Multivariate Analytical Figures Of Merit Research Articles

A systematic study on the effect of different error structures on pseudo‐univariate and multivariate figures of merit

AbstractIn this study, the effect of different error structures on psedounivariate and multivariate analytical figures of merit in simulated data of hyphenated chromatographic systems was investigated. Different error structures (e.g., homoscedastic, heteroscedastic, and correlated) were investigated. For this purpose, five components systems at five concentration levels with three replicates were simulated. Different types of error were added to the data. Multivariate Curve Resolution‐Alternating Least Squares (MCR‐ALS) and Maximum Likelihood Principal Component Analysis (MLPCA‐MCR‐ALS) methods were used. After resolution, pseudo‐univariate and multivariate analytical figures of merit were calculated and compared. As it expected, the detection limit for noisy datasets is higher than the noise‐free datasets, whereas the slopes of the calibration curves are not significantly different. Comparing the results generally showed that the detection limit values in multivariable mode were better than the univariate mode. The LODs of data (pseudo‐univariate and multivariate) with homoscedastic and correlated error structure by MCR‐ALS and MLPCA‐MCR‐ALS were the same. The analysis of data with heteroscedastic error structure by MLPCA‐MCR‐ALS had a lower detection limit than analysis with MCR‐ALS. The figures of merit obtained from WLS and OLS regression in heteroscedastic datasets were compared and better LODs were obtained after WLS method.

An innovative chemometric approach for simultaneous determination of polycyclic aromatic hydrocarbons in oil-contaminated waters based on dispersive micro-solid phase extraction followed by gas chromatography

In the present study, an analytical strategy was developed using reduced graphene oxide (rGO) as an effective sorbent in dispersive micro-solid phase extraction (DMSPE) for simultaneous determination of seven polycyclic aromatic hydrocarbons (PAHs) combined with gas chromatography (GC-FID). rGO was synthesized using modified Hummer’s method and characterized using scanning electron microscope(SEM), atomic force microscope (AFM) and Raman spectroscopy. A rotatable central composite design (CCD) combined with multiple linear regression (MLR) and analysis of variance (ANOVA) was used for designing, modelling and optimization of the extraction procedure. In this regard, principal component analysis (PCA) was used to develop a general response using the scores on the first PC instead of GC peak areas of seven PAHs to develop a global model. Finally, optimum DMSPE conditions were found as 0.7 mL sorbent volume, 0.05 mg mL−1 sorbent amount, 2.2 mL sample volume, 0.5 mL solvent extraction volume, 7.8 w w−1 salt concentration and 20 min vortex time. The optimized method was then used for identification and quantification of target PAHs in standard and real samples using partial least squares regression (PLSR). Multivariate analytical figures of merit (AFOMs) for PLS model including sensitivity (SEN), analytical sensitivity (γ), limit of detection (LOD) and limit of quantitation (LOQ) were calculated by focusing on estimation of signal and concentration which were in the range of (0.37–1.19), (0.87–2.49), (2.39–10.36 ng mL−1) and (7.17–21.36 ng mL−1), respectively. Thoroughly, multivariate analytical figures of merit were better than univariate ones. Finally, the proposed strategy was successfully tested for the analysis of real oil-contaminated sea water samples. The relative recovery (RR) and relative standard deviation (RSD) were in the range of (9.6–96.86) and (1.54–28.44), respectively.

Evaluation of partial least-squares regression with multivariate analytical figures of merit for determination of 10 pesticides in milk

