Robust regression and outlier detection in the evaluation of robustness tests with different experimental designs

Robustness tests are usually based on an experimental design approach. As designed experiments generally lead to a large variability among the results, erroneous results are often not readily detected. As a consequence, the ordinary least squares (OLS) estimates of the effects of the robustness test can be biased. Here, two robustness tests are studied, which both contain a suspicious result. Moreover, simulated datasets are considered to examine the influence of the extent of the outlier as well as the influence of multiple outliers. On the one hand, different methods are applied to inspect the results of the experiments for outliers: the half-normal plot of the OLS residuals, the normal probability plot of the effects and a method, which is based on experimental design reconstruction. On the other hand, two robust regression methods are applied to calculate the effects with a minimum influence of possible outliers. The different methods are compared and it is evaluated under which circumstances they can be applied.     

Robust and non-parametric statistics in the evaluation of figures of merit of analytical methods. Practices for students

A set of laboratory practices is proposed in which evaluation of the quality of the analytical measurements is incorporated explicitly by applying systematically suitable methodology for extracting the useful information contained in chemical data. Non-parametric and robust techniques useful for detecting outliers have been used to evaluate different figures of merit in the validation and optimization of analytical methods. In particular, they are used for determination of the capability of detection according to ISO 11843 and IUPAC and for determination of linear range, for assessment of the response surface fitted using an experimental design to optimize an instrumental technique, and for analysis of a proficiency test carried out by different groups of students. The tools used are robust regression, least median of squares (LMS) regression, and some robust estimators as median absolute deviation (m.a.d.) or Huber estimator, which are very useful as an alternatives to the usual centralization and dispersion estimators.     

A consensus least squares support vector regression (LS-SVR) for analysis of near-infrared spectra of plant samples

Consensus modeling of combining the results of multiple independent models to produce a single prediction avoids the instability of single model. Based on the principle of consensus modeling, a consensus least squares support vector regression (LS-SVR) method for calibrating the near-infrared (NIR) spectra was proposed. In the proposed approach, NIR spectra of plant samples were firstly preprocessed using discrete wavelet transform (DWT) for filtering the spectral background and noise, then, consensus LS-SVR technique was used for building the calibration model. With an optimization of the parameters involved in the modeling, a satisfied model was achieved for predicting the content of reducing sugar in plant samples. The predicted results show that consensus LS-SVR model is more robust and reliable than the conventional partial least squares (PLS) and LS-SVR methods.     

The construction of simultaneous optimal experimental designs for several polynomials in the calibration of analytical methods

In this paper a criterion is described for the construction of experimental designs for the evaluation of calibration models in analytical chemistry. The proposed criterion seeks a compromise between the D-optimal designs for estimating the parameters of different polynomial models. A computer algorithm is presented for a sequential construction of experimental designs using the optimality criterion. The performance of the optimality criterion and the computer algorithm is elaborated for the problem of discrimination between a first- to a third-degree polynomial for the calibration of analytical methods. An experimental design consisting of replicate measurements at five distinct levels equally spaced over the calibration range proved a good solution.     

Multivariate analytical sensitivity in the determination of selenium, copper, lead and cadmium by stripping voltammetry when using soft calibration

A new approach to the multivariate sensitivity concept based on the determination of the capability of discrimination of a method of analysis is shown. Thus the analytical sensitivity is defined in this work by the analyte concentration that a analytical method is able to discriminate, which implies the estimation of the ‘false noncompliance’ and ‘false compliance’. In this approach the estimation of the multivariate analytical sensitivity is independent of scale factors and calibration models, and allows one to study the behavior of a analytical method for several concentrations and matrix. The estimation of this parameter in the simultaneous determination of selenium, copper, lead and cadmium by stripping voltammetry when using soft calibration is carried out, showing that different multivariate analytical sensitivities are obtained for each metal.     

