies method for computing p-values. Moreover, we tested for association of advanced 15481974 prostate cancer risk with the 320 SNPs individually using unconditional multivariate logistic regression adjusting for age, institution, and genetic ancestry. Odds ratios (ORs), 95 confidence intervals (95 CI) and P-values were estimated using both co-dominant and logadditive models. To adjust for genetic ancestry in all analyses, we included the first principal component of the principal component analysis of the 39 AIMs as covariate. Moreover, to identify SNPs 16574785 with potential opposite effects in African Americans and Caucasians, we also stratified all analyses by reported ethnicity. Our strategy evaluated disease risk association at multiple levels of SNP groupings (whole set, sub-pathways, genes, and individual SNPs). To account for the multiple tests done while incorporating the correlation between SNPs and 4-IBP chemical information genotype coding, we used apermutation procedure to obtain the empirical distribution of statistical tests under the null Fruquintinib site hypothesis of no association with the set of SNPs or SNP. Then for each level of SNP groupings, we calculated a family-wise error rate by comparing the P-value of each test to the distribution of the minimum P-values obtained from 1000 permuted data sets. Reported P-values are two-sided and analyses were done using R v2.13.1 [43].Results Study Subject CharacteristicsThe case-control sample included 1,030 subjects whose average age at diagnosis or recruitment was 65.87 (SD: 8.46) years, and was comprised of 194 African Americans (18.8 ) and 836 Caucasians (81.2 ). Age and ethnicity were similarly distributed in advanced prostate cancer cases and controls (Table 1).Association with Advanced Prostate Cancer RiskTaken together, the whole set of 320 SNPs in the innate immunity and inflammation pathway was significantly associated with advanced prostate cancer risk (P = 0.02). Of the 6 subpathways analyzed, the intracellular antiviral molecules and the extracellular pattern recognition sub-pathways were nominally associated with advanced prostate cancer risk (P = 0.02 for both) but not associated after correction for multiple testing (P = 0.12 and P = 0.11, respectively). Interestingly, 4 genes in these 2 sub-pathways were also nominally associated with prostate cancer risk: TLR1 and TLR6 in the extracellular pattern recognition sub-pathway (P = 0.002 and P = 0.04, respectively), and OAS1 and OAS2 in the intracellular antiviral molecules sub-pathway (P.N arbitrary distribution with mean 0 and variance y, testing the null hypothesis, bGm = 0, is equivalent to testing y = 0 (i.e., a variance-component test score done using the corresponding mixed model). For a case-control sample with n individuals sampled and p variants genotyped, G is the n6p matrix of genotypes, and K = GGT is an n6n linear kernel matrix, which defines the genetic similarity between all individuals for the p SNPs. The function that links each element of the matrix K to the genotypes G is the kernel function. To test for the association between the disease and the SNP-set, the variance-component score statistic Q follows a mixture of chi-square distributions. y Q { K {?y where, is the predicted mean of the vector of disease status values y (y) under the null hypothesis, obtained by regressing y on the adjustment covariates only. For theses analyses, we used the linear kernel (equivalent to fitting the unconditional multivariate logistic regression) and the exact Davies method for computing p-values. Moreover, we tested for association of advanced 15481974 prostate cancer risk with the 320 SNPs individually using unconditional multivariate logistic regression adjusting for age, institution, and genetic ancestry. Odds ratios (ORs), 95 confidence intervals (95 CI) and P-values were estimated using both co-dominant and logadditive models. To adjust for genetic ancestry in all analyses, we included the first principal component of the principal component analysis of the 39 AIMs as covariate. Moreover, to identify SNPs 16574785 with potential opposite effects in African Americans and Caucasians, we also stratified all analyses by reported ethnicity. Our strategy evaluated disease risk association at multiple levels of SNP groupings (whole set, sub-pathways, genes, and individual SNPs). To account for the multiple tests done while incorporating the correlation between SNPs and genotype coding, we used apermutation procedure to obtain the empirical distribution of statistical tests under the null hypothesis of no association with the set of SNPs or SNP. Then for each level of SNP groupings, we calculated a family-wise error rate by comparing the P-value of each test to the distribution of the minimum P-values obtained from 1000 permuted data sets. Reported P-values are two-sided and analyses were done using R v2.13.1 [43].Results Study Subject CharacteristicsThe case-control sample included 1,030 subjects whose average age at diagnosis or recruitment was 65.87 (SD: 8.46) years, and was comprised of 194 African Americans (18.8 ) and 836 Caucasians (81.2 ). Age and ethnicity were similarly distributed in advanced prostate cancer cases and controls (Table 1).Association with Advanced Prostate Cancer RiskTaken together, the whole set of 320 SNPs in the innate immunity and inflammation pathway was significantly associated with advanced prostate cancer risk (P = 0.02). Of the 6 subpathways analyzed, the intracellular antiviral molecules and the extracellular pattern recognition sub-pathways were nominally associated with advanced prostate cancer risk (P = 0.02 for both) but not associated after correction for multiple testing (P = 0.12 and P = 0.11, respectively). Interestingly, 4 genes in these 2 sub-pathways were also nominally associated with prostate cancer risk: TLR1 and TLR6 in the extracellular pattern recognition sub-pathway (P = 0.002 and P = 0.04, respectively), and OAS1 and OAS2 in the intracellular antiviral molecules sub-pathway (P.
