Linearity testing

Richter S, Goldberg SA, Mason PB, Traina AJ, Schwieters JB (2001) Linearity tests for secondary electron multipliers used in isotope ratio mass spectrometry. Inti J Mass Spectrom 206 105-127 Rihs S, Condomines M, Sigmarsson O (2000) U, Ra, and Ba incorporation dining precipitation of hydrothermal carbonates imphcations for Ra-Ba dating of impure travertines. Geochim Cosmochim Acta 64 661-671... 

Figure 1 Ultraviolet spectra for benzaldehyde and benzoic acid solvent, methanol reference, methanol cell, 1.0 cm. (From Pfeiffer, C. D., Larson, J. R., and Ryder, J. F., Linearity testing of ultraviolet detectors in liquid chromatography, Anal. Chem., 54, 1622, 1983. Copyright American Chemical Society Publishers. With permission.)...

Sole use of the correlation coefficient (r) alone is not recommended as a means to demonstrate linearity. The correlation coefficient describes the relation between two random parameters, and shows no relevance for the analytical calibration [31]. The correlation coefficient does not indicate the linearity or lack thereof, unless r exceeds 0.999 [8, 32, 33]. If the value of r is less than 0.999, other parameters such as Vxo, Xp value, ANOVA linear testing, etc., should be calculated. Ebel [34] described using the transformation of r (i.e., Vu ) for expressing the degree of linearity, where the acceptance value of (1 — r ) should be less than 0.05. Camag (Muttents) described the sdv parameter (i.e., the relative standard deviation of the calibration curve) for expressing the linearity of a calibration curve for TLC/HPTLC in its CATS software, and can be calculated as follows ... 

So we now proceed to present various linearity tests that can be found in the statistical literature ... 

This is the basis for our new test of linearity. It has all the advantages we described it gives an unambiguous determination of whether any nonlinearity is affecting the relationship between the test results and the analyte concentration. It provides a means of distinguishing between different types of nonlinearity, if they are present, since only those that have statistically significant coefficients are active. It also is more sensitive than any other statistical linearity test including the Durbin-Watson statistic. The tables... 

Another interesting comparison is between the coefficients for the functions representing the best-fitting models for the data and the coefficients for the functions that result from performing the linearity test as described in the previous chapter [4], We have not looked at these before since they are not directly involved in the linearity test. Now, however, we consider them for their pedagogic interest. These coefficients, for the case of testing a quadratic nonlinearity of the data from Figure 67-1, are listed in Table 67-2. 

For autosampler precision, 10 consecutive lO-pL injections of an eth-ylparaben solution (20 J,g/mL) are used (Figure 6). A Waters Symmetry column packed with 5- J,m particles is used. The manufacturer s specification for peak area precision at 0.5% RSD is adopted as the acceptance criterion. This stringent precision criterion is required for precise assay testing of drug substances typically specified at 98-102% purity. The linearity test is performed by single injections of 5, 10, 40, and 80 pL of the... 

Regarding OQ validation, if one has only an isocratic pump available, it is recommended that one does not perform a detector linearity test at this time. However, this test can be subsequently performed as part of either the PQ validation or individual method validation, both of which typically test the performance of the system as a whole (holistically). 

Finally, Experiment 28 is used to check for any autosampler/ system sample carryover. A blank water sample is injected immediately following the highest injected volume of the preceding precision/repeatability/linearity test. Any carryover is then calculated as in the procedure described earlier under Autosampler in section (j) of the OQ guidelines. 

Linearity tests have been comprehensively reviewed and explained in [39]. PAs are generally used as response in CE however, they can be corrected by dividing them by their respective migration time (tjvi) to take into account any possible drift of this parameter.For the establishment of linearity, a minimum of five concentrations has been recommended. ... 

Table 5.1 summarises the characteristics of a method that require validation together with the method features contributing to these characteristics and some example test procedures. It can be seen that there is a certain amount of overlap in the contributions and their test procedures for the various characteristics. For instance, a linearity test can give information on both the accuracy and the sensitivity of a method. The ruggedness test is normally included as part of a precision study, however it can also contribute to other performance characteristics such as sensitivity and method limitations. Despite this it fits best as part of a precision study where it can be used to effectively and efficiently link repeatability to reproducibility tests. 

A steady pressure should be maintained within the flow cell when performing the detector linearity test. Filling the flow cell with the test solution manually with a syringe sometimes leads to pressure fluctuations and hence unstable readings. An alternative is to use the pump to deliver test solution to the flow cell. However, this option requires a large volume of test solution. 

The test sample to use in qualification should be a small molecule that is soluble in water, has a strong UV chromophore, and possesses a charge at the intended separation pH value. A nonvolatile compound is also desirable, especially when used for assessing peak area reproducibility during the detector linearity test. Some examples of test samples that can be used are benzoic acid, 4-hydroxyphenylacetic acid, 4-hydroxybenzoic acid, and 4-hydroxyacetophenone. 

Mollmann, H., P. Rhodewald, J. Barth, M. Verho, and H. Derendorf. 1989. Pharmacokinetics and dose linearity testing of methylprednisolone phosphdteopharm. Drug Disposl0 453-464. 

Even though linearity tests are satisfactory (correlation coefficient r is above 0.995) for characterizing the spectro(photo)meter performance, in most of the cases, the curves show that the increase of the spectral bandwidth causes an apparent decrease in absorbance from the true absorbance. The accuracy of the spectro(pho-to)metric results is related both to the performance of the instrument and to the uncertainty due to the linear calibration curve (of the instrument) and, therefore, this uncertainty component must be evaluated. 

At least five concentrations within the range specified above for the linearity test should be used. When a linearity test is needed for an assay and... 

Signal-to-noise (S/N) ratio may become important when measuring analytes at low concentrations. Related to this measurement may be the limits of detection (LOD) or quantification (LOQ), which may be of particular importance in trace analysis. For methods determining analytes over a large concentration range, a linearity test can be incorporated into the SST. 

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