Sensitivity and Specificity Calculations on Enhancer based Data
The data is separated into 5 enhancers (PCBP3, FOXP2_RORB, D2, DA, SST) with two markers each for them. The PCBP3 & SST has markers in only one channel, while the others have the markers on two channels. We detect the cells marked by enhancers and the antibodies along with the DAPI channel for each image, using morphological operations.
An example of the enhancer PCBP3 is shown here.
True-positives are calculated within a distance of 10 pixels from the marker. The specificity and sensitivity is calculated as follows:
\[sensitivity = \frac{\|E \bigcap M\|}{\|M\|}\] \[specificity = \frac{\|D\| - \|M\| - \|E\| + TP}{\|D\| - \|M\|}\]where, \(TP = \|E \bigcap M\|\), \(FN = \|D - M\| - TP\), \(TN = \|D\| - \|M\| - \|E\| + TP\), and
\(\|E\|\) is the number of cells marked by the enhancer virus, \(\|M\|\) is the number of marker labeled cells, and \(\|D\|\) is the number of cells marked by DAPI.
The following formula has been derived based on the "Sensitivity and specificity" calculations stated in the Wikipedia
TP, FP, FN and TN are True-positives, False-positives, False-negatives and True-negatives, respectively, as per standard definitions.
The results for specificity and sensitivity for each image are given in the following Table. Column 1: Shows the name of the enhancers; Column 2: Shows the name of the markers; Column 3: Shows the name of the individual file Index-Number; Column 4: Shows the number of the detected cells marked by the enhancer; Column 5: Shows the number of the detected cells marked in the DAPI channel; Column 6: Shows the number of the detected cells marked by the marker; Column 6: Shows the number of True-positives; Column 6: Shows the Specificity; Column 6: Shows the Sensitivity </p>