Ricard Boqué

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

This paper gives an introduction to multivariate calibration from a chemometrics perspective and reviews the various proposals to generalize the well-established univariate methodology to the multivariate domain. Univariate calibration leads to relatively simple models with a sound statistical underpinning. The associated uncertainty estimation and figures of merit are thoroughly covered in several official documents. However, univariate model predictions for unknown samples are only reliable if the signal is sufficiently selective for the analyte of interest. By contrast, multivariate calibration methods may produce valid predictions also from highly unselective data. A case in point is quantification from near-infrared (NIR) spectra. With the ever-increasing sophistication of analytical instruments inevitably comes a suite of multivariate calibration methods, each with its own underlying assumptions and statistical properties. As a result, uncertainty estimation and figures of merit for multivariate calibration methods has become a subject of active research, especially in the field of chemometrics.

Data fusion methodologies for food and beverage authentication and quality assessment – A review

The ever increasing interest of consumers for safety, authenticity and quality of food commodities has driven the attention towards the analytical techniques used for analyzing these commodities. In recent years, rapid and reliable sensor, spectroscopic and chromatographic techniques have emerged that, together with multivariate and multiway chemometrics, have improved the whole control process by reducing the time of analysis and providing more informative results. In this progression of more and better information, the combination (fusion) of outputs of different instrumental techniques has emerged as a means for increasing the reliability of classification or prediction of foodstuff specifications as compared to using a single analytical technique. Although promising results have been obtained in food and beverage authentication and quality assessment, the combination of data from several techniques is not straightforward and represents an important challenge for chemometricians. This review provides a general overview of data fusion strategies that have been used in the field of food and beverage authentication and quality assessment.

Estimating uncertainties of analytical results using information from the validation process

A new approach for calculating uncertainties of analytical results based on the information from the validation process is proposed. This approach complements the existing approaches proposed to date and can be applied to any validated analytical method. The precision estimates generated during the process of assessment of the accuracy take into account the uncertainties of preprocessing steps and analytical measurement steps as long as the different factors that influence these steps are representatively varied in the whole validation process. Since the accuracy of an analytical method should be always assessed before applying it to future working samples, little extra work needs to be done to estimate the final uncertainty. Other sources of uncertainty not previously considered (e.g. uncertainty associated to sampling, to differences between the test-sample and the working sample, etc.) are subsequently included and mathematically combined with the uncertainty arising from the assessment of the accuracy to provide the overall uncertainty. These ideas are illustrated with a case study of the determination of copper in contaminated land.

Multiway multiblock component and covariates regression models

In this paper the general theory of multiway multiblock component and covariates regression models is explained. Unlike in existing methods such as multiblock PLS and multiblock PCA, in the new proposed method a different number of components can be selected for each block. Furthermore, the method can be generalized to incorporate multiway blocks to which any multiway model can be applied. The method is a direct extension of principal covariates regression and therefore works in a simultaneous fashion in which a clearly defined objective criterion is minimized. It can be tuned to fulfil the requirements of the user. Algorithms to calculate the components will be presented. The method will be illustrated with two three‐block examples and compared to existing approaches. The first example is with two‐way data and the second example is with a three‐way array. It will be shown that predictions are as good as with the existing methods, but because for most blocks fewer components are required, diagnostic properties of the method are improved. Copyright

Limit of detection estimator for second-order bilinear calibration

A new approach is developed for estimating the limit of detection in second-order bilinear calibration with the generalized rank annihilation method (GRAM). The proposed estimator is based on recently derived expressions for prediction variance and bias. It follows the latest IUPAC recommendations in the sense that it concisely accounts for the probabilities of committing both types I and II errors, i.e. false positive and false negative declarations, respectively. The estimator has been extensively validated with simulated data, yielding promising results.

