On the construction of experimental designs for a given task by jointly optimizing several quality criteria: Pareto-optimal experimental designs

Experimental designs for a given task should be selected on the base of the problem being solved and of some criteria that measure their quality. There are several such criteria because there are several aspects to be taken into account when making a choice. The most used criteria are probably the so-called alphabetical optimality criteria (for example, the A-, E-, and D-criteria related to the joint estimation of the coefficients, or the I- and G-criteria related to the prediction variance). Selecting a proper design to solve a problem implies finding a balance among these several criteria that measure the performance of the design in different aspects. Technically this is a problem of multi-criteria optimization, which can be tackled from different views. The approach presented here addresses the problem in its real vector nature, so that ad hoc experimental designs are generated with an algorithm based on evolutionary algorithms to find the Pareto-optimal front. There is not theoretical limit to the number of criteria that can be studied and, contrary to other approaches, no just one experimental design is computed but a set of experimental designs all of them with the property of being Pareto-optimal in the criteria needed by the user. Besides, the use of an evolutionary algorithm makes it possible to search in both continuous and discrete domains and avoid the need of having a set of candidate points, usual in exchange algorithms.Projects CTQ2011-26022(SpanishMinisteriodeEconomíayCompetitividad)andBU108A11-2(JuntadeCastillayLeón)

Kinetic models of migration of melamine and formaldehyde from melamine kitchenware with data of liquid chromatography

European legislation has established a specific migration limit (SML) of 15 mg kg−1 for formaldehyde and 2.5 mg kg−1 for melamine. Formaldehyde resins are used in the manufacture of melamine kitchenware. Formaldehyde is listed in group 1 of the IARC list of carcinogenic compounds. To determine the quantity of formaldehyde and melamine as potential migrants from different types of melamine kitchenware (glass, mug, cutlery, big cup and bowl), a HPLC-DAD method has been implemented. This method is an alternative to the ones proposed in technical guidelines to determine formaldehyde by UV–vis spectrophotometry and melamine by HPLC. The final objective was to fit the migration kinetic curves of these two analytes in melamine kitchenware. After the method was validated, decision limit (CCα) and detection capability (CCβ) were calculated for both analytes, when the probabilities of false positive (α) and false negative (β) were fixed at 0.05; being CCβ 0.269 mg L−1 and 0.311 mg L−1 for melamine and formaldehyde respectively. CCα and CCβ were also calculated at the SML of both analytes. The migration testing were conducted with simulant B (3% acetic acid (w/v) in aqueous solution), the conditions of each exposure being 70 °C for 2 h. The quantities of melamine and formaldehyde found in the third exposure of the total kitchenware analysed were between 0.21 and 1.09 mg L−1 and between 0.55 and 3.86 mg L−1, respectively. Migration kinetic curves were built for each type of kitchenware with the data of sixteen consecutive migration cycles (70 °C each 30 min). The SML for melamine was surpassed in the mug, in the big cup and in the bowl after eleven, thirteen and one cycles, respectively. When more cycles were carried out in the mug, the values of the accumulated quantity of formaldehyde and melamine were 15.30 and 6.79 mg L−1, respectively, after thirty-two cycles. Both concentrations exceeded the corresponding SML.MINECO (AEI/FEDER, UE) and Consejería de Educación de la Junta de Castilla y León through projects CTQ2017-88894-R and BU012P17 respectively (all co-financed with FEDER funds

Univariate data analysis versus multivariate approach in liquid chromatography. An application for melamine migration from food contact materials

