Range of an analytical method

According to USP 28 [1], the range of an analytical method can be defined as the interval between upper and lower levels (in the Pharmaceutical Industry usually a range from 80 to 120% of the target concentrations tested) of the analyte that have been demonstrated to be determined with a acceptable level of precision, accuracy, and linearity. Routine analyses should be conducted in this permitted range. For pharmacokinetic measurements, a wide range should be tested, where the maximum value exceeds the highest expected body fluid concentration, and the minimum value is the QL. 

The range of an analytical method is the interval between the upper and lower analytical concentration of a sample where the method has been shown to demonstrate acceptable accuracy, precision, and linearity. 

The working range of an analytical method is the interval between the upper and lower concentrations of the analyte in the sample for which it has been demonstrated that the method has acceptable precision, accuracy and linearity. This interval is normally derived from linearity studies and depends on the intended application of the method. However, validating over a range wider than actually needed provides confidence that the routine standard levels are well removed from nonlinear response concentrations, and allows quantitation of crude samples in support of process development. The range is normally expressed in the same units as the test results obtained by the analytical method. 

The linear range of an analytical method is the analyte concentration range over which response is proportional to concentration. A related quantity defined in Figure 4-12 is dynamic range—the concentration range over which there is a measurable response to analyte, even if the response is not linear. 

The range of an analytical method is the interval between the upper... 

The working range of an analytical method denotes the range between the lower and upper concentration, for which accurate determinations are feasible. 

Range Ihe range of an analytical method refers to the interval between the upper and lower concentration for which it has been demonstrated that there is a suitable level of accuracy, precision, and linearity Repeatability A measme of the precision of the method over a short period of time using the same sample solution Resistance to mass transfer The time taken for the analyte to transfer from the mobile to the stationary phase... 

Figure 1-13 illustrates the definition of the dynamic range of an analytical method, which extends from the lowest concentration at which quantitative measurements can be made (limit of quantitation, or LOO) to the concentration at which the calibration curve departs from linearity by a specified amount (limit of linearity, or LOL). Usually, a deviation of SSI. from linearity is considered the upper limit. Deviations from linearity are common at high concentrations because of nonideal detector responses or chemical effects. The lower limit of quantitative measurements is generally taken to be equal to ton times the standard deviation of repetitive measurements on a blank, or 10j . At this point, the relative standard deviation is about 3(1% and decreases rapidly as concentrations become larger. 

FIGURE 1-13 Useful range of an analytical method. LOQ = limit of quantitative measurement LOL = limit of linear... 

Other features of an analytical method that should be borne in mind are its linear range, which should be as large as possible to allow samples containing a wide range of analyte concentrations to be analysed without further manipulation, and its precision and accuracy. Method development and validation require all of these parameters to be studied and assessed quantitatively. 

To demonstrate the validity of an analytical method, data regarding working range/ calibration, recovery, repeatability, specificity and LOQ have to be provided for each relevant sample matrix. Most often these data have to be collected from several studies, e.g., from several validation reports of the developer of the method, the independent laboratory validation or the confirmatory method trials. If the intended use of a pesticide is not restricted to one matrix type and if residues are transferred via feedstuffs to animals and finally to foodstuffs of animal origin, up to 30 sets of the quality parameters described above are necessary for each analyte of the residue definition. Table 2 can be used as a checklist to monitor the completeness of required data. 

Verification implies that the laboratory investigates trueness and precision in particular. Elements which should be included in a full validation of an analytical method are specificity, calibration curve, precision between laboratories and/or precision within laboratories, trueness, measuring range, LOD, LOQ, robustness and sensitivity. The numbers of analyses required by the NMKL standard and the criteria for the adoption of quantitative methods are summarized in Table 10. 

The limit of detection (LOD) is an important criterion of the efficiency of an analytical method. It is characterized by the smallest value of the concentration of a compound in the analytical sample. The detectable amount of anilide compounds is in the range 0.01-0.5 ng by GC and 0.1 ng by HPLC. The limit of quantitation (LOQ) ranges from 0.005 to 0.01 mg kg for vegetables, fruits and crops. The recoveries from untreated plant matrices with fortification levels between 10 and 50 times the LOD and the LOQ are 70-120%. The relative standard deviation (RSD) at 10-50 times the level of the LOD and LOQ are <10 % and <20%, respectively. 

The LOD is an important criterion of the efficiency of an analytical method. It defines the smallest value of the concentration of a compound in the analytical sample. Detectable amounts of neonicotinoid insecticides range from 0.5 to 1 ng by HPLC. The LOQ ranges from 0.005 to 0.01 mg kg for vegetables, fruits and crops. 

The accuracy of an analytical method is given by the extent by which the value obtained deviates from the true value. One estimation of the accuracy of a method entails analyzing a sample with known concentration and then comparing the results between the measured and the true value. The second approach is to compare test results obtained from the new method to the results obtained from an existing method known to be accurate. Other approaches are based on determinations of the per cent recovery of known analyte spiked into blank matrices or products (i.e., the standard addition method). For samples spiked into blank matrices, it is recommended to prepare the sample at five different concentration levels, ranging over 80-120%, or 75-125%, of the target concentration. These preparations used for accuracy studies usually called synthetic mixtures or laboratory-made preparations . 