ABSTRACT A multi-residue method using gas chromatography coupled with flame ionisation detector has been developed for simultaneous determination of 10 pesticides in milk. The methodology involved a sample clean-up procedure using ‘quick, easy, cheap, effective, rugged and safe’ followed by a preconcentration step based on dispersive liquid–liquid microextraction. In this regard, acetonitrile was added to the milk sample with specific pH and ionic strength, and the mixture was rigorously shaken. The extracts were centrifuged; then, the organic phase (acetonitrile) was transferred to a test tube and was mixed with deionised water. The mixture was sonicated and chloroform was added as an acceptor phase in an ultrasonic bath. Partial least squares (PLS) regression has been utilised to build a multivariate calibration model in the concentration range of 0.5–100 ng mL−1 and then multivariate analytical figures of merit including sensitivity, analytical sensitivity, limit of detection and limit of quantitation were calculated for PLS model. The values of relative recovery (RR) and relative standard deviation were satisfactory (77.69–147.69% and 1.6–9.7%, respectively). Method validation was performed in accordance with European Union guidelines. The European Union criteria (RR 70–120%, relative standard deviation <20%) were met for the majority of pesticides. The limits of detection and limits of quantitation ranged from 4.16–27.41 ng mL−1 to 11.89–82.23 ng mL−1, respectively. The above method was successfully applied to the analysis of milk samples. Pesticide concentration in real-milk samples (2.49–10.48 ng mL−1) was compared with the maximum residue limits. It is concluded that this comprehensive chemometric-based strategy is a reliable and easy method for the determination of pesticides in milk.

Feasibility of the determination of three flavan-3-ols metabolites in urine samples via parallel factor analysis of fluorescence emission matrices

Flavan-3-ols are the most abundant flavonoids in diet and the analysis and quantification of flavan-3-ol metabolites could report valuable information to assess their absorption mechanisms and bioavailability. In our research, we have studied the feasibility of the determination of three flavan-3-ols metabolites (3-hydroxyphenylacetic acid, 4-hydroxyphenylacetic acid and syringic acid) in urine samples using parallel factor analysis of fluorescence excitation emission matrices. In the optimised conditions, urine samples were directed analysed after diluting in water, centrifuged and filtered. The procedure was successfully applied to quantify the concentration of the selected flavan-3-ols catabolites in urine samples with recoveries ranging between 85 and 93%. For instance, multivariate analytical figures of merit show low sensitivity and selectivity and LOD between 39μg/L and 53μg/L. The proposed procedure is fast, simple, reliable and cheap method to quantify flavan-3-ols metabolites in urine and constitutes a powerful tool for screening their abundance in different food matrices after consumption.

A systematic study on the effect of noise and shift on multivariate figures of merit of second-order calibration algorithms

In the present study, multivariate analytical figures of merit (AFOM) for three well-known second-order calibration algorithms, parallel factor analysis (PARAFAC), PARAFAC2 and multivariate curve resolution-alternating least squares (MCR-ALS), were investigated in simulated hyphenated chromatographic systems including different artifacts (e.g., noise and peak shifts). Different two- and three-component systems with interferences were simulated. Resolved profiles from the target components were used to build calibration curves and to calculate the multivariate AFOMs, sensitivity (SEN), analytical sensitivity (γ), selectivity (SEL) and limit of detection (LOD). The obtained AFOMs for different simulated data sets using different algorithms were used to compare the performance of the algorithms and their calibration ability. Furthermore, phenanthrene and anthracene were analyzed by GC-MS in a mixture of polycyclic aromatic hydrocarbons (PAHs) to confirm the applicability of multivariate AFOMs in real samples. It is concluded that the MCR-ALS method provided the best resolution performance among the tested methods and that more reliable AFOMs were obtained with this method for the studied chromatographic systems with various levels of noise, elution time shifts and presence of unknown interferences.

Multivariate analytical figures of merit as a metric for evaluation of quantitative measurements using comprehensive two-dimensional gas chromatography–mass spectrometry

The present contribution is devoted to develop multivariate analytical figures of merit (AFOMs) as a new metric for evaluation of quantitative measurements using comprehensive two-dimensional gas chromatography–mass spectrometry (GC×GC–MS). In this regard, new definition of sensitivity (SEN) is extended to GC×GC–MS data and then, other multivariate AFOMs including analytical SEN (γ), selectivity (SEL) and limit of detection (LOD) are calculated. Also, two frequently used second- and third-order calibration algorithms of multivariate curve resolution-alternating least squares (MCR-ALS) as representative of multi-set methods and parallel factor analysis (PARAFAC) as representative of multi-way methods are discussed to exploit pure component profiles and to calculate multivariate AFOMs. Different GC×GC–MS data sets with different number of components along with various levels of artifacts are simulated and analyzed. Noise, elution time shifts in both chromatographic dimensions, peak overlap and interferences are considered as the main artifacts in this work. Additionally, a new strategy is developed to estimate the noise level using variance-covariance matrix of residuals which is very important to calculate multivariate AFOMs. Finally, determination of polycyclic aromatic hydrocarbons (PAHs) in aromatic fraction of heavy fuel oil (HFO) analyzed by GC×GC–MS is considered as real case to confirm applicability of the proposed metric in real samples. It should be pointed out that the proposed strategy in this work can be used for other types of comprehensive two-dimensional chromatographic (CTDC) techniques like comprehensive two dimensional liquid chromatography (LC×LC).

