Sensitivity and specificity
As the majority of diagnostic studies express diagnostic performance results in terms of sensitivity (S ) and specificity (C ), we show how MI relates to these measures.
\begin{equation} I\left(D,T\right)=H\left(D\right)+H\left(T\right)-H\left(D,T\right)=Sp\left(\log_{2}\left(\frac{S\left(\left(1-S\right)p+C\left(1-p\right)\right)}{\left(1-S\right)\left(Sp+\left(1-C\right)\left(1-p\right)\right)}\right)\right)+C\left(1-p\right)\left(\log_{2}\left(\frac{C\left(Sp+\left(1-C\right)\left(1-p\right)\right)}{\left(1-C\right)\left(\left(1-S\right)p+C\left(1-p\right)\right)}\right)\right)\ \ \ \ \ \ \ \ +p\log_{2}\left(\frac{\left(1-S\right)\left(Sp+\left(1-C\right)\left(1-p\right)\right)}{\left(1-C\right)\left(\left(1-S\right)p+C\left(1-p\right)\right)}\right)+\log_{2}\left(\frac{\left(1-C\right)}{\left(Sp+\left(1-C\right)\left(1-p\right)\right)}\right)\nonumber \\ \end{equation}