Determination of sugars in depilatory formulations: a green analytical method employing infrared detection and partial least squares regression

A green analytical method was developed for the analysis of sugar-based depilatories. Three independent partial least squares (PLS) regression models were built for the direct determination of glucose, fructose and maltose without any sample pretreatment based on their attenuated total reflectance - Fourier transform infrared (ATR-FTIR) spectra. The models showed adequate prediction capabilities with root-mean-square-errors of prediction ranging from 7.04 to 12.55 mg sugar g⁻¹ sample. As a reference procedure, gradient liquid chromatography with on-line infrared detection, employing background correction based on cubic smoothing splines, was used. The analysis revealed changes in the sugar concentration due to the formulation process as compared to information on the ingredients provided by the manufacturers. Although fructose, glucose and sucrose were declared to be used for the production of depilatories, in the final products only fructose, glucose and maltose were determined. This fact was attributed to pH and temperature conditions employed during the production process as well as to the use of glucose syrup instead of crystalline glucose. The present ATR-FTIR-PLS method enables an accurate, cheap and fast determination without solvent consumption or toxic waste generation and offers therefore a green screening alternative to methods employing chromatographic techniques.     

Capacitively coupled contactless conductivity detection as an alternative detection mode in CE for the analysis of kanamycin sulphate and its related substances

A method was developed to determine simultaneously kanamycin, its related substances and sulphate in kanamycin sulphate using capacitively coupled contactless conductivity detection. Kanamycin is an aminoglycoside antibiotic that lacks a strong UV-absorbing chromophore. Due to its physicochemical properties, CE in combination with capacitively coupled contactless conductivity detection was chosen. The separation method uses a BGE composed of 40 mM 2-(N-morpholino)ethanesulphonic acid monohydrate and 40 mM L-histidine, pH 6.35. A 0.6 mM N-cetyltrimethyl ammonium bromide (CTAB) solution was added as electroosmotic flow modifier in a concentration below the critical micellar concentration (CMC). Ammonium acetate 50 mg/L was used as internal standard. In total, 30 kV was applied in reverse polarity on a fused-silica capillary (65/41 cm; 75 μm id). The optimized separation was obtained in less than 6 min with good linearity (R(2)=0.9999) for kanamycin. It shows a good precision expressed as RSD on the relative peak areas equal to 0.3 and 1.1% for intra-day and inter-day precision, respectively. The LOD and LOQ are 0.7 and 2.3 mg/L, respectively. Similarly, for sulphate, a good linearity (R(2)=0.9996) and precision (RSD 0.4 and 0.6% for intra-day and inter-day, respectively) were obtained.     

Tutorial on evaluation of type I and type II errors in chemical analyses: From the analytical detection to authentication of products and process control

Uncertainty is inherent in all experimental determinations. Nevertheless, these measurements are used to make decisions including the performance of the own measurement systems. The link between the decision and the true implicit system that generates the data (measurement system, production process, category of samples, etc.) is a representation of this uncertainty as a probability distribution. This representation leads to the probabilistic formalization of the possibility of making errors. In the context of regulations established by official agencies, it is important to use these statistical decision methods in some cases because the own norm makes them mandatory and, in general, because this is the way of reasonably evaluating whether a working hypothesis is rejected on the basis of the experimental data.The aim of the present tutorial is to introduce some ideas and basic methods for the critical analysis of experimental data. With this goal, the basic elements of the Neyman-Pearson theory of hypothesis testing are formally introduced in connection with the common problems in chemical analysis and, if this is the case, their relation to the norms of regulatory agencies. The notion of decision with ‘enough quality’ is modelled when explicitly considering: (1) the null, H₀, and alternative, H₁, hypotheses. (2) The significance level of the test, which is the probability, α, of rejecting H₀ when it is true, and the power of the test, 1 − β, β being the probability of accepting H₀ when it is false. (3) The difference between H₀ and H₁ that has to be detected with experimental data. (4) The needed sample size. These four concepts should be explicitly defined for each problem and, under the usual assumption of normal distribution of the data, the mathematical relations among these concepts are shown, which allow the analyst to design a decision rule with pre-set values of α and β.To illustrate the unifying character of this inferential methodology, several situations are exposed along the tutorial: the design of a hypothesis test to decide on the performance characteristics of analytical methods, the capability of detection of both quantitative and qualitative analytical methods (including its generalization to the case of multivariate and/or multiway signals), the analytical sensitivity with multivariate signals, the class-modelling and the process control.     

