True-positive result

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... 

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). 

Fig. 26.1 Relative frequency distribution curves obtained during field evaluation of a competitive ELISA for drug residues the area represented by (A) contains the true-positive results (D) true-negative results (B) false-positive results (C) false-negative results.

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. 

It would appear that the examination of step sections of patient prostates, although more difficult, might at first seem to be as near an absolute gold standard as possible. However, the great majority of prostatic carcinomas (>99%) are clinically indolent and do not decrease life span or increase mor-bidity. A more reasonable true-positive result should reflect identification of those carcinomas that will progress to cause increased morbidity or mortality if neglected. 

The above limitations in sensitivity and specificity of biochemical tests are compounded by the large numbers of patients commonly tested for pheochromocytomas, very few of whom have the tumor. The low pretest prevalence of pheochromocytomas means that false-positive biochemical results usually far outnumber true-positive results, making it difficult to unequivocally confirm the tumor in the vast majority of patients with positive results. 

Huestis MA> Mitchell JM, Cone EJ. Lowering the federally mandated cannabinoid immunoassay cutoff increases true-positive results. Clin Chem 1994 40 729-33. 

False Negative Results True Positive Results... 

Once a bioassay measurement has been taken and determined to be a true positive result, that result can be used to calculate the associated intake of radioactive material. Additional information beyond the bioassay data is needed to complete this calculation. The most important factors are the solubility type of the radioactive material, the date of the intake. 

FIGURE 92.2 Schematic diagram of a sandwich immunoassay for cardiac troponin, (a) True positive result in the presence of the antigen, (b) False-positive result in the presence of an interfering antibody. HAMA = human antimouse antibody. 

The ability to identify and quantify cyanobacterial toxins in animal and human clinical material following (suspected) intoxications or illnesses associated with contact with toxic cyanobacteria is an increasing requirement. The recoveries of anatoxin-a from animal stomach material and of microcystins from sheep rumen contents are relatively straightforward. However, the recovery of microcystin from liver and tissue samples cannot be expected to be complete without the application of proteolytic digestion and extraction procedures. This is likely because microcystins bind covalently to a cysteine residue in protein phosphatase. Unless an effective procedure is applied for the extraction of covalently bound microcystins (and nodiilarins), then a negative result in analysis cannot be taken to indicate the absence of toxins in clinical specimens. Furthermore, any positive result may be an underestimate of the true amount of microcystin in the material and would only represent free toxin, not bound to the protein phosphatases. Optimized procedures for the extraction of bound microcystins and nodiilarins from organ and tissue samples are needed. 

Eight combinations are possible with the true/false answers to the following three questions (1) is 5res, i = ires,2 , (2) is b = bjl, (3) is ymean.I = ymean.z A rigorous treatment is given in Ref. 34. First, question 1 must be answered if Hq is retained, question 2 must be answered. Only if this also leads to a positive result can question 3 be posed. 

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... 

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...

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. 

This is not a proper use of the phrase false positive. In bioassay terms, a result is said to be a false negative when a true positive effect is missed, and a false positive when a true negative effect is reported as positive. A cancer effect at an MTD is not a true false... 

The confirmation rate for the selected set was dramatically higher than the typical 60 to 80% observed historically, internally, and in the literature [30]. The results showed a 90.5% confirmation rate (9.5% false positive rate) at >30% inhibition, giving 3683 confirmed actives. The confirmation rate rose to 97.4% when considering only compounds selected from enriched clusters and fell to 84.9% when considering compounds selected by diversity. This supports the hypothesis that actives selected from highly enriched clusters are significantly more likely to confirm, that is, be true positives, than other compounds because of the presence of surrogate replicates . 

It is common for liquid nitrogen frozen protein crystals to acquire a patina of ice on the surface of the cryoprotectant. Diffraction of X-rays from even small ice crystals can mask reflections from the protein crystal. In addition, the presence of excessive amounts of ice can obscure the true position of the nylon loop, thereby resulting in the failure to place the crystal in the X-ray beam. It is, therefore, essential to remove ice crystals prior to diffraction analysis. 

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