Bayesian one-class classification models: Application to pharmaceutical quality control using vibrational spectroscopy

In the pharmaceutical and biopharmaceutical industry, many problems dealing with the qualitative quality control (QC) of materials, products and processes are more and more addressed using vibrational (e.g., near-infrared and Raman) spectroscopies combined with one-class classification (OCC)
algorithms. Analytical methods involving vibrational spectroscopies and validated one-class classifiers are now clearly recognized by the European and United States Pharmacopeia as valid strategies to increase the efficiency of pharmaceutical QC. Their prominent applications include the identification of raw materials, the process analytical technology (PAT), the identification and investigation of drug products. These applications are made easier and easier by the emergence of miniaturized handheld
and portable spectrophotometers. Numerous OCC models are used in chemometrics to classify spectra. The most used are parametric
probabilistic models. They explicitly assume a probability model of their classification metrics that is completely determined by a fixed number of parameters. The most prominent of these OCC
models is undoubtedly the soft independent modeling of class analogy (SIMCA). A critical review of these models showed that they have two major limitations. Firstly, their predictive performances and
probabilistic interpretability might be biased because their acceptance regions are not prediction region sensu stricto. Secondly, they are all distance-based. Hence, their decision rules are not chemically
interpretable because spectra are reduced to points in the metric spaces.
This thesis aims at developing OCC models that enable both probabilistic and chemically interpretable decision-makings in pharmaceutical quality control. The ultimate goal is to provide a predictive framework that enables a consistent risk management and a better understanding of the decisions
about the quality compliance of materials, processes and products.
Two types of OCC methods leveraging the concept of Bayesian prediction regions were developed to improve the probabilistic and chemical interpretability of OCC models. Firstly, a Bayesian version of the well-known SIMCA was developed. The concept of prediction intervals derived from generalized linear models (GLMs) was used to construct unbiased and accurate acceptance regions for SIMCA metrics. Secondly, a chemically interpretable OCC method was developed. It uses as acceptance space for
genuine spectra of the target chemical, a prediction band delimited by an upper and a lower critical trajectory in the wavelengths’ space. Test spectra falling substantially outside that band are rejected as non-complying with the target and their deviations with respect to the limits are localized and
quantified at each wavelength, resulting in an outlyingness map or deviation profile for each spectrum. To construct the band, a Bayesian functional regression was used to predict future trajectories of unseen spectra. A functional quantile was then used to choose the boundaries of the most central ones as limits. This novel method satisfactorily classified real near-infrared and Raman spectra, while enjoying the advantage of documenting deviations from critical trajectories in the wavelengths’ space, and hence being more chemically interpretable.