The aim of this work is focused on the melamine migration from food contact materials (FCMs), considering data obtained from univariate analysis versus that obtained from multivariate approach in liquid chromatography coupled to diode array detector. Plastic food contact materials are made from monomers and additives. Moreover, non-intentionally added substances (NIAS) can be part of the composition of the FCM: raw material impurities or process by-products, inks or adhesives. Any compound present within a FCM can migrate to foodstuff. Specific migration of some substances from plastic FCMs to food/simulant is limited by European legislation in force (Commission Regulation No 10/2011). Quantification of analytes in migration samples through a univariate analysis could lead to erroneous results. As an example, in liquid chromatography NIAS can interfere when coeluting with analytes or when they have close retention time. In that case, an overestimation would happen and the verification of the compliance of the specific migration limit (SML) of a substance would be incorrect. A solution to the problem can be found in the application of a chemometric tool with the second-order advantage, which allows the unequivocal identification of analytes. Specifically, for this work, PARAFAC/ PARAFAC2 decomposition technique along with tensors arranged from HPLC-DAD data of migration (test and kinetics) samples were used for the identification and quantification of melamine. Results of melamine quantity found in migration samples from five types of melaware by means of a multivariate approach were compared to results obtained with a univariate data analysis carried out with values of chromatographic peak area as response. The comparison reveals that in test samples, univariate analysis supposes an overestimation in the quantity of melamine of 30 % on average, with respect of the concentration obtained from the multivariate approach. Besides, in kinetics samples it is remarkable that for one migration cycle the melamine found was 10 times above the one that obtained with PARAFAC decomposition. Summing up, multivariate data analysis of migration samples supposes a great advantage in order to comply with the established regulation about migrants and to decrease the false non-compliant results.The authors thank the Consejería de Educación de la Junta de Castilla y León, Spain for financial support through project BU052P20, cofinanced with FEDER funds. M.M. Arce wish to thank JCyL for her postdoctoral contract through project BU052P20

Logical analysis of sample pooling for qualitative analytical testing

When the prevalence of positive samples in a whole population is low, the pooling of samples to detect them has been widely used for epidemic control. However, its usefulness for applying analytical screening procedures in food safety (microbiological or allergen control), fraud detection or environmental monitoring is also evident. The expected number of tests per individual sample that is necessary to identify all ‘positives’ is a measure of the efficiency of a sample pooling strategy. Reducing this figure is key to an effective use of available resources in environmental control and food safety. This reduction becomes critical when the availability of analytical tests is limited, as the SARS-CoV-2 pandemic showed. The outcome of the qualitative analytical test is binary. Therefore, the operation governing the outcome of the pooled samples is not an algebraic sum of the individual results but the logical operator (‘or’ in natural language). Consequently, the problem of using pooled samples to identify positive samples naturally leads to proposing a system of logical equations. Therefore, this work suggests a new strategy of sample pooling based on: i) A half-fraction of a Placket-Burman design to make the pooled samples and ii) The logical resolution, not numerical, to identify the positive samples from the outcomes of the analysis of the pooled samples. For a prevalence of ‘positive’ equal to 0.05 and 10 original samples to be pooled, the algorithm presented here results in an expected value per individual equal to 0.37, meaning a 63% reduction in the expected number of tests per individual sample. With sensitivities and specificities of the analytical test ranging from 0.90 to 0.99, the expected number of tests per individual ranges from 0.332 to 0.416, always higher than other pooled testing algorithms. In addition, the accuracy of the algorithm proposed is better or similar to that of other published algorithms, with an expected number of hits ranging from 99.16 to 99.90%. The procedure is applied to the detection of food samples contaminated with a pathogen (Listeria monocytogenes) and others contaminated with an allergen (Pistachio) by means of Polymerase Chain Reaction, PCR, test.This work was supported by Consejería de Educación de la Junta de Castilla y León through project BU052P20 co-financed with European Regional Development Funds. The authors thank Dr. Laura Rubio for applying the double-blind protocol to dope the samples and AGROLAB S.L.U, Burgos (Spain) for the careful preparation of the pooled samples

Effect of the cleaning procedure of Tenax on its reuse in the determination of plasticizers after migration by gas chromatography/mass spectrometry