Rapid characterization of transgenic and non-transgenic soybean oils by chemometric methods using NIR spectroscopy

Near infrared (NIR) spectroscopy and multivariate classification were applied to discriminate soybean oil samples into non-transgenic and transgenic. Principal Component Analysis (PCA) was applied to extract relevant features from the spectral data and to remove the anomalous samples. The best results were obtained when with Support Vectors Machine-Discriminant Analysis (SVM-DA) and Partial Least Squares-Discriminant Analysis (PLS-DA) after mean centering plus multiplicative scatter correction. For SVM-DA the percentage of successful classification was 100% for the training group and 100% and 90% in validation group for non transgenic and transgenic soybean oil samples respectively. For PLS-DA the percentage of successful classification was 95% and 100% in training group for non transgenic and transgenic soybean oil samples respectively and 100% and 80% in validation group for non transgenic and transgenic respectively. The results demonstrate that NIR spectroscopy can provide a rapid, nondestructive and reliable method to distinguish non-transgenic and transgenic soybean oils.

Measurement uncertainty in analytical methods in which trueness is assessed from recovery assays

We propose a new procedure for estimating the uncertainty in quantitative routine analysis. This procedure uses the information generated when the trueness of the analytical method is assessed from recovery assays. In this paper, we assess trueness by estimating proportional bias (in terms of recovery) and constant bias separately. The advantage of the procedure is that little extra work needs to be done to estimate the measurement uncertainty associated to routine samples. This uncertainty is considered to be correct whenever the samples used in the recovery assays are representative of the future routine samples (in terms of matrix and analyte concentration). Moreover, these samples should be analysed by varying all the factors that can affect the analytical method. If they are analysed in this fashion, the precision estimates generated in the recovery assays take into account the variability of the routine samples and also all the sources of variability of the analytical method. Other terms related to the sample heterogeneity, sample pretreatments or factors not representatively varied in the recovery assays should only be subsequently included when necessary. The ideas presented are applied to calculate the uncertainty of results obtained when analysing sulphides in wine by HS-SPME-GC.

Multivariate detection limits with fixed probabilities of error

Abstract In this paper, a new approach to calculate multivariate detection limits (MDL) for the commonly used inverse calibration model is discussed. The derived estimator follows the latest recommendations of the International Union of Pure and Applied Chemistry (IUPAC) concerning the detection capabilities of analytical methods. Consequently, the new approach: (a) is based on the theory of hypothesis testing and takes into account the probabilities of false positive and false negative decisions, and (b) takes into account all the different sources of error, both in calibration and prediction steps, which affect the final result. The MDL is affected by the presence of other analytes in the sample to be analysed; therefore, it has a different value for each sample to be tested and so the proposed approach attempts to find whether the concentration derived from a given response can be detected or not at the fixed probabilities of error. The estimator has been validated with and applied to real samples analysed by NIR spectroscopy.

Uncertainty of results in routine qualitative analysis

Abstract Uncertainty is a performance characteristic that should be estimated in both quantitative and qualitative results in order to improve knowledge of their reliability. Contrary to quantitative results, uncertainty in qualitative analysis cannot be expressed as an interval around the predicted value. The uncertainty is probabilistic in nature as it might express the probability of taking a wrong decision. In this article, we review four different ways of estimating the uncertainty of a qualitative or screening system: contingency tables; Bayes’ theorem; statistical intervals; and, performance curves. We pay particular attention to their advantages and drawbacks, and their main applications.

Detection limits in classical multivariate calibration models

Abstract This work presents a new approach for calculating multivariate detection limits for the commonly used classical or direct calibration models. The derived estimator, which is in accordance with latest IUPAC recommendations, accounts for the different sources of error related to the calibration and prediction steps. Since the multivariate detection limit for a given analyte is influenced by the presence of other components in the sample, a different detection limit is calculated for each analyte and analysed sample, at the chosen significance levels α and β . The proposed methodology has been experimentally validated by determining four pesticides in water using a FIA method with diode-array detection. The results compare favourably with the ones obtained using previously proposed estimators.