A decision analysis model for KEGG pathway analysis

BMC Bioinformatics

Table 1 The detailed subdivided result of decision coefficient

Subcategory/the secondary pathways	x _i1	⋯	x _ij	⋯	x _it	⋯	x _ip
Direct and indirect determination factor (b ^_j )² and (2b ^_j r _jt b ^*_t ) (j, t = 1, 2, ⋯, p; j ≠ t)	(b ^*₁ )²	⋯	2b ^_j r _j1 b ^₁	⋯	2b ^_t r _t1 b ^₁	⋯	2b ^_p r _p1 b ^₁
	⋮	⋱	⋮	⋮	⋮	⋮	⋮
	2b ^₁ r _1j b ^_j	⋯	(b ^*_j )²	⋯	2b ^_t r _tj b ^_j	⋯	2b ^_p r _pj b ^_j
	⋮	⋮	⋮	⋱	⋮	⋮	⋮
	2b ^₁ r _1t b ^_t	⋯	2b ^_j r _jt b ^_t	⋯	(b ^*_t )²	⋯	2b ^_p r _pt b ^_t
	⋮	⋮	⋮	⋮	⋮	⋱	⋮
	2b ^₁ r _1p b ^_p	⋯	2b ^_j r _jp b ^_p	⋯	2b ^_t r _tp b ^_p	⋯	(b ^*_p )²
DC (R _(j))	R ₍₁₎	⋯	R _(j)	⋯	R _(t)	⋯	R _(p)

r _jt (j, t = 1, 2, ⋯, p; j ≠ t) indicates the correlation coefficient x _ij and x _it. Obviously, the data satisfy r _jt = r _tj and \( {R}_{(j)}={\left({b}_j^{*}\right)}^2+2{\displaystyle \sum_{\begin{array}{l}t=1\\ {}j\ne t\end{array}}^p{b}_j^{*}{r}_{jt}{b}_t^{*}} \) according to the decision analysis method. In order to distinguish between the direct and indirect determination factor clearly, the direct determination factor has been indicated in bold italics

ISSN: 1471-2105