We evaluated the power and false-positive rates of the FLASSO, Flinear, QCMC(0.01), and QCMC(0.05) tests based on the 200 replicates of the GAW17 data set. The significance level of the tests was first set to 1.6 × 10–5, which is the Bonferroni-corrected significance level of 0.05 adjusted by the number of genes, that is, 0.05/3,205. However, because of the small sample sizes in the GAW17 data set, the power of the association tests was poor and could not be compared in our four tests. Therefore we also used the weak significance level of 0.01 for method comparison.
We examined the answers to the GAW17 simulation after our association analyses were completed. In the answers, Q2 is influenced by 72 SNPs in 13 genes, where the MAFs and effect sizes (βi
, the elements of β
) could be found for each causal SNP. Thus the variance contributed by each SNP to the phenotype could be calculated as
under the assumption of an additive model, where q
is the MAF. Therefore we calculated the variance contribution for a gene using:
As shown in Table , both genes VNN3 and VNN1 have a variance contribution of approximately 0.02; SREBF1, BCHE, VLDLR, SIRT1, PDGFD, LPL, and PLAT have variance contributions of approximately 0.01 individually; and RARB, GCKR, VWF, and INSIG1 have variance contributions between 0.0002 and 0.005. The power is dependent on the variance attributed to the gene.
True variance contributions of 13 causal genes given in the GAW17 answers
We evaluated the power of the four methods based on the 13 causal genes using the 200 replicates (Figure ). In general, the LASSO regression outperformed linear regression for all causal genes and gained more than 10% power on the first four genes, as shown in Figure . The QCMC(0.01) method performed better than the QCMC(0.05) method because 91.7% of the MAFs of causal SNPs were less frequent than 0.01. Except for the VNN1 and SREBF1 genes, the LASSO method was more powerful than the two QCMC methods. This is quite easy to understand. The VNN1 gene has two causal SNPs, which have MAFs of 0.006 and 0.17, and all the causal SNP variants are less frequent than 0.005 in the SREBF1 gene. For this reason, both the QCMC(0.01) and the QCMC(0.05) tests are able to collapse the causal SNPs perfectly and thereby lead to a higher power than the LASSO approach for these two genes.
Figure 1 Power to detect 13 causal genes at the significance levels of 0.01 and 1.6 × 10–5 in 200 replicates. The x-axis indicates the 13 genes sorted in decreasing order of the power of the FLASSO test, and the y-axis indicates the corresponding (more ...)
In general, all the tests increased the power when a gene’s contribution to the phenotype variation increased. However, we observed some exceptions, possibly because the power depends on many other factors, such as allele frequency and linkage disequilibrium among the SNPs within a gene. First, although their contributions to the phenotype variation were similar, we had more power to detect VNN1
, which consists of two causal SNPs, with one of them being common (MAF = 0.17), than VNN3
, which consists of seven rare causal SNPs. Second, for the GCKR
gene, which has only one causal SNP, we also had reasonable power, in contrast to its small contribution to the phenotype variation. The association for these two genes was concentrated in a small number of causal SNPs and hence was easier to detect. Third, the SIRT1
genes had a similar number of SNPs, number of causal SNPs, MAFs, and variance contribution; however, SIRT1
gained much more power than VLDLR
did. To understand why, we examined the linkage disequilibrium among each of these genes (using Haploview, http://www.broad.mit.edu/mpg/haploview
) (Figure ). SIRT1
includes a common SNP, C10S3059 (MAF = 0.167), that is in linkage disequilibrium with the causal rare SNP, C10S3048 (MAF = 0.002). The four gametes formed by these two SNPs are CT (83.7%), CC (16.6%), GC (0.1%), and GT (0.1%); and the D
′ value is 0.5 (R2
= 0.003). Among the 55 significant tests of the SIRT1
gene in 200 replicates, 81.8%, 60%, and 50.9% of the LASSO models selected SNP C10S3059, C10S3048, or both, respectively, in their M1 models. However, for VLDLR
, although SNP C9S341 (MAF = 0.095) was also in linkage disequilibrium with the causal SNP C9S444, which has MAF = 0.001 (D
′ = 0.384 and R2
= 0.002), it was not as common as C10S3059 and the linkage disequilibrium pattern was not the same as that for SIRT1
Figure 2 Linkage disequilibrium plot for genes SIRT1 and VLDLR. Linkage disequilibrium plots generated from Haploview. The values of R2 are shown in each cell. The color code in the Haploview plot follows the standard color scheme for Haploview: white, |D′| (more ...)
We also investigated the false-positive rates by counting the frequency of the P-values that were not larger than a specific significance level for all of the 3,192 noncausal genes over the 200 replicates (Table ). For some unknown reason, all four methods had inflated false-positive rates, and the inflation of the FLASSO test was slightly bigger than that of the other three tests, but not significantly so.
False-positive rates at the significance levels of 0.01 and 1.6 × 10–5 (the Bonferroni-corrected significance level of 0.05)