Calibration-curve-based analysis statistics

Two procedures for improving precision in calibration curve-based-analysis are described. A multiple curve procedure is used to compensate for poor mathematical models. A weighted least squares procedure is used to compensate for non-constant variance. Confidence band statistics are used to choose between alternative calibration strategies and to measure precision and dynamic range. 

In chemistry, as in many other sciences, statistical methods are unavoidable. Whether it is a calibration curve or the result of a single analysis, interpretation can only be ascertained if the margin of error is known. This section deals with fundamental principles of statistics and describes the treatment of errors involved in commonly used tests in chemistry. When a measurement is repeated, a statistical analysis is compulsory. However, sampling laws and hypothesis tests must be mastered to avoid meaningless conclusions and to ensure the design of meaningful quality assurance tests. Systematic errors (instrumental, user-based, etc.) and gross errors that lead to out-of-limit results will not be considered here. 

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. 

In chemical analysis, as in many other sciences, statistical methodologies are unavoidable. The calibration curve constitutes an everyday application, just as an analytical result can only be ascertained if an estimation of the possible error has been considered. Once a measurement has been repeated, a statistical exploitation becomes possible. However, the laws of sampling and tests based upon hypotheses must be understood to avoid non-value conclusions, or to ensure the meaningful quality tests. Systematic errors (user-based, instrumental) or gross errors which lead to results beyond reasonable limits do not enter into this chapter. For the tests most frequently met in chemistry only indeterminate errors are considered here. 

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... 

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... 

Quantitative analysis, A series of 5 aqueous standards, covering the concentration range of interest (10-100 ng ml was used to construct a calibration curve. A typical curve is shown in fig.4 in order to demonstrate the linearity and the precision. The curves were obtained by unweighted least squares linear regression based on previous research, which indicated that this type of statistical analysis can be employed with stable isotope labeled internal standards and for a 10-fold range of x-values because the errors associated with the y-values are approximately constant (16). Using the regression line(fig.4) in reverse, a standard error of 1. 2 ng ml could be... 

There have been many new developments in color measurement systems technology in recent years. A major breakthrough is in the area of portable color measurement techniques. Newly developed portable spectrophotometers (Figure 6-13h) now make it possible to measure and analyze data on the production floor. Some portable spectrophotometers are also capable of displaying an actual spectral reflectance curve. Bench-top spectrophotometers have been updated to allow more computer control of the lens, UV filter, and specular port. The ability to calibrate the UV component of the color spectrum is an important feature for measuring fluorescent colors accurately. Advances in windows-based software has improved the capabilities for statistical analysis of color measurements, color corrections, and color formulation. 

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