A self‐guided search for good local minima of the sum‐of‐squared‐error in nonlinear least squares regression

Hard modeling of nonlinear chemical or biological systems is highly relevant as a model function together with values for model parameters provides insights in the systems' functionalities. Deriving values for said model parameters via nonlinear regression, however, is challenging as usually one of the numerous local minima of the sum‐of‐squared errors (SSEs) is determined; furthermore, for different starting points, different minima may be found. Thus, nonlinear regression is prone to low accuracy and low reproducibility. Therefore, there is a need for a generally applicable, automated initialization of nonlinear least squares algorithms, which reaches a good, reproducible solution after spending a reasonable computation time probing the SSE‐hypersurface. For this purpose, a three‐step methodology is presented in this study. First, the SSE‐hypersurface is randomly probed in order to estimate probability density functions of initial model parameter that generally lead to an accurate fit solution. Second, these probability density functions then guide a high‐resolution sampling of the SSE‐hypersurface. This second probing focuses on those model parameter ranges that are likely to produce a low SSE. As the probing continues, the most appropriate initial guess is retained and eventually utilized in a subsequent nonlinear regression. It is shown that this “guided random search” derives considerably better regression solutions than linearization of model functions, which has so far been considered the best‐case scenario. Examples from infrared spectroscopy, cell culture monitoring, reaction kinetics, and image analyses demonstrate the broad and successful applicability of this novel method. Copyright © 2014 John Wiley & Sons, Ltd.     

Dual-sensitive probe 1-imidazole-2-(5-benzoacridine)-ethanone for the determination of amines in environmental water using HPLC with fluorescence detection and online atmospheric chemical ionization-mass spectrometry identification

Dual-sensitive probe of 1-imidazole-2-(5-benzoacridine)-ethanone (IBAE) for the determination of free amines with fluorescence detection and online highly sensitive atmospheric chemical ionization-mass spectrometry identification (APCI-MS) has been developed. 2-(Benzoacridine)-5-acetic acid (BAAA) reacts with coupling agent N,N′-carbonyldiimidazole (CDI) to form a highly activated amide intermediate 1-imidazole-2-(5-benzoacridine)-ethanone (IBAE), which is dual-sensitive probe. The amide intermediate (IBAE) reacts preferably with amines in dimethylformamide (DMF) solvent to give the high yields of derivatives. IBAE-amine derivatives are not only sensitive to fluorescence but also to MS ionizable efficiency. The percent ionization δ values change from 0 to 57.32% in aqueous acetonitrile and from 0 to 62.14% in aqueous methanol. The relative standard deviations of the peak areas with fluorescence detection for each amine are <1.24% (40 ng/ml, n = 6). The fluorescence detection limits (at a signal-to-noise ratio of 3) are in the range of 0.15-0.50 ng/ml. The online APCI-MS detection limits are in the range of 2.07-8.51 ng/ml (at a signal-to-noise ratio of 3). Therefore, the facile IBAE intermediate derivatization allowed the development of a highly sensitive and specific method for the quantitative analysis of trace levels of amines in environmental water.     

A review of techniques for the determination of polycyclic aromatic hydrocarbons in air

We provide an extensive review of the common methodologies employed in the analysis of airborne polycyclic aromatic hydrocarbons (PAHs). The review focuses on gas-chromatography-based approaches, in the light of their universal application with excellent separation, resolution, and sensitivity.We first describe collection methods for airborne PAHs in the gas and particle phases. We then evaluate the efficiency of extraction techniques employed for separating target PAHs from sampling media, using conventional solvent-based and emerging thermal-desorption approaches.We also describe commonly employed analytical methods with respect to their applicability to PAHs in gas and particle phases, collected from diverse environmental settings. As an essential part of basic quality assurance, we examine each method with special emphasis on key parameters (e.g., limit of detection and reproducibility).Finally, we address the likely directions of methodological developments, their limitations, and the future prospects for PAH analysis.     

