Statistical certainty

In some cases, a limit of quantitation (quantification) may need to be considered where it is necessary not only to detect the presence of an analyte but also to determine the amount present with a reasonable statistical certainty. The limit of quantitation of an individual analytical procedure is the smallest amount of an analyte in a sample, which can be quantitatively determined with acceptable uncertainty. More detail can be found in Section 4.6.4. 

Limit of detection The lowest amount of an analyte that can be measured with reasonable statistical certainty. 

The strong point of molecular dynamic simulations is that, for the particular model, the results are (nearly) exact. In particular, the simulations take all necessary excluded-volume correlations into account. However, still it is not advisable to have blind confidence in the predictions of MD. The simulations typically treat the system classically, many parameters that together define the force field are subject to fine-tuning, and one always should be cautious about the statistical certainty. In passing, we will touch upon some more limitations when we discuss more details of MD simulation of lipid systems. We will not go into all the details here, because the use of MD simulation to study the lipid bilayer has recently been reviewed by other authors already [31,32]. Our idea is to present sufficient information to allow a critical evaluation of the method, and to set the stage for comparison with alternative approaches. 

Within the statistical certainty of the data, no general correlation was found between overpotential and TPB length. This could mean that no such... 

In a report on a research project quantification of extrapolation factors (Kalberlah and Schneider 1998), it is noted that extrapolation factors are intended to replace lack of knowledge by a plausible assumption, and that instimtions with responsibihty for establishing the mles must decide which level of statistical certainty, e.g., applicable for 50% or for 90% of a representative selection of substances, is desired for the selection of a standard value. It is furthermore noted that extrapolation factors are required for (1) time extrapolation, e.g., from a subchronic to a chronic duration of exposure (2) extrapolation from the LOAEL to the NAEL (3) interspecies extrapolation, i.e., from experimental animals to humans and (4) intraspecies extrapolation, i.e., from groups of persons with average sensitivity to groups of persons characterized by special sensitivity. In addition to these extrapolations, route-to-route extrapolation, e.g., oral-to-inhalation or dermal-to-oral must also be discussed. 

It has been suggested by, e.g.. Slob and Pieters (1998), Kalberlah and Schneider (1998), Vermeire et al. (1999), and KEMI (2003) to use probabihty distributions for the various types of assessment factors in order to achieve a more precise estimation of the degree of statistical certainty and to avoid the piling up of worst-case assumptions in the overall assessment factor. 

The decision limit CCa is the limit at and above which it can be concluded with an error probability of a that a sample is noncompliant. If a permitted limit (PL) has been established for a substance (group or the regulated compounds), the result of a sample is noncompliant if the decision limit is exceeded (CCa = xPL + 1. 64vMri.). If no permitted limit has been established (group A), the decision limit is the lowest concentration level at which the method can discriminate with a statistical certainty of 1-a that the particular analyte is present (CCa = + 2.33.vs impic). The detection capability CCp is the smallest content of the substance that may be detected, identified, and/or quantified in a sample with an error probability of p (CCp = CCa + 1.65xsampie). 

Usually, the goal is to minimize the number of samples, yet meet a specific level of statistical certainty. The total uncertainty, E, at a specific confidence level is selected. The value of E and the confidence limits are determined by the measurement quality required ... 

If Eapp and In Aapp indeed obey to the Constable-Cremer relation, then there must be an isokinetic relation between all catalysts. At the isokinetic temperature, the activities for all catalysts are the same. However, it is very difficult to establish this isokinetic relation with statistical certainty. Therefore, a second, more reliable way to establish the presence of an isokinetic behavior is to plot all activity plots in one graph, and to check if there is an isokinetic temperature 7] where all activity plots intersect. Since the parameters in such a plot... 

The (1-statistic is compared with the critical values in Table 6.6. The lowest or largest value in the dataset is identified as a straggler or as an outlier if the (1-statistic is larger than the critical value with a statistical certainty of 95 or 99 percent, respectively. 

The neutron results are certain to be more accurate for three reasons. First, the relative expansion of the crystals upon swelling has also been measured macroscopi-cally and agrees with the neutron results to the limit of experimental error [7], Second, the neutron results have much greater statistical certainty. A single neutron scattering... 

