Brain Architecture Project

Uncovering the blueprint of the brain,
across multiple species

Sensitivity and Specificity Calculations on Enhancer-based Data

The data is separated into 5 enhancers (PCBP3, FOXP2_RORB, D2, DA, SST), each with two markers. The PCBP3 and SST have markers in only one channel, while the others have markers on two channels. We detect cells marked by enhancers and antibodies, along with the DAPI channel, for each image using morphological operations.

An example of the enhancer PCBP3 is shown here.

PCBP3 Example
Figure: Combined image for 3 channels: Ch2 = enhancer PCBP3, Ch3 = marker anti-PCBP3, Ch1 = DAPI.

True-positives are calculated within a distance of 10 pixels from the marker.

The following formula has been derived based on the "Sensitivity and specificity" definitions, where

\[sensitivity = \frac{number\ of\ true\ positives}{π‘›π‘’π‘šπ‘π‘’π‘Ÿ\ π‘œπ‘“\ π‘‘π‘Ÿπ‘’π‘’\ π‘π‘œπ‘ π‘–π‘‘π‘–π‘£π‘’π‘  + π‘›π‘’π‘šπ‘π‘’π‘Ÿ\ π‘œπ‘“\ π‘“π‘Žπ‘™π‘ π‘’\ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’π‘ }\] \[specificity = \frac{𝑛umber\ π‘œπ‘“\ π‘‘π‘Ÿπ‘’π‘’\ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’π‘ }{π‘›π‘’π‘šπ‘π‘’π‘Ÿ\ π‘œπ‘“\ π‘‘π‘Ÿπ‘’π‘’\ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’π‘  + π‘›π‘’π‘šπ‘π‘’π‘Ÿ\ π‘œπ‘“\ π‘“π‘Žπ‘™π‘ π‘’\ π‘π‘œπ‘ π‘–π‘‘π‘–π‘£π‘’π‘ }\]

Thus, the specificity and sensitivity are 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-labelled cells, and \(\|D\|\) is the number of cells marked by DAPI.

TP, FP, FN and TN are the numbers of True-positives, False-positives, False-negatives and True-negatives, respectively, as per standard definitions.

The folowing table shows the Calculations of the sensitivity and sensitivity is based on the code available on GitHub. The Data is available for download as Bioformat images in the last column or as channel-wise images as shown in the thumbnail here. The Thumbnail images are RGB image for a single enhancer, where the RED channel shows the cells stained the marker, GREEN channel shows the cells marked by the Enhancer, and the BLUE channel shows the DAPI marked cells.

Table. Results for specificity and sensitivity per image.