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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 the diagram above, this positive post-test probability, that is, the posttest probability of a target condition given a positive test result, is calculated as: Positive posttest probability = True positives / (True positives + False positives) Similarly: The post-test probability of disease given a negative result is calculated as:
In fact, post-test probability, as estimated from the likelihood ratio and pre-test probability, is generally more accurate than if estimated from the positive predictive value of the test, if the tested individual has a different pre-test probability than what is the prevalence of that condition in the population.
A positive result in a test with high specificity can be useful for "ruling in" disease, since the test rarely gives positive results in healthy patients. [5] A test with 100% specificity will recognize all patients without the disease by testing negative, so a positive test result would definitively rule in the presence of the disease. However ...
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).
The probability for false positives varies by each type of home test, but Ellume specifically says on its online FAQs that "there is a chance that this test can give a positive result that is ...
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.
The updated probability would be a combination of the base rate and the likelihood of the test result given the disease status. The base rate is also important in decision-making , particularly in situations where the cost of false positives and false negatives are different. [ 3 ]