Three-way models and detection capability of a gas chromatography-mass spectrometry method for the determination of clenbuterol in several biological matrices: the 2002/657/EC European Decision

Clenbuterol has been extracted by mixed solid-phase extraction from two biological matrices (bovine hair and urine) and detected by GC/MS (selected ion monitoring (SIM) and full-SCAN modes). The analytical signal has been modelled with univariate and three-way models, namely DTLD, PARAFAC, PARAFAC2, Tucker3 and trilinear PLS. Since clenbuterol is a banned substance a comparative study of the capability of detection (CCβ, X₀=0) has been performed as a function of the sample (hair, 74 μg kg⁻¹ and urine, 0.36 μg l⁻¹), the mode in which the signals are monitored (SCAN, 283 μg kg⁻¹ and SIM, 74 μg kg⁻¹) and the statistical model (univariate, 283 μg kg⁻¹ and trilinear PLS, 20.91 μg kg⁻¹). The capability of detection has been calculated as stated in ISO 11843 and Decision 2002/657/EC setting in all cases the probabilities of false positive and of false negative at 0.05.The identification of the mass spectra must be done to confirm the presence of clenbuterol and has been carried out through PARAFAC. The correlation coefficient between the spectra estimated by PARAFAC and the library spectra is 0.96 (hair, SCAN mode) and 1.00 (hair and urine, SIM mode).The Decision 2002/657/EC advocates the use of independent mass fragments to identify banned compounds. These recommendations together with the effect of the number of ions registered on the capability of detection have lead us to select five uncorrelated fragments (86, 243, 262, 264 and 277) from the data set of 210 ions by hierarchical clustering of variables.     

Hidden information in principal component analysis of ToF‐SIMS data: On the use of correlation loadings for the identification of significant signals and structure elucidation

In this paper, an improved approach to interpret results of principal component analysis (PCA) of time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) spectra is presented. Signals are typically observed in different intensity ranges in a single ToF‐SIMS spectrum due to different sensitivity factors and surface concentrations. This can complicate the PCA interpretation, because loadings are reported to be strongly affected by these intensity changes. In contrast, it is shown here that correlation loadings are unaffected by these differences. In particular, correlation loadings were successfully used to identify signals with relatively low intensity but high significance. These signals may be overlooked when only loadings are used. This is particularly true in failure analysis, where ToF‐SIMS is used to screen for initially unknown signals that may be relevant for the characteristics/failure of a product. As a model study, the concept was applied to investigate ageing of Li‐ion batteries by ToF‐SIMS. In this data set, the significance of impurities that affect the quality of Li‐ion batteries was identified only by correlation loadings, whereas the loadings were found to overestimate the influence of other matrix signals. In addition, correlation loadings aid in the chemical identification and helped to successfully assign unknown peaks.     

Identification and quantification of carbamate pesticides in dried lime tree flowers by means of excitation-emission molecular fluorescence and parallel factor analysis when quenching effect exists

A non-separative, fast and inexpensive spectrofluorimetric method based on the second order calibration of excitation-emission fluorescence matrices (EEMs) was proposed for the determination of carbaryl, carbendazim and 1-naphthol in dried lime tree flowers. The trilinearity property of three-way data was used to handle the intrinsic fluorescence of lime flowers and the difference in the fluorescence intensity of each analyte. It also made possible to identify unequivocally each analyte. Trilinearity of the data tensor guarantees the uniqueness of the solution obtained through parallel factor analysis (PARAFAC), so the factors of the decomposition match up with the analytes. In addition, an experimental procedure was proposed to identify, with three-way data, the quenching effect produced by the fluorophores of the lime flowers. This procedure also enabled the selection of the adequate dilution of the lime flowers extract to minimize the quenching effect so the three analytes can be quantified. Finally, the analytes were determined using the standard addition method for a calibration whose standards were chosen with a D-optimal design.     

Reusable sensor based on functionalized carbon dots for the detection of silver nanoparticles in cosmetics via inner filter effect

