False-positive predictive value

For understanding sensitivity, specificity, false negative predictive value, and false positive predictive value, consider the four cells and two column margins of Table 2, where individuals are cross-classified with respect to their true sero-status versus observed sero-status. Sensitivity is represented by Se = / (testing outcome + truth is +) and specificity is Sp = / (testing outcome - truth is -). With these definitions and with p denoting the probability of an individual having... 

Why did the posterior probability increase so much the second time One reason was that the prior probability was considerably higher in the second calculation than in the first (27% versus 2%), based on the fact that the first test yielded positive results. Another reason was that the specificity of the second test was quite high (98%), which markedly reduced the false-positive error rate and therefore increased the positive predictive value. 

Patients and blood donors are routinely screened for exposure to HIV by means of ElISA and Western blot assays of blood samples (F uie 1-7-15). The assays are designed to detect antibodies to HIV in the blood of the test subject The ELISA is used as the primary screening assay because it is very sensitive. Because the reference interval for the test is set to include everyone with antibodies to HIV, it also gives false positives and thus has a rather low positive predictive value, especially in low-risk populations. The Western blot (or immunoblot) is used as the confirmatory test for HIV exposure. In the Western blot technique, specific HIV proteins are separated by gel electrophoresis and blotted to a filter. The filter is incubated with the test sample. If the sample contains antibodies to HIV, they will bind to the proteins on the filter. The filter is next washed and incubated with a labeled goat anti-human IgG to visualize any bound human antibodies. The Western blot is highly specific. The combination of an ELISA and Western blot has a positive predictive value of greater than 99%,... 

Fig. 3. Predictive performance for active peptides by an ANN model. The positive predictive value (PPV, number of true positives/(true positives + false positives)) is shown versus the rate of positive predictions ((true positives + false positives)/(all predictions)) for varying ANN output threshold. ANN outputs above the threshold are positive predictions (i.e., predict peptide is active). For example, the threshold value of 0.5 on the curve corresponds to about 30% of the peptides are predicted to be active (positive) from the position on the x-axis, and the PPV is 0.27 from the y-axis. For the threshold value of 0.999, the PPV is 0.90, but only 2% of peptides are predicted active.

Equation (3), which is an application of Bayes theorem, is referred to as the Positive Predictive Value. The parameter p is unknown but believed to be very small (<0.01) for large virtual libraries. 1 - p is the power (or 1 - type II error, where ft is the false negative error rate) and a is the type I error, also called the size of a test in the hypothesis testing context, or the false positive error rate. The last equation defines the probability that a molecule is determined to be a hit in a biochemical assay given that the virtual screen predicts the molecule to be a hit. This probability is of great interest because it is valuable to have an estimate of the hit rate one can expect for a subset of molecules that are selected by a virtual screen. 

Accuracy (concordance) Predictive value positive Predictive value negative False negative rate ... 

Clinicians should not order smallpox laboratory testing for moderate or low-risk patients. Given that the global prevalence of smallpox is zero, the positive predictive value of a positive laboratory test for smallpox is extremely low, especially in patients who do not meet the case definition. Testing only high-risk patients for smallpox reduces the likelihood of false positive lab results with their attendant serious consequences. 

TABLE 48-4 Comparison of True and False Positives and Positive Predictive Values at Different Specificities Assuming a Prevalence of Celiac Disease of 3% in the Population (n i 000) Tested (Test Sensitivity of 95%)... 

Specificity True Positives False Positives Positive Predictive Value. ... 

Sn being the sensitivity (or the true positive rate, TPR or recall), Sp the specificity (or the true negative rate, TNR), FNR the false negative rate, FPR the false positive rate, PPV the positive predictive value (or precision), and NPV the negative predictive value. 

Positive predictive value = TP/(TP + FP). This is also called the precision. This is the number of cases correctly classified as belonging to A divided by the total number of cases classified (both correctly and incorrectly) as belonging to A. Alternatively, it is the probability that a case classified as belonging to A really does belong to A. It gives an indication of the relative number of false positives and is an important PM when an FP is undesirable. For example, if a patient does not have cancel it is important that the patient not be classified as having cancer. 

Distinctions between these PMs are sometimes subtle but a little thought will show how they are applicable to your data. All these PMs may range from zero to one, inclusive. The better the classifier, the larger the sensitivity, specificity, and positive predictive value, and the smaller the false alarm rate. These PMs do not appear to have been used much in chemical applications, but have been used in an atomic physics application. For further details on them consult Chapter 7 of Ref. 62, and also Refs. 242 and 243. 

The low predictive values of pharmacogenetic tests for most polymorphic variants means there will be false positive (when PPV is low) and false negative (when NPV is low) test results. Both reduce the clinical utility of the tests. There are a number of reasons for the reduced predictive values. 

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