Usefulness of Information Criteria for the Selection of Calibration Curves

The reliability of analytical results obtained with quantitative analytical methods is highly dependant upon the selection of the adequate model used as calibration curve. To select the adequate response function or model the most used and known parameter is the determination coefficient R². However it is well known that it suffers many inconvenient, such as leading to overfitting the data. A solution proposed is to use the adjusted determination coefficient R²adj that aims at reducing this problem. However there is another family of criteria that exists to allow the selection of an adequate model: the information criteria AIC, AICc and BIC. These criteria have rarely been used in analytical chemistry to select the adequate calibration curve. This works aims at assessing the performance of the statistical information criteria as well as R² and R²adj for the selection of an adequate calibration curve. They are applied to several analytical methods covering liquid chromatographic methods as well as electrophoretic ones involved in the analysis of active substances in biological fluids or aimed at quantifying impurities in drug substances. In addition, Monte-Carlo simulations are performed to assess the efficacy of these statistical criteria to select the adequate calibration curve.