Individual Testing
Expected Values
- Tests Used
- each person tested separately
$$=$$
- true positive (TP)
- eqv. with hit
$$=$$
- true negative (TN)
- eqv. with correct rejection
$$=$$
Sample Pooling
Expected Values
- Optimal Total Cost
- cost at optimal pool size
$$=$$
- Tests Used
- pools and retests
$$=$$
- Minimum Tests Possible
- tests used at optimal pool size
$$=$$
- true positive (TP)
- eqv. with hit
$$=$$
- true negative (TN)
- eqv. with correct rejection
$$=$$
- effective sensitivity / true positive rate (TPR)
- $$\mathrm {TPR} ={\frac {\mathrm {TP} }{\mathrm {P} }}={\frac {\mathrm
{TP}
}{\mathrm {TP} +\mathrm {FN} }}=1-\mathrm {FNR} $$
$$=$$
- effective specificity / true negative rate (TNR)
- $$\mathrm {TNR} ={\frac {\mathrm {TN} }{\mathrm {N} }}={\frac {\mathrm
{TN}
}{\mathrm {TN} +\mathrm {FP} }}=1-\mathrm {FPR} $$
$$=$$
- miss rate or false negative rate (FNR)
- $$\mathrm {FNR} ={\frac {\mathrm {FN} }{\mathrm {P} }}={\frac {\mathrm
{FN}
}{\mathrm {FN} +\mathrm {TP} }}=1-\mathrm {TPR} $$
$$=$$
- fall-out or false positive rate (FPR)
- $$\mathrm {FPR} ={\frac {\mathrm {FP} }{\mathrm {N} }}={\frac {\mathrm
{FP}
}{\mathrm {FP} +\mathrm {TN} }}=1-\mathrm {TNR} $$
$$=$$
- false discovery rate (FDR)
- $$\mathrm {FDR} ={\frac {\mathrm {FP} }{\mathrm {FP} +\mathrm {TP}
}}=1-\mathrm {PPV} $$
$$=$$
-
false omission
rate
(FOR)
- $$\mathrm {FOR} ={\frac {\mathrm {FN} }{\mathrm {FN} +\mathrm {TN}
}}=1-\mathrm {NPV} $$
$$=$$
- Prevalence Threshold (PT)
- $$PT={\frac {{\sqrt {TPR(-TNR+1)}}+TNR-1}{(TPR+TNR-1)}}$$
$$=$$
- Threat score (TS)
- $$\mathrm {TS} ={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN}
+\mathrm
{FP} }}$$
$$=$$
- accuracy(ACC)
- $$\mathrm {ACC} ={\frac {\mathrm {TP} +\mathrm {TN} }{\mathrm {P}
+\mathrm
{N} }}={\frac {\mathrm {TP} +\mathrm {TN} }{\mathrm {TP} +\mathrm {TN}
+\mathrm {FP} +\mathrm {FN} }}$$
$$=$$
- balanced accuracy (BA)
- $$\mathrm {BA} ={\frac {TPR+TNR}{2}}$$
$$=$$
- F1
score
- is the harmonic mean of precision and sensitivity
- $$\mathrm {F} _{1}=2\cdot {\frac {\mathrm {PPV} \cdot \mathrm {TPR}
}{\mathrm {PPV} +\mathrm {TPR} }}={\frac {2\mathrm {TP} }{2\mathrm {TP}
+\mathrm {FP} +\mathrm {FN} }}$$
$$=$$
- Matthews correlation
coefficient (MCC)
- $$\mathrm {MCC} ={\frac {\mathrm {TP} \times \mathrm {TN} -\mathrm {FP}
\times \mathrm {FN} }{\sqrt {(\mathrm {TP} +\mathrm {FP} )(\mathrm {TP}
+\mathrm {FN} )(\mathrm {TN} +\mathrm {FP} )(\mathrm {TN} +\mathrm {FN}
)}}}$$
$$=$$
- Fowlkes–Mallows index (FM)
- $$\mathrm {FM} ={\sqrt {{\frac {TP}{TP+FP}}\cdot {\frac
{TP}{TP+FN}}}}={\sqrt {PPV\cdot TPR}}$$
$$=$$
- informedness
or bookmaker informedness (BM)
- $$\mathrm {BM} =\mathrm {TPR} +\mathrm {TNR} -1$$
$$=$$
- markedness(MK)
or deltaP
- $$\mathrm {MK} =\mathrm {PPV} +\mathrm {NPV} -1$$
$$=$$