Fig 1.
Conceptual difference between the conventional score test and the proposed new score tests.
Conceptual difference between the conventional score test (CST) and the proposed new score tests (PM1 and PM2). Outcomes (Y) and covariates (E) are observed in all individuals. NA indicates missing genotype. In CST, null estimation is performed for each SNP excluding individuals with missing genotype. On the other hand, null estimation required in PM1 or PM2 is common in all SNP.
Table 1.
Type I error rates of the conventional score test and the proposed methods.
Fig 2.
Q-Q plot of the conventional score test and the proposed methods.
Chi-squared (1-df or 2-df) Q-Q plot of the top 500 conventional score test, the proposed method 1, and the proposed method 2 score statistics for missing rate is 5% and minor allele frequency (MAF) is 10% and 30% in null simulation.
Fig 3.
G test Power of the conventional score test and the proposed methods at MAF 30%.
G test Power of the conventional score test (CST), the proposed method 1 (PM1), and the proposed method 2 (PM2) under missing rate (2%, 5%, 10%), minor allele frequency (MAF) (30%), and the number of case/control (1,000, 5,000). The x-axis denotes genetic odds ratios (ORg = exp(βg)). The significance level is 5 × 10−8.
Fig 4.
G-GE test Power of the conventional score test and the proposed methods at the number of case/control is 1,000.
G-GE test Power of the conventional score test (CST), the proposed method 1 (PM1), and the proposed method 2 (PM2) under genetic odds ratios (ORg = exp(βg) = 1.1, 1.2), missing rate (2%, 5%, 10%), minor allele frequency (MAF) (30%), and the number of case/control is 1,000. The x-axis denotes gene-environment interaction odds ratios (ORge = exp(βge)). The significance level is 5 × 10−8.
Fig 5.
G-GE test Power of the conventional score test and the proposed methods at the number of case/control is 5,000.
G-GE test Power of the conventional score test (CST), the proposed method 1 (PM1), and the proposed method 2 (PM2) under genetic odds ratios (ORg = exp(βg) = 1.1, 1.2), missing rate (2%, 5%, 10%), minor allele frequency (MAF) (30%), and the number of case/control is 5,000. The x-axis denotes gene-environment interaction odds ratios (ORge = exp(βge)). The significance level is 5 × 10−8.
Fig 6.
Manhattan plots of each chromosome for ADNI-GWAS dataset with all SNPs.
Manhattan plots of each chromosome for ADNI-GWAS dataset. P-values using the conventional score test (CST), the proposed method 1 (PM1) test, the proposed method 2 (PM2) test, the Wald test, and the likelihood ratio test are shown in order from the top. The black and gray points highlight different chromosomes.
Fig 7.
Comparisons of the proposed methods and the conventional score test P-values with the subset SNPs with missing genotypes.
Comparisons of the proposed methods (PM1 and PM2) and the conventional score test (CST) P-values that displays only top 1,000. SNPs are stratified by missing rate (low missing SNPs: 0% < Missing rate < 1%, high missing SNPs: Missing rate ≥ 1%).
Table 2.
Run times (CPU sec) from the proposed methods and the conventional tests.