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For the figure that shows low sensitivity and high specificity, there are 8 FN and 3 FP. Using the same method as the previous figure, we get TP = 40 - 3 = 37. The number of sick people is 37 + 8 = 45, which gives a sensitivity of 37 / 45 = 82.2 %. There are 40 - 8 = 32 TN. The specificity therefore comes out to 32 / 35 = 91.4%.
A high ROC AUC, such as 0.9 for example, might correspond to low values of precision and negative predictive value, such as 0.2 and 0.1 in the [0, 1] range. If one performed a binary classification, obtained an ROC AUC of 0.9 and decided to focus only on this metric, they might overoptimistically believe their binary test was excellent.
The sensitivity of an electronic device, such as a communications system receiver, or detection device, such as a PIN diode, is the minimum magnitude of input signal required to produce a specified output signal having a specified signal-to-noise ratio, or other specified criteria. In general, it is the signal level required for a particular ...
The relationship between sensitivity and specificity, as well as the performance of the classifier, can be visualized and studied using the Receiver Operating Characteristic (ROC) curve. In theory, sensitivity and specificity are independent in the sense that it is possible to achieve 100% in both (such as in the red/blue ball example given above).
They use the sensitivity and specificity of the test to determine whether a test result usefully changes the probability that a condition (such as a disease state) exists. The first description of the use of likelihood ratios for decision rules was made at a symposium on information theory in 1954. [ 1 ]
The log diagnostic odds ratio can also be used to study the trade-off between sensitivity and specificity [5] [6] by expressing the log diagnostic odds ratio in terms of the logit of the true positive rate (sensitivity) and false positive rate (1 − specificity), and by additionally constructing a measure, :
Youden's J statistic is = + = + with the two right-hand quantities being sensitivity and specificity.Thus the expanded formula is: = + + + = (+) (+) In this equation, TP is the number of true positives, TN the number of true negatives, FP the number of false positives and FN the number of false negatives.
The article states (under the "Sensitivity" and "Specificity" sections respectively) that "negative results in a high sensitivity test are used to rule out the disease" (referred to by the mnemonic "SNOUT" later in the article) and that "a positive result from a test with high specificity means a high probability of the presence of disease ...