Table 2.

Formulas for statistics for selecting a threshold for a continuous variable X to discriminate a binary outcome Y based on the probabilities in Table 1

Odds Ratio	Youden’s Statistic	Chi-Square
$\frac{\mathit{\text{ad}}}{\mathit{\text{bc}}}$	$\frac{a}{a+c}+\frac{d}{b+d}-1$	$\frac{{(\mathit{\text{ad}}-\mathit{\text{bc}})}^2}{(a+b)(c+d)(b+d)(a+c)}$
Kappa Statistic	Relative Risk*	Gini Index
$\frac{(a+d)-((a+b)(a+c)+(c+d)(b+d))}{1-((a+b)(a+c)+(c+d)(b+d))}$	$\frac{a/(a+b)}{c/(c+d)}$	$(P_y(1-P_y))-(\frac{\mathit{\text{ab}}}{a+b}+\frac{\mathit{\text{cd}}}{c+d})$
Specificity	Misclassification	Sensitivity
$\frac{d}{b+d}$	$1-\frac{a+d}{N}$	$\frac{a}{a+c}$
Accuracy Area	Minimax	Minimum ROC**
$\frac{a}{a+c}·\frac{d}{b+d}$	max (b, c)	$\sqrt{{(1-\frac{a}{a+c})}^2+{(1-\frac{d}{b+d})}^2}$

^*For cohort study

^**Measures the distance from the ROC curve to the point (0,1)