Probability of false positive

Long and Winefordner along with several other authors agree on a value of k = 3, which allows a confidence level of 99.86% if the values of xb follow a normal distribution, and 89% if the values of Xb do not follow a normal distribution. A value of k = 2 has also been used by some workers, but this decreases the confidence level in Cl. The definition of LOD was later expanded on by lUPAC in 1995 to include the probabilities of false positives and negatives. 

All detection systems feature a trade-off between the probability of detection (POD) of the target substance and the probability of false (positive) alarms (PFA). POD refers to the probability that the instrument will detect a threat material that is present PFA refers to the probability that the instrument will alarm when a threat material is not present at a given threshold level. The overall concentration of the target substance affects this trade-off higher concentrations are easier to detect, resulting in performance closer to the optimum operating point (perfect detection with zero false alarms). In addition, where data are accumulated over time, one can increase POD and decrease PFA by increasing the accumulation time. 

A method proposed by Schweder and Spjotvoll (1982) is based on a plot of the cumulative distribution of observed p values. Farrar and Crump (1988) have published a statistical procedure designed not only to control the probability of false positive findings, but also to combine the probabilities of a carcinogenic effect across tumor sites, sexes, and species. 

Although most pharmaceutical statisticians and toxicologists agree on the need to control the probability of false positive results, there is no consensus as to which method is most appropriate or most acceptable to regulatory agencies, The FDA and other such agencies will accept a variety of statistical procedures but will often reanalyze the data and draw their own conclusions based on their analyses. 

SPMD dialysates (extracts), rinses of the exterior membrane surface (only SPMDs exposed to air), and aliquots thereof often contain a number of classes of chemicals. Figure 6.1 shows various levels of processing and enrichment used for SPMD derived bioassay samples. We strongly recommend the use of SPMDs with triolein purified by the method of Lebo et al. (2004) for bioassays to reduce the probability of false-positive results or for controls that fail to meet quality control... 

Resolving power R is a measure of specificity and is a primary factor contributing to the probability of false positives. The salient issue is the probability that a background signal will overlap with a target explosives signal. We can qualitatively express this probability using a Poisson distribution function of the form... 

For any given sample size, there is a zero-sum trade-off between false negafives and false positives. But as we increase the sample size, the 5 percent false-positive critical value shrinks, and the true incidence difference gets closer to the new critical value and relatively farther from the null hypothesis. Thus, the probability of false negatives is reduced while the probability of false posifives remains constant. Notice that in the examples presented in Figures 1 and 2, with an assumed truth of 5.2 percent cancer incidence difference and a constant 5 percent probability of false-positive errors, the probability of false-negative errors fell from 89 to 50 percent as the sample size rose from 50 to 1,000. 

The primary choice in this assessment is whether to utilize a biochemical or biophysical screen as the primary filter. Although it seems like an either/or choice, this is a false dichotomy. The most successful fragment screens obtain orthogonal data, i.e. both biochemical and biophysical data in parallel or in quick succession. With orthogonal data, the probability of false positives (or negatives) is reduced. Most commonly biochemical and biophysical data are obtained. However, all the different biochemical and biophysical screens can be considered orthogonal. We would recommend that if two biophysical methods are to be used at least one should be a direct method (discussed below). As is noted many times in this book, rapid iterations among the various data sources are the key to a successful process. 

Table 1.1 Expected trial performance (%) for various trial scenarios on the basis of precision and the probability of false- positive and falsenegative trial outcomes.

Because most reference intervals exclude a fraction of those patients without disease, there is an expected falsepositive rate. As multiple tests are added to panels, the probability of false-positive results increases. Efforts to establish multivariate reference intervals that correct for multiple tests and their interrelationships have been made, but the concept has not found widespread acceptance. Although the concept is mathematically quite reasonable, those who have investigated the utility of multivariate reference intervals believe that more work needs to be done before they will be useful. 

OCC), that the sensor system can apply to an unknown sample of one or more known analytes. The larger the value of n, the smaller (and more desirable) the probability of false positives (Pfp) would be. Furthermore, to qualitatively find a relationship between n, FAR and Pfp, we made assumptions and imposed constraints, in line with reasonable expectations about the behavior of Pfp, as discussed in Section 9.3.5.4. 

Fig. 9.3.15 Probability of false positives and ROC output vs. orthogonal channel capacity (OCC).

Andrew SM, Frobish RA, Paape MJ, Maturin LJ, Evaluation of selected antibiotic residue screening tests for milk from individual cows and examination of factors that affect the probability of false-positive outcomes, J. Dairy Sci. 1997 80(ll) 3050-3057. 

Fig.9.1. Free-response receiver operating characteristic (ROC) curves for screen-film mammography (Square boxes, dotted line) and full-field digital mammography (dosed diamonds, solid line) based on rating scale of 0-100. Scale for a -axis is probability of false-positive finding occurring on two screen-...

In the comparison phase, apart from the experimental peptide masses and the proteinase used to digest the proteins, some optional attributes may be specified to reflect experimental conditions and to reduce the search space. These optional attributes may include information coming from the sample such as species of origin, M, or pi of the whole protein with the accepted error range, possible chemical or artefactual modifications like carboxymethylation of cysteines or oxidation of methionines. Other parameters to be specified include the mass tolerance or the minimum number of matching peptides required for a protein to be suggested as a possible match. Providing a maximum of information available about the sample helps to decrease the number of candidate proteins, to reduce the probability of false positive matches, and thus to increase the confidence of the identification. However, one must be careful not to miss the correct protein either. 

In their more reeent documents, ISO and lUPAC recommend that the detection limit (minimum detectable amounts) should be derived from the theory of hypothesis testing and take into account the probabilities of false positives (a) and false negatives (fi). Thus, the limit of detection is defined... 

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