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We also filtered out SNPs with a genotype missing rate >5%. The remaining missing genotypes were resampled from nonmissing individuals. Xi=1,ifanyxi,j=10,otherwise Next, we grouped variants into sets based on RefSeq gene ALPI annotations [10], requiring SNPs lie between the RefSeq transcript start site and transcript end site. SNPs outside gene boundaries were not analyzed. In total, 10,148 genes from odd-numbered chromosomes were used. Finally, we collapsed singletons within each gene. A singleton was a variant being observed only once among all the samples. The rationale of collapsing singletons was that the distribution of singletons as 1 variable may reflect the association between genotype and phenotype. Hence, we created 1 supervariant for each gene by combining all the singletons within it using the following rules: for each sample, (a) the genotype was set to be 1, if there was at least 1 variant observed; (b) otherwise, the genotype was set to be 0. Rare-variant association tests We employed 3 recently published rare association tests, qMSAT [7], C-alpha [8], and CMC [9]. The qMSAT is a quality-weighted multivariate score association test that can utilize genotype quality information. However, genotype quality score information was not available in the GAW18 raw VCF files. Without utilizing quality information, the qMSAT test was equivalent to OTX015 mouse the linear sequence kernel association test (SKAT) [6], Sum of Squared U statistic test (SSU) [11], and C-alpha. The C-alpha test compared the assumed binomial distribution of rare variants in cases versus controls via a homogeneity test. CMC, a combined multivariate and collapsing method, collapsed variants in subgroups according to allele frequencies and combines these subgroups using Hotelling's T2 test. For these 3 tests, we used permutation to evaluate association significance. Because permutation was computationally expensive, we utilized a 2-step strategy in searching and testing candidate loci. Specifically, we first used 1000 permutations, from which we can identify candidates with estimated p value Rucaparib nmr approximately 2.2 million rare variants, which were assigned to 10,148 genes for testing. We then performed the 3 tests, qMSAT, C-alpha, and CMC, using R (http://www.r-project.org). The qMSAT, C-alpha, and CMC identified 10, 6, and 7 genes with an estimated p value