Area of Feasible Figures of Merit (AF-FOMs) for second-order multivariate calibrations in Multivariate Curve Resolution (MCR)

Background: The significance and necessity of using powerful multivariate curve resolution (MCR) techniques in the study and investigation of chemical systems are clear and obvious. It has long been recognized the importance of using second-order data to extract both quantitative and qualitative information in analytical chemistry through multivariate calibration instead of univariate calibration. Although the calculation of analytical figures of merit (AFOMs) in multivariate calibrations seems to be complicated, in recent years these parameters have been reported for each developed analytical method based on multivariate calibrations.

Results: It is well-known that using MCR to analyze second-order data may not produce a unique solution, a phenomenon associated with rotational ambiguity, which leads to the existence of a region or area of feasible solutions (AFS). This fact led us to argue that, instead of having uniquely defined AFOMs (sensitivity, selectivity, limit of detection, limit of quantitation, etc.), there should be an AFOM for every possible solution in the AFS. Following this argument, we report for the first time the generation of the Area of Feasible FOMs (AF-FOMs). The existence of a range of different FOMs in the AFS can be fully interpreted. It can also be predicted which AFOMs will have maximum or minimum values in each feasible band, and what kind of incremental or decremental changes will occur. Herein, the systematic grid search method was used to compute all feasible solutions and to calculate the AFOMs inside the feasible band.

Significance: The claims were supported by analyzing artificially generated two-component data sets. The data sets include a single calibrated analyte and a single uncalibrated interferent, which was only present in the test samples. In addition, real experimental data aimed at the determination of therapeutic drugs in both water and human urine samples were analyzed. Finally, the arguments were generalized to a three-component simulated system, having a single analyte and two uncalibrated interferents.