True positive rate

A new tumor marker is evaluated using the same criteria used for many diagnostic tests (i.e., sensitivity, specificity, and accuracy). The diagnostic sensitivity and specificity are best represented by a receiver operating characteristic (ROC) curve. The ROC curve is constructed with the true-positive rate versus false-positive rate at various decision levels. As a test improves in its diagnostic performance, it shifts upward and to the left as the true-positive rate increases and the false-positive rate decreases. 

In clinical chemistry and medical diagnostics the true positive rate is called sensitivity rate and the true negative rate specificity rate (O Rangers and Condon [2000]) without any relation to the general definition of the terms sensitivity and specificity and their use in analytical chemistry (see Sects. 7.2 and 7.3). 

PPR is the probability of obtaining positive responses, TPR true positive rate (Eq. 4.48), TNR true negative rate (Eq. 4.49), FPR false positive rate (Eq. 4.50), FNR false negative rate (Eq. 4.51), X/ and xu are the lower and upper limits of the unreliability region... 

These are well-known classification parameters true positive rate (p ), false positive rate (pnx), true negative rate (qnx), and false negative rate (qK). They can be easily obtained from the previous computations where we calculated the number of taxon and nontaxon members in each interval. For example, to calculate the true positive rate, we sum the number of taxon members in intervals above the hitmax, plus half of taxon members in the hitmax interval and divide this by the total number of taxon members in the sample. To calculate the false negative rate, we sum number of taxon members in intervals below the hitmax, plus half of the taxon members in the hitmax interval and divide this by the total number of taxon members in the sample. 

Many of the commonly used enrichment descriptors are based on two values. The first value is the sensitivity Se, true positive rate, Equation 3.3), which describes the ratio of the number of active molecules found by the VS method to the number of all active database compounds ... 

The recognition accuracy estimation described above faces one very important problem what is the best choice for the threshold value 0 To solve this problem, statistical decision theory is used. ° The basis for this is an analysis of the so-called the Received Operating Characteristic (ROC) curve. By tradition, ROC is plotted as a function of true positive rate TPj TP + FN) (or sensitivity) versus false positive rate FPj TN+FP) (or 1-Specificity) for all possible threshold values 0. Figure 6.5 presents an example of such a ROC curve for the results obtained with our computer program PASS in predicting antineoplastic activity. 

The second phase is the determination of the number or percentage of true positive results achieved with the test in a population of animals that have been dosed with the compound of interest. This is an essential phase in the development of residue methods and the rigorous assessment of the true positive rate requires confirmation by a separate accepted assay method(s). In addition, part of this study may need to be performed under field conditions, particularly if the test is intended to be used in a non-laboratory environment. 

Figure 15-2 Receiver operating characteristic curve of prostate-specific antigen (PSA). Each point on the curves represents a different decision level.The sensitivity (true-positive rate) and I— the specificity (false-positive rate) can be read for Tests A and B. The true-positive and false-positive rates are demonstrated using 4 and IO Xg/L as decision thresholds.

For the case at hand. Figure 15-2 shows the ROC curve for PSA using Chan s data. The x-axis plots the fraction of nondiseased patients who were erroneously categorized as positive for a specific decision threshold. This false-positive rate is mathematically the same as 1 - specificity. The y-axls plots the true-positive rate (the sensitivity). A hidden third axis is contained in the curve itself the curve is drawn through points that represent different decision cutoff levels. The whole curve is a graphical display of the performance of the test. 

Sensitivity (= recall) a/(a + c) Fraction of positives correctly predicted positive, true positive rate... 

The true positive rate is the probability that a participant has the disease given that she or he has tested positive. This is denoted by P( )-l- T-l-) and is also referred to as predictive value positive. The complement, 1 - P(D+ T-t) = P(D- T+), is the false-positive rate. 

If the true-positive rate is low (or the falsepositive rate high) a number of participants will... 

We illustrate this concept for the true-positive rate, which is ... 

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. 

Sensitivity the probability of correctly identifying a case of disease. Sensitivity is the proportion of truly diseased persons in the screened population who are identified as diseased by the screening test. This is also known as the true positive rate. ... 

Enrichment metrics are frequently derived from ttvo basic values, the sensitivity (Se) and the specificity (Sp). Se or true positive rate is the ratio of the number of selected active molecules and the number of all biological active database molecules (5.1) [9, 65]. 

To compare the performance of a number of classification models, a receiver operating characteristic (ROC) curve can be used. These were first developed to correctly detect Japanese aircraft from their radar signatures after the attack on Pearl Harbour. ROC curves are widely used in evidence-based medicine. The y-axis is the sensitivity (true positive rate) and the x-axis is (1-specificity) the false... 

Most diagnostic tests are imperfect and, particularly when we use a binary approach - results are either "positive" or "negative" - there are some misclassification errors, inaccuracies. Some subjects with the condition of interest will be missed or some without the condition will be mistakenly considered affected, or both will happen. The ability of a test to properly identify or classify subjects or conditions of interest can be expressed as the sensitivity and specificity of the test. For clinical purposes these are defined as follows SENSITIVITY (TRUE POSITIVE RATE) Fraction of all affected... 

The ROC curve can also be constructed as a plot of true positive rate (sensitivity) versus true negative rate (specificity) instead of versus false positive rate... 

Figure 4. Hypothetical receiver operating characteristic (ROC) curves showing three possible relations between tests A and B. In each case, test A exhibits a true positive rate of 98% and a false positive rate of 30%, while test B exhibits a true positive rate of 70% and a false positive rate of 2%. Left panel Both tests have identical ROC curves, and thus, equivalent diagnostic accuracy. Middle panel Test B has a better ROC curve. Right panel Test A has a better curve.

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