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In medicine and statistics, sensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a medical condition. If individuals who have the condition are considered "positive" and those who do not are considered "negative", then sensitivity is a measure of how well a test can identify true ...
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 ]
Example of receiver operating characteristic (ROC) curve highlighting the area under the curve (AUC) sub-area with low sensitivity and low specificity in red and the sub-area with high or sufficient sensitivity and specificity in green.
Recall in this context is also referred to as the true positive rate or sensitivity, and precision is also referred to as positive predictive value (PPV); other related measures used in classification include true negative rate and accuracy. [12] True negative rate is also called specificity.
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, :
In diagnostic testing, the main ratios used are the true column ratios – true positive rate and true negative rate – where they are known as sensitivity and specificity. In informational retrieval, the main ratios are the true positive ratios (row and column) – positive predictive value and true positive rate – where they are known as ...
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.