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In information retrieval, the positive predictive value is called precision, and sensitivity is called recall. Unlike the Specificity vs Sensitivity tradeoff, these measures are both independent of the number of true negatives, which is generally unknown and much larger than the actual numbers of relevant and retrieved documents.
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
Precision and recall are then defined as: [12] = + = + 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]
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. [1] [2] This involves estimating sensitivity indices that quantify the influence of an input or group of inputs on the output.
Diagram relating pre- and post-test probabilities, with the green curve (upper left half) representing a positive test, and the red curve (lower right half) representing a negative test, for the case of 90% sensitivity and 90% specificity, corresponding to a likelihood ratio positive of 9, and a likelihood ratio negative of 0.111.
In evidence-based medicine, likelihood ratios are used for assessing the value of performing a diagnostic test.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 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, :
The false positive rate (FPR) is the proportion of all negatives that still yield positive test outcomes, i.e., the conditional probability of a positive test result given an event that was not present. The false positive rate is equal to the significance level. The specificity of the test is equal to 1 minus the false positive rate.