When the number of components or reactions is too large, or the mechanism is too complex to deduce with statistical certainty, then response surface models can be used instead. Methods for the statistical design of experiments can be applied, reducing the amount of experimental data that must be collected to form a statistically meaningful correlation of selectivity and yield to the main process parameters. See Montgomery (2001) for a good introduction to the statistical design of experiments. 

Two statistical limits (CCa and CCfi) have been established for determination of the concentrations above which a method reliably distinguishes and quantifies residues, on the basis of method variability and the risk of an incorrect decision. The decision limit (CCa) is the concentration of a residue in a sample at which it is decided that the sample is non-compliant with a pre-defined statistical certainty (a... 

Decision 2002/657/EC defines the detection capability (CCP) as the smallest content of the substance that may be detected, identified and/or quantified in a sample with an error probability of For substances where no permitted limit has been established, the detection capability is the lowest concentration at which a method is able to detect truly contaminated samples with a statistical certainty of... 

In the case of analytes with an established regulatory limit, CCP is the concentration at which the method is able to detect permitted limit concentrations with a statistical certainty of 1—P in other words, CCP is the concentration at which only <5% false-compliant results remain. In this case, CCP must be less than or equal to the regulatory limit. 

Once the model provides a good fit of experimental observations, the statistical certainties of the model parameters are inspected. If parameters are highly correlated, it is often possible to alter one parameter and compensate for the alteration with another parameter without compromising the fit of model. For example, in the compartmental model of the dynamics of )3-carotene metabolism, /3-carotene absorption was highly (positively) correlated with the irreversible loss of /3-carotene from the EHT compartment. Therefore, the absorption of /3-carotene and its irreversible loss from the EHT could be increased simultaneously, along with minor adjustments to a few other FTCs, without materially altering the compartmental model s prediction of the experimental observations. 

It must be realized, however, that the data used to build a particular compartmental model may not always provide sufficient statistical certainty of a given parameter s value. Because retinol-d4 and retinyl-d4 ester were not measured individually in the plasma after the subject ingested the /3-carotene-dg, we were unable to determine with statistical certainty the FTCs specifically for retinyl ester. Movement of retinyl ester from the enterocyte into the plasma was highly correlated with its removal from the plasma into the liver via chylomicron remnant. Therefore, the FTCs describing movement of retinyl ester from the enterocyte to the plasma and from the plasma to the liver could be increased simultaneously without compromising the model s prediction of the experimental observations. 

When some of the model parameters lack sufficient statistical certainty, the investigator may search the scientific literature for relevant information and use it to set constraints on the numerical values of some parameters of the model. Several statistical constraints were added in constructing the model shown in Fig. 3. The FTC of retinyl ester from the chylomicron retinyl ester to the fast turnover liver retinyl ester compartment was constrained to be inside the range of two statistical deviations of 60 36/day (mean ... 

SD) in order to correspond with the known half-life of chylomicron retinyl esters (IS 10 min) in healthy adult men (Cortner et aL, 1987). Also, the model intestinal absorption of j8-carotene was constrained to be inside the range of two statistical deviations of 15 4.5% based on a j8-carotene balance study (Bowen et aL, 1993) in which 4.3 0.8 punol of a 28-jiunol dose of /3-carotene was absorbed in healthy subjects. Each of these constraints was achieved by including additional data points in the model. Finally, the irreversible loss of retinol from the model system was constrained to a minimum value of 0.7 pimol/day based on the rate of vitamin A depletion in humans (Sauberlich et aL, 1974). These additions to the model provided good statistical certainty on all model parameters, as the FSDs of the FTCs were <25% (see Table I). 

For reporting an error interval with a given statistical certainty, the expression in Eq. (2.27) is to be multiplied by a factor k, for example, k = 2 for a 95% probability (cf. Table 2.5) to find the results in this interval. 

The factor 3 provides sufficient statistical certainty to account for the errors due to transformation from the signal to the concentration domain, for the necessary assumptions on the distribution of the blank values, and for the limited number of measurements, which only allow an estimate of the standard deviation of the blank value (sg). 

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