Binding the gap between experiments, statistics, and method comparison: A tutorial for computing limits of detection and quantification in univariate calibration for complex samples.

The present tutorial aims to review the most frequently reported criteria for the calculation of the limits of detection (LOD) and quantification (LOQ) in univariate calibration, summarizing their fundamentals, advantages, and limitations. The current criteria for estimating LOD and LOQ are based on diverse theoretical and/or empirical assumptions and require different amounts of experimental data, making the calculation rather complex in some cases. Moreover, alternative forms for calculating LOD/LOQ frequently lead to dissimilar results. This scenario might worsen in the case of complex analytical systems. Throughout this tutorial, different forms of calculating LOD/LOQ are illustrated using previously reported experimental datasets in the environmental chemistry field as examples. The influence of the sample matrix during the estimation of LOD/LOQ parameters is investigated through one calibration approache. The discrepancies in the obtained results with different criteria for the calculation of LOD/LOQ are highlighted. Finally, general guidelines and recommendations regarding experimental and data processing issues are proposed, aiming to promote fair criteria for the comparison of different analytical methodologies in terms of prediction ability and detection capability.

Chromatographic Applications in the Multi-Way Calibration Field.

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

Achieving the analytical second-order advantage with non-bilinear second-order data.

Multi-way calibration based on second-order data constitutes a revolutionary milestone for analytical applications. However, most classical chemometric models assume that these data fulfil the property of low rank bilinearity, which cannot be accomplished by all instrumental methods. Indeed, various techniques are able to generate non-bilinear data, which are all potentially useful for the development of novel second-order calibration methodologies. However, the achievement of the second-order advantage in these cases may be severely limited, since methods for comprehensive modelling of non-bilinear second-order data remain only partially explored. In this research, the analytical performance of three well-known second-order models, namely non-bilinear rank annihilation (NBRA), unfolded partial least-squares with residual bilinearization (U-PLS-RBL) and multivariate curve resolution - alternating least-squares (MCR-ALS) is systematically assessed through sets of simulated and experimental non-bilinear second-order data, involving one analyte and one interferent. Although it is not possible to establish a single strategy to model any type of non-bilinear second-order data with the studied methods, each approach may lead to successful predictions under certain circumstances. It is shown that the prediction capacity is severely affected by data properties such as the level of instrumental noise, the rank of the response matrices and the signal selectivity pattern of the analyte.

Prospective inference of bioprocess cell viability through chemometric modeling of fluorescence multiway data.

In this investigation, the fermentation step of a standard mammalian cell-based industrial bioprocess for the production of a therapeutic protein was studied, with particular emphasis on the evolution of cell viability. This parameter constitutes one of the critical variables for bioprocess monitoring since it can affect downstream operations and the quality of the final product. In addition, when the cells experiment an unpredictable drop in viability, the assessment of this variable through classic off-line methods may not provide information sufficiently in advance to take corrective actions. In this context, Process Analytical Technology (PAT) framework aims to develop novel strategies for more efficient monitoring of critical variables, in order to improve the bioprocess performance. Thus, in this work, a set of chemometric tools were integrated to establish a PAT strategy to monitor cell viability, based on fluorescence multiway data obtained from fermentation samples of a particular bioprocess, in two different scales of operation. The spectral information, together with data regarding process variables, was integrated through chemometric exploratory tools to characterize the bioprocess and stablish novel criteria for the monitoring of cell viability. These findings motivated the development of a multivariate classification model, aiming to obtain predictive tools for the monitoring of future lots of the same bioprocess. The model could be satisfactorily fitted, showing the non-error rate of prediction of 100%.

Interference-free calibration with first-order instrumental data and multivariate curve resolution. When and why?

The possibility of building an interference-free calibration with first-order instrumental data with multivariate curve resolution-alternating least-squares (MCR-ALS) has been a recent topic of interest. When the protocols were successful, MCR-ALS proved to be suitable for the extraction of chemically meaningful information from first-order calibration datasets, even in the presence of unexpected species, i.e., constituents present in the test samples but absent in the calibration set. This may represent an interesting advantage over classical first-order models, e.g. partial least-squares regression (PLS). However, the predictive capacity of MCR-ALS models can be severely affected by rotational ambiguity (RA), which is usually present in first-order datasets when interferents occur, and has not been always characterized in the published analytical protocols. The aim of this report is to discuss important issues regarding MCR-ALS modelling of first-order data for a calibration scenario with a single analyte and one interferent through simulated and experimental data. Specifically, the question of when and why MCR-ALS allows one to build interference-free calibration models with first-order data is studied in terms of signal overlapping, extent of RA, and especially the role of ALS initialization procedures in prediction performance. The aim is to alert analytical chemists that interference-free MCR-ALS with first-order data may not always be successful.

Sensitivity for Multivariate Calibration Based on Multilayer Perceptron Artificial Neural Networks.

The use of machine learning for multivariate spectroscopic data analysis in applications related to process monitoring has become very popular since non-linearities in the relationship between signal and predicted variables are commonly observed. In this regard, the use of artificial neural networks (ANN) to develop calibration models has demonstrated to be more appropriate and flexible than classical multivariate linear methods. The most frequently reported type of ANN is the so-called multilayer perceptron (MLP). Nevertheless, the latter models still lack a complete statistical characterization in terms of prediction uncertainty, which is an advantage of the parametric counterparts. In the field of analytical calibration, developments regarding the estimation of prediction errors would derive in the calculation of other analytical figures of merit (AFOMs), such as sensitivity, analytical sensitivity, and limits of detection and quantitation. In this work, equations to estimate the sensitivity in MLP-based calibrations were deduced and are here reported for the first time. The reliability of the derived sensitivity parameter was assessed through a set of simulated and experimental data. The results were also applied to a previously reported MLP fluorescence calibration methodology for the biopharmaceutical industry, yielding a value of sensitivity ca. 30 times larger than for the univariate reference method.

Modelling of bioprocess non-linear fluorescence data for at-line prediction of etanercept based on artificial neural networks optimized by response surface methodology.

In the last years, regulatory agencies in biopharmaceutical industry have promoted the design and implementation of Process Analytical Technology (PAT), which aims to develop rapid and high-throughput strategies for real-time monitoring of bioprocesses key variables, in order to improve their quality control lines. In this context, spectroscopic techniques for data generation in combination with chemometrics represent alternative analytical methods for on-line critical process variables prediction. In this work, a novel multivariate calibration strategy for the at-line prediction of etanercept, a recombinant protein produced in a mammalian cells-based perfusion process, is presented. For data generation, samples from etanercept processes were daily obtained, from which fluorescence excitation-emission matrices were generated in the spectral ranges of 225.0 and 495.0 nm and 250.0 and 599.5 nm for excitation and emission modes, respectively. These data were correlated with etanercept concentration in supernatant (measured by an off-line HPLC-based reference univariate technique) by implementing different chemometric strategies, in order to build predictive models. Partial least squares (PLS) regression evidenced a non-linear relation between signal and concentration when observing actual vs. predicted concentrations. Hence, a non-parametric approach was implemented, based on a multilayer perceptron artificial neural network (MLP). The MLP topology was optimized by means of the response surface methodology. The prediction performance of MLP model was superior to PLS, since the first is able to cope with non-linearity in calibration models, reaching percentage mean relative error in predictions of about 7.0% (against 12.6% for PLS). This strategy represents a fast and inexpensive approach for etanercept monitoring, which conforms the principles of PAT.