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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.
The easiest way to calculate the net present value of an investment is using an online NPV calculator. You can also make these calculations in Excel. You can also make these calculations in Excel.
In clinical practice, post-test probabilities are often just estimated or even guessed. This is usually acceptable in the finding of a pathognomonic sign or symptom, in which case it is almost certain that the target condition is present; or in the absence of finding a sine qua non sign or symptom, in which case it is almost certain that the target condition is absent.
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.
The number of sick people in the data set is equal to TP + FN, or 32 + 3 = 35. The sensitivity is therefore 32 / 35 = 91.4%. Using the same method, we get TN = 40 - 3 = 37, and the number of healthy people 37 + 8 = 45, which results in a specificity of 37 / 45 = 82.2 %.
The Positive predictive value (PPV) of a test is the proportion of persons who are actually positive out of all those testing positive, and can be calculated from a sample as: PPV = True positive / Tested positive. If sensitivity, specificity, and prevalence are known, PPV can be calculated using Bayes' theorem.