The ability of an analytical method to elicit test results that are directly, or by a well defined mathematical transformation, proportional to the concentration of analyte in samples within a given range [AOAC]... 

The precision of an analytical method is usually expressed as the standard deviation or relative standard deviation (coefficient of variation) of a series of measurements. Precision represents repeatability or reproducibility of the analytical method under normal operating conditions. Precision determinations permit an estimate of the reliability of single determinations and are commonly in the range of 0.3 to 3% for dosage form assays. 

The purpose of an analytical method is the deliverance of a qualitative and/or quantitative result with an acceptable uncertainty level. Therefore, theoretically, validation boils down to measuring uncertainty . In practice, method validation is done by evaluating a series of method performance characteristics, such as precision, trueness, selectivity/specificity, linearity, operating range, recovery, LOD, limit of quantification (LOQ), sensitivity, ruggedness/robustness, and applicability. Calibration and traceability have been mentioned also as performance characteristics of a method [2, 4]. To these performance parameters, MU can be added, although MU is a key indicator for both fitness for purpose of a method and constant reliability of analytical results achieved in a laboratory (IQC). MU is a comprehensive parameter covering all sources of error and thus more than method validation alone. 

Even using uncertainty factors, the problem of determining the reliability of qualitative methods has not be solved because the usual statistical approaches are often not applicable. In residue analysis, this problem is often amplified because concenftations frequently are in the low or even sub-ppb range. Most promising appears to be a model that helps in estimating, in arbitrary units, the overall selectivity of an analytical method on the basis of partial selectivity indices. Selectivity indices are nothing more than a combination of the above-mentioned tools with the experience obtained within the European Union from recognized laboratory experts (26). 

The peroxy complex of titanium(IV), Ti(02)(edta)2, has been used as part of an analytical method for either titanium(IV) or H202. More recently the structural nature of TiO(edta)2- in solution and the reaction of TiO(edta)2- with H202 to form Ti(02)(edta)2 have been investigated over the pH range 2.0-5.2. Two distinctly different primary coordination spheres in terms of spectral properties and reactivities towards H202 are observed for TiO(edta)2" solutions in this pH range. As shown in Scheme 2, these are the aquated forms (A), TiO(edtaH )(H20), 2, having two coordinated carboxylates and two amines and one coordinated water, and the fully chelated forms (B), TiO(edtaH ) 2, with three carboxylates and two amines coordinated to titanium(IV).115... 

The linearity of an analytical method is its ability to elicit test results that are directly, or by means of well-defined mathematical transformation, proportional to the concentration of analytes in samples within a given range. Linearity is determined by a series of three to six injections of five or more standards whose concentrations span 80-120% of the expected concentration range. The response should be—directly or by means of a well-defined mathematical calculation—proportional to the concentrations of the analytes. A linear regression equation applied to the results should have an intercept not significantly differ-... 

In a probabilistic risk assessment, both variability and uncertainty in input variables can be taken into consideration. Variability represents the true heterogeneity in time, space, and of different members of a population. Examples of variability are interindividual variability in consumption and in sensitivity to, for instance, an allergen. Uncertainty is a lack of knowledge about the true value of the quantity. An example of uncertainty is associated with the limit of detection of an analytical method and the exploration of the threshold value outside the range of measurements. In contrast to the variability, uncertainty can be decreased, for example, by increasing the number of data points or using a more accurate method of analysis. 

To assess the method bias of an analytical method, the appropriate RMs should be chosen. A list of available BCR RMs can be found on the website of the Institute for Reference Materials and Measurements (IRMM) of the Joint Research Centre, European Commission, Geel Establishment (www.irmm.jrc.be/rm/ intro.html). The validity of assessing the method bias by means of RMs depends on the assumption that the analytical method is otherwise unbiased as well as on the range of appropriate matrix RMs available. It should not be overlooked, however, that there may be a matrix mismatch between the test material and the most appropriate RMs available [32]. 

The representativeness of a spiking experiment to asses the method bias is an important issue in food analysis. It has been questioned whether one can evaluate the extraction of substances in a matrix by means of a spiking experiment. The extraction efficiency of incurred and spiked analytes is seldom the same. For some substances, it is hard to find real blank materials. Furthermore, several parameters have influence on the uncertainty of the experimentally determined method bias [32]. It should be stressed that, as it may be concentration-dependent, the method bias should be evaluated for the entire concentration range of the analytical method. 

Validation is the determination of the attributes, or figures of merit, of an analytical method for one or more analytes in one or more sample matrices by one or more analysts in one or more analytical laboratories and the acceptance of the attributes as reasonable and useful by the users of the data. There are many levels of analytical method validation ranging from the validation of a method for a single analyte in a single matrix by a single analyst in a single laboratory to a multi-analyte, multi-matrix, multi-analyst, and multi-laboratory validation. 

Determination of Linearity and Range Determine the linearity of an analytical method by mathematically treating test results obtained from analysis of samples with analyte concentrations across the claimed range of the method. The treatment is normally a calculation of a regression line by the method of least squares of test results versus analyte concentrations. In some cases, to obtain proportionality between assays and sample concentrations, the test data may have to be subjected to a mathematical transformation before the regression analysis. The slope of the regression line and its variance (correlation coefficient) provide a mathematical measure of linearity the y-intercept is a measure of the potential assay bias. 

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