This paper presents the simultaneous determination of a UV stabilizer (benzophenone (BP)) together with four plasticizers (butylated hydroxytoluene (BHT), diisobutyl phthalate (DiBP), bis(2-ethylhexyl) adipate (DEHA) and diisononyl phthalate (DiNP)) in Tenax by gas chromatography/mass spectrometry and PARAFAC, using DiBP-d4 as internal standard. Regulation (EU) No. 10/2011 establishes Tenax as food simulant E for testing specific migration from plastics into dry foodstuffs. This simulant must be cleaned before its use to eliminate impurities. Tenax is expensive, so its reuse would save costs. A two-way ANOVA was used to study some parameters affecting the cleaning and the extraction of Tenax. The most adequate conditions were chosen taking the values of the coefficient of variation and the average recovery rates of spiked Tenax samples into account. A study to determine if some analytes remain in Tenax when it is reused and the effect that the cleaning procedure may have in the adsorption capability of Tenax was proposed. This study led to the conclusion that Tenax could not be reused in this multiresidue determination. All the analytes were unequivocally identified in all the stages of this work and trueness was verified at a 95% confidence level in all cases. A calibration based on PARAFAC provided the following values of capability of detection (CCβ): 2.28 μg L−1 for BHT, 10.57 μg L−1 for BP, 7.87 μg L−1 for DiBP, 3.04 μg L−1 for DEHA and 124.8 μg L−1 for DiNP, with the probabilities of false positive and false negative fixed at 0.05. The migration of the analytes from a printed paper sample into Tenax was also studied. The presence of BHT in the food simulant was confirmed and the amount released of this analyte from the paper was 2.56 μg L−1.Ministerio de Economía y Competitividad (CTQ2014-53157-R) and Junta de Castilla y León (BU012P1

A modified entropy-based performance criterion for class-modelling with multiple classes

The paper presents a new proposal for a single overall measure, the diagonal modified confusion entropy (DMCEN), to assess the performance of class-models jointly computed for several classes, a versatile index regarding sensitivity and specificity, and that supports class weighting. The characteristics of the proposed figure of merit are illustrated as against other usual performance measures and show how the index is more sensitive to the variations in the class-models than similar published indexes. Besides, a benchmark value representing a random modelling is also defined for DMCEN to be used as initial level to assess the quality of the built class-models. Furthermore, systematic comparisons have been conducted by using the degree of consistency C and the degree of discriminancy D when comparing the proposed DMCEN to the usual total efficiency (a geometric mean between sensitivity and specificity). Simulations show that, for a hundred thousand sensitivity/specificity matrices with four categories, C is almost 0.7 on average, well above the needed 0.5, and there is more than 62% probability that DMCEN detects differences when the total efficiency does not. Illustration of the application of the index is shown with an experimental data set with four categories.Spanish Ministerio de Ciencia, Innovaci on y Universidades (AEI) and Consejería de Educaci on de la Junta de Castilla y Le on through projects CTQ2017-88894-R and BU052P20 respectively (both co-financed with European Regional Development Funds

A computational approach to partial least squares model inversion in the framework of the process analytical technology and quality by design initiatives

In the context of the paradigms founding the Quality by Design and Process Analytical Technology initiatives, the work herein presents a computational approach to support the decision-making process, in particular, about the feasibility of a product defined for some a priori given quality characteristics. The approach is based on the computation of the pareto-optimal front when simultaneously minimizing the expected differences between the predicted and the desired characteristics. Thus, the feasibility is tackled as an optimization problem with the novelty of doing so simultaneously for all the characteristics, preserving the correlation structure, but by separately handling each individual characteristic. With data from a low-density polyethylene production process, with fourteen process variables and five measured characteristics of the final polyethylene, solutions are found to define the Design Space for targeted quality characteristics on the product, and without the need of explicitly inverting the PLS (Partial Least Squares) prediction model fitted to the process.Junta de Castilla y León (BU012P17), and also Spanish MINECO and Agencia Estatal de Investigación under research projects CTQ2014-53157-R, and CTQ2017-88894-

Optimization of a headspace solid-phase microextraction and gas chromatography/mass spectrometry procedure for the determination of aromatic amines in water and in polyamide spoons

