A consensus modeling approach to update a spectroscopic calibration

A spectroscopic calibration model is only valid to predict samples within the current calibration sample space span. This space is characterized by the calibration spectral variances set by the sample matrix properties and instrument environment (the primary conditions). Prediction samples commonly have new spectral variances (the secondary conditions) and dynamic model maintenance is needed. Previous work has shown that variants of Tikhonov regularization (TR) are capable of accomplishing this task by updating the primary model with only a few secondary condition samples (a current standardization set). An aspect of the TR variants is a weight (tuning parameter) for the small standardization set augmented to the full primary calibration sample set. In past work, this tuning parameter in combination with a second regularization parameter is graphically assessed to select a single updated model. Developed in this paper is a novel graphical consensus approach that selects a family of models across a range of tuning parameter values. Thresholds on model merit values are used to identify appropriate updated models. Model merits can be R-2, intercept, and slope for the primary calibration and standardization sets, root mean square error (RMSE) terms, and/or the model vector magnitude. Two previously used TR variants are studied. One TR modification requires analyte reference values and the other variation uses no reference values. The TR consensus approach with reference samples is applied to updating a laboratory based near infrared (NIR) primary calibration model to predict active pharmaceutical ingredient (API) tablet concentrations from NIR spectra measured on tablets produced in the full production secondary conditions. The TR approach without reference samples updates a NIR pure component analyte model at one temperature to new temperature dependent sample matrix conditions. In both studies, consensus models predict equivalently to individual models selected by previously developed graphical approaches. The consensus approach is also applied to model updating by partial least squares (PLS). While PLS and TR predict similarly, PLS can be limited by the discrete factorization process. The described consensus approach is also applicable to just primary calibration. (C) 2012 Elsevier B.V. All rights reserved.