Statistical validation calibration curve

Calibration curve data should be assessed to determine the appropriate mathematical regression that describes the instrument s response over the range of thecalibration curve (Section8.5). The report should include the back-calculated concentration values, accuracies, slopes, y-intercepts and correlation coefficients (R) and the coefficients of determination (R ) (Equation[8.18] in Section 8.3.1) for aU curves used in the validation. The value should be > 0.98 for each calibration curve. The R value (if used) must be > 0.99 for each calibration curve. An example table used to summarize the calibration curve statistics for each run used for method validation is shown as Table 10.2. 

Several overall conclusions can be drawn based on the statistical evaluation of the data submitted by the participants of the DR CALUX intra-and interlaboratory validation study. First, differences in expertise between the laboratories are apparent based on the results for the calibration curves (both for the curves as provided by the coordinator and for the curves that were prepared by the participants) and on the differences in individual measurement variability. Second, the average results, over all participants, are very close to the true concentration, expressed in DR CALUX 2,3,7,8-TCDD TEQs for the analytical samples. Furthermore, the interlaboratory variation for the different sample types can be regarded as estimates for the method variability. The analytical method variability is estimated to be 10.5% for analytical samples and 22.0% for sediment extracts. Finally, responses appear dependent on the dilution of the final solution to be measured. This is hypothesized to be due to differences in dose-effect curves for different dioxin responsive element-active substances. For 2,3,7,8-TCDD, this effect is not observed. Overall, based on bioassay characteristics presented here and harmonized quality criteria published elsewhere (Behnisch et al., 2001a), the DR CALUX bioassay is regarded as an accurate and reliable tool for intensive monitoring of coastal sediments. 

Finally, there is the need for proper documentation, which can be in written or electronic forms. These should cover every step of the measurement process. The sample information (source, batch number, date), sample preparation/analytical methodology (measurements at every step of the process, volumes involved, readings of temperature, etc.), calibration curves, instrument outputs, and data analysis (quantitative calculations, statistical analysis) should all be recorded. Additional QC procedures, such as blanks, matrix recovery, and control charts, also need to be a part of the record keeping. Good documentation is vital to prove the validity of data. Analyt-... 

An important extension of our large validation studies involves the use of data bases from field studies in the development of improved statistical methods for a variety of problems in quantitative applications of immunoassays. These problems include the preparation and analysis of calibration curves, treatment of "outliers" and values below detection limits, and the optimization of resource allocation in the analytical procedure. This last area is a difficult one because of the multiple level nested designs frequently used in large studies such as ours (22.). We have developed collaborations with David Rocke and Davis Bunch (statisticians and numerical analysts at Davis) in order to address these problems within the context of working assays. Hopefully we also can address the mathematical basis of using multiple immunoassays as biochemical "tasters" to approach multianalyte situations. 

Chapter 5 discusses in depth the statistical considerations related to LB A development and validation. In addition to the most appropriate algorithms for describing the nonlinear calibration curves typically found in LBAs, the authors also provide further insight into the performance characteristics to be evaluated during assay validation, including the concepts of total error in prestudy validation and the use of the 4-6-X rule. The decision rules at the prestudy validation and routine assay implementation stages are also discussed in some detail in Chapter 5. 

There have been various attempts to place the concept of detection limit on a more firm statistical ground. The International Conference on Harmonization (ICH see Chapter 4) of Technical Requirements for Registration of Pharmaceuticals for Human Use has proposed guidelines for analytical method validation (Ref. 18). The ICH Q2B guideline on validation methodology suggests calculation based on the standard deviation, s, of the response and the slope or sensitivity, S, of the calibration curve at levels approaching the limit. For the limit of detection (LOD),... 

The UV absorption in the 260 nm region is frequently used to evaluate styrene content in styrene-based polymers (2, 2, 3, 4, 5, 6, 7). Calibration curves for polystyrene solutions are usually based on the assumptions that the UV absorption of the copolymer depends only on the total concentration of phenyl rings, and the same linear relationship between optical density and styrene concentration that is valid for polystyrene holds also for its copolymers. These assumptions are quite often incorrect and have caused sizable errors in the analysis of several statistical copolymers. For example, anomalous patterns of UV spectra are given by random copolymers of styrene and acrylonitrile (8), styrene and butadiene (8), styrene and maleic anhydride (8), and styrene and methyl methacrylate (9, 10, 11). Indeed, the co-monomer unit can exert a marked influence on the position of the band maxima and/or the extinction... 

The definition of calibration function does not specify that the measurement be made in the presence of potential interferants. This serves as an introduction to a discussion of the appropriate approach to calibration in an analytical method for veterinary drug residues, such as antibiotics. Construction of a calibration curve requires a sufficient number of standard solutions to define the response in relation to concentration, where the number of standard solutions used is a function of the concentration range. In most cases, a minimum of five concentrations (plus a blank, or zero ) is considered appropriate for characterization of the calibration curve during method validation. It is also typically recommended that the curve be statistically tested and expressed, usually through linear regression analysis. However, for LC/ESI-MS analysis of residues, the function tends to be quadratic. The analytical range for the analysis is usually defined by the minimum and maximum concentrations used in establishing the calibration curve. 

FDA work will tolerate an SIS cross-contribution of up to 20 % of the response of the analyte being quantified at the LLOQ concentration. Note that these fitness for purpose guidelines are based largely on practical experience without (thus far) any statistical justification. Ultimately this question should be settled by visual examination of the experimental calibration curve together with careful evaluation of the accuracy and precision over the entire range of analyte concentration for the specified SIS concentration used to generate the calibration. In any event, the cross-contributions (if any) must be carefully monitored during all phases of method validation and sample analysis and also must be fully discussed in the method description and final report. 

For study sample analysis the calibration curve and QC samples are evaluated separately, and run acceptance is based upon criteria estabhshed for both curves and QCs. For validation runs, however, only the standard curve and other factors such as carryover are considered for run acceptance and aU of the results for the various types of validation QCs, e.g., precision and accuracy, stability, etc., are reported and used for statistical analysis. It is important at this time to emphasize the distinction between a failed and rejected validation run. Runs may be rejected for specific assignable cause such as documented evidence that the method was run incorrectly or hardware failure (Section 10.5.2c). Data from failed runs on the other hand, such as those where an excessive number of calibrators are considered to be outhers or QCs used to assess precision and accuracy do not meet the... 

A sample of known nitrogen content will be run after each calibration. The sample can also be analyzed periodically throughout a series of analyses to check the functioning of the instrument and the validity of the calibration curve. This sample can be an National Institute for Standards and Technology Standard Reference Material (SRM) material, an acridine in xylene standard prepared to have a nitrogen value not used to calibrate the instrument, or any other material that has been analyzed repeatedly such that sufficient data are available to determine a statistical mean. The results of the analysis of the known sample will be within 10 % of the certified or accepted value for the operation and calibration of the instrument to be considered acceptable. If the results are not within 10% of the accepted value, perform appropriate corrective maintenance on the instrument and repeat the calibration procedure described in 9.4. 

As for immunoassays for pharmaceutical proteins, in-study validation of biomarker assays should include one set of calibrators to monitor the standard curve as well as a set of QC samples at three concentrations analyzed in duplicate for the decision to accept or reject a specific run. Recommended acceptance criterion is the 6-4-30 rule, but even more lenient acceptance criteria may be justified based on statistical rationale developed from experimental data [14]. 

---