Development of modern chemometrics methods for the analysis of high-dimensional data issued from process monitoring and experimental studies
(2025)
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- Chemometrics is a multidisciplinary science at the interface between chemistry, and statistics, aiming to extract insights from high-dimensional data such as in omics sciences or industrial processes. The objectives of this thesis are twofold: (1) disentangle the effects of experimental factors from designed experiments and observational studies using ANOVA-based multivariate methods, and (2) develop interpretable and predictive models for real-time monitoring of chemical reactions in pharmaceutical manufacturing. The goals are to move beyond traditional methods by extending established tools, introducing innovative algorithms and workflows, and providing open-source resources for the community. In a first part, ASCA+ and APCA+ methodologies are introduced as extensions of ASCA and APCA for unbalanced and complex multifactorial designs, using least squares estimators within the General Linear Model to decompose multivariate responses into effect matrices, followed by PCA for visualization. Enhanced with permutation tests and Type III sums of squares, they enable improved factor disentanglement and statistical inference on different metabolomics datasets. These foundations are implemented in a new R package called limpca which automates ASCA+/APCA+ workflows, featuring data exploration, modeling, visualization. It is ready for extensions such as confidence ellipses for visual inference, variable importance measures with multiple testing corrections, and extensions to continuous variables. Limpca is available on Bioconductor, enhancing accessibility for the analysis of experimental and observational studies. In a second part, unsupervised chemometric approaches (PCA, NMF, and MCR) are evaluated for visualizing reaction kinetics in PAT frameworks. Using mid-infrared spectroscopy and UPLC data from pharmaceutical batches, NMF and MCR stand out with non-negative decompositions yielding physically meaningful loadings (resembling pure spectra) and scores (aligning with concentration profiles). Combined with one-step PLSR or two-step regression, they support real-time prediction without off-line sampling, enhancing anomaly detection and QbD compliance. Supervised NMF (SNMF), a novel algorithm that adds a supervised penalty to balance prediction and interpretability is then introduced. Tested on simulated reaction data, SNMF outperforms unsupervised NMF in accuracy while preserving non-negativity, rivaling PLSR in trade-offs via gradient descent and multiplicative updates. This opens doors to hybrid models for real-time release testing. Beyond pharmaceuticals, these methodologies apply to R&D, analytical chemistry, and general multivariate analysis. All codes and datasets are shared online, with limpca included in Bioconductor.
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Thiel, M. (2025). Development of modern chemometrics methods for the analysis of high-dimensional data issued from process monitoring and experimental studies.