We report a low cost selective analytical method based on inner filter effect (IFE) for citrate-silver nanoparticle (cit-AgNP) detection, in which fluorescent amine-derivatized carbon dots (a-CDs) act as the donor and aggregated cit-AgNPs as the energy receptor. Carbon dots (CDs) were chemically modified with ethylenediamine (EDA) moieties via amidic linkage displaying an emission band at 440 nm. The presence of cit-AgNPs produces a remarkably quenching of a-CD fluorescence via IFE, since the free amine groups at CD surface induce the aggregation of cit-AgNPs accompany by a red-shifting of their characteristic plasmon absorption wavelength, which resulted in “turn-on” of the IFE-decreased in CD fluorescence. The proposed method, which involves the use of chelating agents for removal of metal ions interferences, exhibits a good linear correlation for detection of cit-AgNPs from 1.23 × 10⁻⁵ to 6.19 × 10⁻⁵ mol L⁻¹, with limits of detection (LOD) and quantification (LOQ) of 5.17 × 10⁻⁶ and 1.72 × 10⁻⁵ mol L^−1, respectively. This method demonstrates to be efficient and selective for the determination of cit-AgNPs in complex matrices such as cosmetic creams and reveals many advantages such as low cost, reusability, high sensitivity and non time-consuming compared with other traditional methods.     

A validated solid-liquid extraction method for the HPLC determination of polyphenols in apple tissues Comparison with pressurised liquid extraction

A solid-liquid extraction procedure followed by reversed-phase high-performance liquid chromatography (RP-HPLC) coupled with a photodiode array detector (DAD) for the determination of polyphenols in freeze-dried apple peel and pulp is reported. The extraction step consists in sonicating 0.5 g of freeze-dried apple tissue with 30 mL of methanol-water-acetic acid (30:69:1, v/v/v) containing 2 g of ascorbic acid/L, for 10 min in an ultrasonic bath. The whole method was validated, concluding that it is a robust method that presents high extraction efficiencies (peel: >91%, pulp: >95%) and appropriate precisions (within day: R.S.D. (n = 5) <5%, and between days: R.S.D. (n = 5) <7%) at the different concentration levels of polyphenols that can be found in apple samples. The method was compared with one previously published, consisting in a pressurized liquid extraction (PLE) followed by RP-HPLC-DAD determination. The advantages and disadvantages of both methods are discussed.     

Fast and simple method for the detection and quantification of 15 synthetic dyes in sauce,cotton candy,and pickle by liquid chromatography/tandem mass spectrometry

A simple and sensitive liquid chromatography/tandem mass spectrometry (LC-MS/MS) method for the simultaneous determination of 15 illegal dyes (Sudan I, Sudan II, Sudan III, Sudan IV, Sudan Red G, Sudan Orange G, Sudan Red 7B, Para Red, Dimethyl Yellow, Rahodamine B, Sudan Black B, Sudan Red B, Auramine O, Toluidine Red and Orange II) was developed and validated in sauce, cotton candy, and pickle. The samples were extracted with acetonitrile without the use of solid-phase extraction cartridges. Chromatographic separation was achieved on a Zorbax Eclipse Plus C18 column with a flow rate of 500 µL/min at 45 °C, using a gradient elution with A (10 mM ammonium formate in water with 0.1% formic acid) and B (10 mM ammonium formate in acetonitrile (ACN) with 0.1% formic acid) as the mobile phase. The detection was performed on a AB Sciex 6500 Qtrap mass analyzer under multiple reaction monitoring mode. Limit of detection, quantification, linearity, and precision were determined during the validation process. Recoveries ranged from 82% to 119% for all synthetic dyes, in exception to Orange II in cotton candy and pickle, where signal was suppressed due to high matrix interference and poor ionization. This method offers a simple and rapid approach to detect and quantify prohibited dyes in foodstuff that can be utilized in food contaminant laboratories.     

Combining chromatography and chemometrics for the characterization and authentication of fats and oils from triacylglycerol compositional data—A review

The characterization and authentication of fats and oils is a subject of great importance for market and health aspects. Identification and quantification of triacylglycerols in fats and oils can be excellent tools for detecting changes in their composition due to the mixtures of these products. Most of the triacylglycerol species present in either fats or oils could be analyzed and identified by chromatographic methods. However, the natural variability of these samples and the possible presence of adulterants require the application of chemometric pattern recognition methods to facilitate the interpretation of the obtained data. In view of the growing interest in this topic, this paper reviews the literature of the application of exploratory and unsupervised/supervised chemometric methods on chromatographic data, using triacylglycerol composition for the characterization and authentication of several foodstuffs such as olive oil, vegetable oils, animal fats, fish oils, milk and dairy products, cocoa and coffee.