Fig. 1.

(A) Type I error for the p-value combination methods. The x-axis represents correlation $corr\left({\mathit{p}}_{\mathrm{y}},{\mathit{p}}_{\mathrm{z}}\right)=r$. The y-axis represents Type I error. (B) Statistical power for the p-value combination methods. The x-axis represents correlation $corr\left({\epsilon }_{\mathit{ng}},{\phi }_{\mathit{ng}}\right)=w$. The y-axis represents statistical power. (C) Computation time of the proposed method (${\mathit{p}}_{\mathbf{N}}$) and the permutation method (${\mathit{p}}_{\mathbf{P}}$). The x-axis indicates number of thousand permutations (K). The y-axis indicates computation time. Red, green, and blue lines denote gene sizes G of 10,000, 20,000, and 30,000, respectively. The squares, triangles, and circles denote sample sizes N of 3,000, 5,000, and 7,000, respectively. Solid, dotted, and dot-dashed lines represent correlation coefficients $r$ of 0.1, 0.5, and 0.9, respectively. (D)–(F) Estimation accuracy of p-value. The x-axis represents the p-values of the benchmark method ($p_{\mathrm{P}}$). The y-axis indicates the p-values of the other p-value combination methods: $p_{\mathrm{F}}$, brown; $p_{\mathrm{N}}$, blue; $p_{\mathrm{D}}$, green). The results based on correlation coefficients $r=$ 0.3, 0.5, and 0.7 are arranged from left to right.