Procedure for the Selection and Validation of a Calibration Model II-Theoretical Basis.

In the first part of this paper (I-Description and application), an automated, stepwise and analyst-independent process for the selection and validation of calibration models was put forward and applied to two model analytes. This second part presents the mathematical reasoning and experimental work underlying the selection of the different components of this procedure. Different replicate analysis designs (intra/inter-day and intra/inter-extraction) were tested and their impact on test results was evaluated. For most methods, the use of intra-day/intra-extraction measurement replicates is recommended due to its decreased variability. This process should be repeated three times during the validation process in order to assess the time stability of the underlying model. Strategies for identification of heteroscedasticity and their potential weaknesses were examined and a unilateral F-test using the lower limit of quantification and upper limit of quantification replicates was chosen. Three different options for model selection were examined and tested: ANOVA lack-of-fit (LOF), partial F-test and significance of the second-order term. Examination of mathematical assumptions for each test and LC-MS-MS experimental results lead to selection of the partial F-test as being the most suitable. The advantages and drawbacks of ANOVA-LOF, examination of the standardized residuals graph and residuals normality testing (Kolmogorov-Smirnov or Cramer-Von Mises) for validation of the calibration model were examined with the last option proving the best in light of its robustness and accuracy. Choosing the correct calibration model improves QC accuracy, and simulations have shown that this automated scheme has a much better performance than a more traditional method of fitting with increasingly complex models until QC accuracies pass below a threshold.