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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.
In a classification task, the precision for a class is the number of true positives (i.e. the number of items correctly labelled as belonging to the positive class) divided by the total number of elements labelled as belonging to the positive class (i.e. the sum of true positives and false positives, which are items incorrectly labelled as belonging to the class).
PPV is best understood by comparison to two other approaches where a penalty is applied for risk: The risk-adjusted rate of return applies a risk-penalty by increasing the discount rate when calculating the Net Present Value (NPV); The certainty equivalent approach does this by adjusting the cash-flow numerators of the NPV formula.
Understanding Net Present Value (NPV) The net present value uses the present value of cash inflows and the present value of cash outflows to estimate the profitability of an investment or project ...
A positive net present value indicates that the projected earnings generated by a project or investment (in present dollars) exceeds the anticipated costs (also in present dollars). This concept is the basis for the Net Present Value Rule, which dictates that the only investments that should be made are those with positive NPVs.
Predictive values can be used to estimate the post-test probability of an individual if the pre-test probability of the individual can be assumed roughly equal to the prevalence in a reference group on which both test results and knowledge on the presence or absence of the condition (for example a disease, such as may determined by "Gold ...
For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. [2] In many cases, the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam.
Here the same Prevalence 40% and improved PPV=96.7%, so PPV>>P. But now NPV=73.75% which has pulled further ahead of (1-Prevalance) So perhaps to both PPV & BPV article we should add "Ideally a test is better able to both identify and exclude those with a condition (PPV & NPV) than the underlying prevalance rate.