Table 2 Formulas and thresholds for the ROR, RRR and BCPNN methods

ROR

\(\:\text{R}\text{O}\text{R}=\frac{(\text{a}/\text{c})}{(\text{b}/\text{d})}=\frac{\text{a}\text{d}}{\text{b}\text{c}}\)

\(\:\text{S}\text{E}\left(\text{l}\text{n}\text{R}\text{O}\text{R}\right)=\sqrt{\begin{array}{c}(\frac{1}{\text{a}}+\frac{1}{\text{b}}+\frac{1}{\text{c}}+\frac{1}{\text{d}})\end{array}}\)

a ≥ 3and 95%Cl (lower limit) > 1 represents the generation of a signal

\(\:95\% {\rm{Cl}} = {{\rm{e}}^{{\rm{ln(ROR)}} \pm \:1.96}}\sqrt {\begin{array}{*{20}{c}}{(\frac{1}{{\rm{a}}} + \frac{1}{{\rm{b}}} + \frac{1}{{\rm{c}}} + \frac{1}{{\rm{d}}})}\end{array}} \)

BCPNN

\(\:\gamma\:={\gamma\:}_{11}\frac{(C+\alpha\:)(C+\beta\:)}{\left({C}_{x}+{\alpha\:}_{1}\right)\left({C}_{y}+{\beta\:}_{1}\right)}\)

\(\:C=E\left(IC\right)={\text{l}\text{o}\text{g}}_{2}\frac{\left({C}_{xy}+{\gamma\:}_{11}\right)(C+\alpha\:)(C+\beta\:)}{(C+\gamma\:)\left({C}_{x}+{\alpha\:}_{1}\right)\left({C}_{y}+{\beta\:}_{1}\right)}\)

a ≥ 3 and IC-2SD > 0 represent the generation of a signal

\(\:V\left( {IC} \right) = \frac{1}{{{{({\rm{ln}}2)}^2}}}\left\{ {\left( {\frac{{C - {C_{xy}} + \gamma \: - \gamma {\:_{11}}}}{{\left( {{C_{xy}} + \gamma {\:_{11}}} \right)(1 + C + \gamma \:)}}} \right) + \left( {\frac{{C - {C_x} + \alpha \: - \alpha {\:_1}}}{{\left( {{C_x} + \alpha {\:_1}} \right)(1 + C + \alpha \:)}}} \right) + \left( {\frac{{C - {C_y} + \beta \: - \beta {\:_1}}}{{\left( {{C_y} + \beta {\:_1}} \right)(1 + C + \beta \:)}}} \right)} \right\}\)

\(\:IC-2SD=E\left(IC\right)-2\sqrt{V\left(IC\right)}\)

\(\:{\alpha\:}_{1}={\beta\:}_{1}=1;\alpha\:=\beta\:=2;{\gamma\:}_{11}=1\)

\(\:C=a+b+c+d;{C}_{x}=a+b;{C}_{y}=a+c;{C}_{xy}=a\)

RRR

\( {\rm{RRR = }}\,\frac{{{\rm{a}}\,{\rm{ \times }}\,\left( {{\rm{a}}\,{\rm{ + }}\,{\rm{b}}\,{\rm{ + }}\,{\rm{c}}\,{\rm{ + }}\,{\rm{d}}} \right)}}{{\left( {{\rm{a}}\,{\rm{ + }}\,{\rm{c}}} \right)\,{\rm{ \times }}\,\left( {{\rm{a}}\,{\rm{ + }}\,{\rm{b}}} \right)}} \)