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Table 2 The decision analysis and path analysis results of simulated data

From: A decision analysis model for KEGG pathway analysis

\( \begin{array}{l}{x}_j\\ {}\mathrm{t}\mathrm{o}\\ {}y\end{array} \)

b ∗ j

x j  ↔ x k  → y

r jk b ∗ k

2b ∗ j r jk b ∗ k

\( {\displaystyle \sum_{k\ne j}{r}_{jk}{b}_k^{\ast }} \)

r jy

\( {\displaystyle \sum_{j\ne k}{r}_{kj}{b}_j^{\ast }} \)

R (j)

\( \begin{array}{l}{x}_1\\ {}\mathrm{t}\mathrm{o}\\ {}y\end{array} \)

0.383

x 1 ↔ x 2 → y

−0.162

−0.124

0.002

0.385

−0.700

0.148

x 1 ↔ x 3 → y

2.504

1.916

x 1 ↔ x 4 → y

−2.340

−1.795

\( \begin{array}{l}{x}_2\\ {}\mathrm{t}\mathrm{o}\\ {}y\end{array} \)

−1.097

x 2 ↔ x 1 → y

0.057

−0.124

0.243

−0.854

−0.416

0.670

x 2 ↔ x 3 → y

−0.198

0.433

x 2 ↔ x 4 → y

0.384

−0.842

\( \begin{array}{l}{x}_3\\ {}\mathrm{t}\mathrm{o}\\ {}y\end{array} \)

−2.593

x 3 ↔ x 1 → y

−0.369

1.196

2.009

−0.584

−0.278

−3.697

x 3 ↔ x 2 → y

−0.084

0.434

x 3 ↔ x 4 → y

2.462

−12.772

\( \begin{array}{l}{x}_4\\ {}\mathrm{t}\mathrm{o}\\ {}y\end{array} \)

2.471

x 4 ↔ x 1 → y

−0.362

−1.795

−3.117

−0.647

0.506

−9.300

x 4 ↔ x 2 → y

−0.170

−0.843

x 4 ↔ x 3 → y

−2.585

−12.799