Decision threshold

Specific IgE Assay. Two radioimmunoassays are available in France using a quaternary ammonium compoimd coupled to Sepharose [30, 31]. The sensitivity of these tests was equivalent at 88%, the specificity reaches 90%. A morphine-based immunoassay has been proposed in Australia [14]. More recently, Ebo et al. [32] investigated a rocuronium ImmimoCAP and set the sensitivity at 85%, the specificity being absolute, provided an assay-specific decision threshold is applied. An ImmimoCAP (Phadia A) is available. 

The Decision Rules. The NIOSH action level is a statistical decision threshold designed to help employers attain a high degree of confidence that no more than a small fraction of any employee s daily exposures exceed the standard. After developing the action level, NIOSH provided a set of decision rules to be used by employers who want to determine if their workplaces meet this objective an exposure estimate smaller than the action level indicates that the employer has probably achieved the objective an estimate larger than the standard probably indicates a serious... 

The challenge to the statistician is to select values for AL and UAL such that when the decisions are made, they are made correctly and with sufficient confidence. It is beyond the scope of this paper to debate the assumptions underlying the various competing derivations for values to be assigned to the AL and the UAL. Instead, I propose to compare the decision probabilities which result from the various proposed decision thresholds. All that is required for this comparison is knowledge of pdtf(X) and repeated applications of Equations A-ll and A-12, with AL = Xq and UAL = Xg, to compute the decision probabilities. 

The subjectivity of the qualitative assessment (see section 5.1.2.2) also opens the possibility of conscious or unconscious bias by the assessor. For this reason, it is desirable to report the steps from (1) to (5) in a transparent way so that others can review and evaluate the judgements that have been made. This has the advantage that it is always possible to do and that it is sufficient if the result is clearly conservative (protective) overall. However, it has disadvantages with regard to subjectivity when the outcome is not clearly conservative and when using separate uncertainty factors for many parameters that can lead to compounding conservatism. If an exposure/risk assessment contains a number of conservative assumptions, then the above table is likely to end up with an overall assessment that the true risk is probably lower than the quantitative estimate. However, if the assessment attempts to use realistic estimates/distributions for most inputs, then a table of unquantified uncertainties is the likely result. This undoubtedly is a difficulty for decision-makers unless the assessor can evaluate the combined uncertainty relative to the decision-makers decision threshold. 

Some of the examples and discussion in this chapter draw on the two-class classification problem, which here is hit versus inactive . The word active refers to a validated hit, that is, a molecule that truly does exhibit some level of the desired biological response. A key point is that an assay is itself an estimator. With this in mind, definitions and a discussion of error rates are given in the context of predictive models. Borrowing from the terminology of signal detection, the sensitivity of a model refers to the fraction of observed hits that are classified as (or predicted to be) hits by the model, and specificity refers to the fraction of observed inactives classified as inactives by the model. An observed hit is not necessarily an active molecule, but simply a molecule for which the primary screening result exceeded a decision threshold. Whether such a molecule turns out to be an active is a problem that involves the sensitivity of the assay, but the task at hand is for... 

Let / denote predicted by the model to be inactive and I denote observed to be inactive in the assay by exceeding the decision threshold , with analogous definitions for A, predicted to be a hit , and A, observed to be a hit . With the null hypothesis that a compound is inactive, we have ... 

Figure 8. Sensitivity, specificity, and positive discovery rate as a function of decision threshold the two reference lines correspond to two decision thresholds. The rates are estimated from predictions made for molecules not in the training set of the model.

Hg). The combined standard uncertainty is given within brackets/ Decision thresholds are given according to ISOJ Reference date June 1, 2005... 

The background reduction presented in this paper, which is in the order of a factor of 2-3, may sound insignificant but has proven important for several projects where the peak count rate is near the decision threshold. In e.g. the case of measuring Co in samples from Hiroshima, the background reduction accomplished here was the difference between a positive or negative detection. 

ISO, Determination of the detection limit and decision threshold for ionizing radiation measurements Part 3, ISO. 2000, ISO 11929-3 2000. 

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. 

Decision theory operates on the basis of an "objective function" which is in some way optimized through the setting of a decision threshold. A lucid presentation to alternative strategies for formulating detection decisions has been given by Liteanu and Rica (S, p. 192). The essence of the matter is that a threshold value kg for the Likelihood Ratio is derived from a) prior probabilities for the null and alternative hypotheses, b) a cost or... 

The logistic regression model can be used in a classification problem by assigning the class into one of the two classes according to the predicted value. The default decision threshold uses 0.5 to predict class membership, but it can be adjusted to reflect prior probabilities, for example, i/(no + i). where n,- is a sample size in class i. The decision mle assigns a subject to class 1 if y > 0.5 and to class 0 if y < 0.5, where y is the fitted value. 

For simplicity, we assume throughout that the different types of errors are equally costly. Since the signals are pulse coded, the value of r chosen is the average value over the pulse width. The decision threshold r is the value of r for which the equality in (7.146) holds. Using (7.142), (7.143a), and (7.144) for sinewave signals and Gaussian noise, rj, is therefore the solution to the transcendental equation... 

Thus, Vq is a function only of The decision threshold is therefore a... 

We suppose that the method is going to be used for purposes of monitoring and approval at given limits of specifications. The task in optimizing is to reach the best precision available. Thus, when specified limits are approached, we will provide enhanced margins for decision thresholds at an unchanged significance level. The calibration data are presented in Table 5. 

ISO 11929 2010, Determination of the characteristic limits (decision threshold, detection limit, and limits of the confidence interval) for measurements of ionizing radiation - fundamentals and application. Reviewed 2014. Available from the ISO store, link http //www.iso.org/iso/catalogue detail.htm csnumber=43810. 

From the probability density distributions of the discriminant scores u for class A and B an optimal decision threshold Mo can be determined, If an unknown has to be classified it is assigned to class A if its discriminant variable is lower than Mo, Otherwise to class B, In the case of a substantial overlap of the probability density distributions an interval may be defined for a rejection of classifications. The decision vector (a linear combination of the features) together with the rule how to assign the classes is called a classifier. 

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