True positives

Note from Fig. 2.20 that although the true position of the boron KLL Auger peak in the N(E) spectrum is at 167 eV, the position in the dN(E)/dE spectrum is taken for purely conventional reasons to be that of the negative minimum, i.e. at 175 eV. 

These values are now better approximations to the true position, velocity and so on, hence the generic term predictor-corrector for the solution of such differential equations. Values of the constants cq through C3 are available in the literature. 

Atmospheric refraction. The apparent position of an object may be shifted vertically with respect to the true position due to refraction in the atmosphere. The shift is A(A) tan where 4> is the zenith distance and A 50 arcsec. This has two effects. 

This group of drugs has often been classified as non-specific protoplasmic poisons and indeed such views are still expressed today. Such a broad generalization is, however, very far from the true position. 

In general the rate of false negatives are by definition difficult to ascertain. There are two general approaches to get a handle on false negatives. The first approach is based on what is known about the aqueous solubility of screening compounds since truly active compounds out of solution are the most common cause of false negatives. One can infer that perhaps 15% of true positives will be missed in an HTS. This inference comes from an analysis of the concordance or lack of concordance between nominal concentrations in DMSO stocks and nominal... 

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. 

True positive rate3 probability that the test result is positive in case that the analyte A is present (above the specification limit) in the test sample... 

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). 

Table 4.3. Scheme of test results for screening procedures tp true positive,)p false positive, tn true negative, fn false negative, n total number of tests...

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. 

Sensitivity the ratio of true positives to total activities ... 

The numerator of Bayes theorem merely describes cell a (the tme-positive results). The probability of being in cell a is equal to the prevalence times the sensitivity, where XD+) is the prevalence (the probability of being in the effected column) and where XT + D+) is the sensitivity (the probability of being in the top row, given the fact of being in the effected column). The denominator of Bayes theorem consists of two terms, the first of which once again describes cell a (the true-positive results) and the second of which describes cell b (the false-positive error rate, or X I + D—), is multiplied by the prevalence of noneffected animals, or... 

In genetics, an even simpler-appearing formula for Bayes theorem is sometimes used. The numerator is the same, but the denominator is merely p 1+). This makes sense because the denominator in a/(a + b) is equal to all of those who have positive test results, whether they are true-positive or false-positive results. 

A program employing a immunochemical stain based test to screen tissues for a specific effect will be discussed as an example. This test uses small amounts of antibody tissues for a specific effect, and the presence of an immunologically bound stain is considered a positive result. If the sensitivity and specificity of the test and the prevalence of biochemical effect are known, Bayes theorem can be used to predict what proportion of the tissues with positive test results will have true-positive results (actually be effected). 

Approximately 35% of all TrEMBL entries can be characterized by a PROSITE signature but only approximately 30% of all TrEMBL entries are true positive matches. The characterization based only on PROSITE would lead to 10% to 20% of false-positive assignments. The confirmation steps reduce the level of characterization by nearly a third to 25%. At this stage, we achieve a level of less than 0.07% of false positive assignments. 

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