In this work, a headspace solid-phase microextraction and gas chromatography coupledwith mass spectrometry (HS-SPME-GC/MS) method for trace determination of primary aromatic amines was developed. The following analytes were investigated: aniline (A), 4,4′-diaminodiphenylmethane (4,4′-MDA) and 2,4-diaminotoluene (2,4-TDA) using 3-chloro-4-fluoroaniline (3C4FA) and 2-aminobiphenyl (2ABP) as internal standards. Prior to extraction the analytes were derivatized in the aqueous solution by diazotation and subsequent iodination. The derivativeswere extracted byHS-SPME using a PDMS/DVB fiber and analyzed by GC/MS. A D-optimal design was used to study the parameters affecting the HS-SPME procedure and the derivatization step. Two experimental factors at two levels and one factor at three levels were considered: (i) reaction time, (ii) extraction temperature, and (iii) extraction time in the headspace. The interaction between the extraction temperature and extraction time was considered in the proposed model. The loadings in the sample mode estimated by a PARAFAC (parallel factor analysis) decomposition for each analyte were the response used in the design because they are proportional to the amount of analyte extracted. The optimum conditions for the best extraction of the analytes were achieved when the reaction time was 20 min, the extraction temperature was 50 °C and the extraction time was 25 min. The interaction was significant. A calibration based on a PARAFAC decomposition provided the following values of decision limit (CCα): 1.07 μgL−1 for A, 1.23 μg L−1 for 2,4-TDA and 0.83 μg L−1 for 4,4′-MDA for a probability of false positive fixed at 5%. Also, the accuracy (trueness and precision) of the procedurewas assessed. Furthermore, all the analyteswere unequivocally identified. Finally, the method was applied to spiked water samples and polyamide cooking utensils (spoons). 3% (w/v) acetic acid in aqueous solution was used as food simulant for testing migration from polyamide kitchenware. Detectable levels of 4,4′-diaminodiphenylmethane and aniline were found in food simulant from some of the investigated cooking utensils.Ministerio de Economía y Competitividad (CTQ2011-26022) and Junta de Castilla y León (BU108A11-2

Simultaneous class-modelling in chemometrics: A generalization of Partial Least Squares class modelling for more than two classes by using error correcting output code matrices

The paper presents a new methodology within the framework of the so-called compliant class-models, PLS2-CM, designed with the purpose of improving the performance of class-modelling in a setting with more than two classes. The improvement in the class-models is achieved through the use of multi-response PLS models with the classes encoded via Error-Correcting Output Codes (ECOC), instead of the traditional class indicator variables used in chemometrics. The proposed PLS2-CM entails a decomposition of a class-modelling problem into a series of binary learners, based on a family of code matrices with different code length, which are evaluated to obtain simultaneous compliant class-models with the best performance. The methodology develops both a new encoding system, based on multi-criteria optimization to search for optimal coding matrices, and a new decoding system, based on probability thresholds to assign objects to classmodels. The whole procedure implies that the characteristics of the dataset at hand affect the final selection of the coding matrix and therefore of built class-models, thus giving rise to a data-driven strategy. The application of PLS2-CM to a variety of cases (controlled data, experimental data and repository datasets) results in an enhanced class-modelling performance by means of the suggested procedure, as measured by the DMCEN (Diagonal Modified Confusion Entropy) index and by sensitivity-specificity matrices. The predictive ability of the compliant class-models has been evaluated.This work is part of the project with reference BU052P20 financed by Junta de Castilla y Leon, Conserjería de Educacion with the aid of European Regional Development Funds

A useful tool for computation and interpretation of trading-off solutions through pareto-optimal front in the field of experimental designs for mixtures

An algorithmic implementation is presented to deal with several responses in mixtures problems, without theoretical limits on the number of responses or on the factors to be blended. Also, constrained and unconstrained domains are handled, as well as domains with both mixtures and discrete variables. Besides, an alternative way of interpreting the results coming from the experimental design for mixtures is presented. It is based on the parallel coordinates plots for visualization in more than the usual three-dimensional Cartesian diagrams or the simplex mixture spaces for at most four experimental factors. Specifically, this is done in cases in which more than one experimental response should be handled, tackling the conflict by estimating trading-off solutions via the computation of the pareto-optimal front, which is fully explored with the parallel coordinates plots. The procedure is shown by two case-studies, taken from the literature. The first one deals with several factors in a constrained experimental domain when trying to optimize a detergent by taking into account two severely conflicting characteristics. The second one is about five chemical components blended with different dosage levels for getting a concrete strong enough, experimental results that are re-evaluated by posing a unique blocked design for analysing the data. The joint use of the pareto-optimal front for mixtures designs and the parallel coordinates plots for its visualization provide the researcher a deeper understanding of the problem under study to make accurate decisions.Spanish Ministerio de Economía y Competitividad through project CTQ2014- 53157-R, a national competitive project co-financed with European FEDER funds