# In genome-wide association studies (GWAS), multiple diseases with shared controls is

In genome-wide association studies (GWAS), multiple diseases with shared controls is one of the case-control study designs. the whole dataset including the controls. We also apply the proposed method to a real GWAS dataset to illustrate the methodologies and the advantages of the proposed design. Some possible limitations of this study design and screening method and their solutions are also discussed. Our findings show the proposed study design and statistical analysis strategy could be more efficient than the usual case-control GWAS as well as those with shared controls. + 1) 3 contingency table, where is the quantity of diseases. Specifically, for a given SNP, you will find three possible genotypes and we have a (+ 1) 3 contingency table, where the (+ 1)th disease is the control. Under the null hypothesis that a particular SNP is usually associated with none of the diseases, the chi-square test statistic based on this (+ 1) 3 contingency table has an asymptotic chi-square distribution with degrees of freedom (df) equal to 2 3 contingency table when the shared controls are ignored. To study NCH 51 manufacture the power properties of the overall chi-square assessments with and without controls, a simulation study is performed to compare the power of the overall test without controls with those assessments with different numbers of controls. These simulation results show that when the number of diseases is not too small (say, greater than or equal to 4), using controls does not provide any gain in the statistical power. 2 Material and Methods 2.1 Pearsons Chi-square Tests for Associations Suppose that a SNP has two alleles, and diseases and a control group can be presented as a (+ 1) 3 contingency table. To detect whether the genotype is usually associated with any disease, we can use the following Pearsons chi-square test: is the quantity of subjects with disease (the + 1 disease is usually representing the control) with MDK genotype = 1, 2, , + 1, = 1, 2, 3, and is the expected value of the . Under the null hypothesis that no association between the genotype and any disease, the genotypic frequencies for each disease should be the same as those of the control and the statistic in (1) has an asymptotic chi-square distribution with 2df. If the controls in the dataset are ignored, we will have a 3 contingency table with the last row being removed. The following chi-square test can be used: is the expected value of the . Similar to the statistic in (1), the statistic in (2) has an asymptotic chi-square distribution with 2(?1) df under the null hypothesis of no associations. Another statistical process that can be used to NCH 51 manufacture detect associated SNPs by comparing one disease with controls is based on the chi-square partition (CSP) method. For one disease, the count data can be presented as a 2 3 table where the rows represent the disease and control and the columns represents the three NCH 51 manufacture genotypes, is usually at-risk) will be applied and the two is usually at-risk. Then, the overall = 2, 4, 6, and 8 with 1,000 cases for each disease, and the ratio of quantity of controls to the number of cases in each diseases, = 0, 0.5, 1, 1.5 and 2. Note that = 0 is the case without controls. We presume Hardy-Weinberg Equilibrium (HWE) holds for controls and the minor allele frequency (maf) 0.1, 0.3 and 0.5 are considered. The genotype frequencies of NCH 51 manufacture the three genotypes for each disease and control are assumed to be trinomial distributed. For given genotype frequencies of controls, the relative risk of genotype to genotype (denoted as to genotype (denoted as diseases. The significance level of the statistical test is set to be = 10?3 and 105 replications are used to estimate the type I error rates and power values of different test procedures. 3 Results 3.1 Real Data Example Based on the GWAS described in Section 2.2, we first compare the overall chi-square assessments with and without controls when they are applied to MHC SNPs..