Simultaneous Determination of Antazoline and Naphazoline by the Net Analyte Signal Standard Addition Method and Spectrophotometric Technique

A novel net analyte signal standard addition method (NASSAM) was used for simultaneous determination of the drugs anthazoline and naphazoline. The NASSAM can be applied for determination of analytes in the presence of known interferents. The proposed method is used to eliminate the calibration and prediction steps of multivariate calibration methods; the determination is carried out in a single step for each analyte. The accuracy of the predictions against the H-point standard addition method is independent of the shape of the analyte and interferent spectra. The net analyte signal concept was also used to calculate multivariate analytical figures of merit, such as LOD, selectivity, and sensitivity. The method was successfully applied to the simultaneous determination of anthazoline and naphazoline in a commercial eye drop sample.

Matrix-free analysis of aflatoxins in pistachio nuts using parallel factor modeling of liquid chromatography diode-array detection data

In the present study a second-order calibration strategy for high performance liquid chromatography with diode-array detection (HPLC-DAD) has been developed using parallel factor analysis (PARAFAC) and has been applied for simultaneous determination of aflatoxins B 1, B 2, G 1 and G 2 in pistachio nuts in the presence of matrix interferences. Sample preparation was based on solvent extraction (SE) followed by solid phase extraction (SPE) on Bond Elut C18 cartridges. Since the sample preparation procedure was not selective to the analytes of interest, exploiting second-order advantage to obtain concentrations of individual analytes in the presence of uncalibrated interfering compounds seemed necessary. Appropriate pre-processing steps have been applied to correct background signals and the effect of retention time shifts. Transferred calibration data set obtained from standardization of solvent based calibration data has been used in prediction step. The results of PARAFAC on a set of spiked and naturally contaminated pistachio nuts indicated that the four aflatoxins could be successfully determined. The method was validated and multivariate analytical figures of merit were calculated. The advantages of the proposed method are using a low-cost SPE step relative to standard method of aflatoxin analysis (immune affinity column assay), a unique and simple isocratic elution program for all samples and a calibration transfer for saving both chemicals and time of analysis. This study show that coupling of SPE-HPLC-DAD with PARAFAC as a powerful second-order calibration method can be considered as an alternative method for resolution and quantification of aflatoxins in the presence of unknown interferences obtained through analysis of highly complex matrix of pistachio samples and cost per analysis can be reduced significantly.

Simultaneous Spectrophotometric Determination of Benzoic Acid, Sorbic Acid, and Ascorbic Acid Using a Net Analyte Signal-Based Method

The net analyte preprocessing/classical least-squares (NAP/CLS) method is a simple chemometric method that has been used for the simultaneous spectrophotometric determination of benzoic acid, sorbic acid, and ascorbic acid. The obtained results indicated that the performances of the NAP/CLS and partial least-squares methods were almost identical. The net analyte signal (NAS) concept was also used to calculate multivariate analytical figures of merit, such as LOD, selectivity, and sensitivity. Wavelength selection was applied based on the concept of NAS regression, and improved the method performance in samples containing nonmodeled interferences. The method afforded recoveries in the range of 98-105%. The proposed method was successfully applied to determination of the analytes in an Iranian soft drink.

Solving matrix effects exploiting the second-order advantage in the resolution and determination of eight tetracycline antibiotics in effluent wastewater by modelling liquid chromatography data with multivariate curve resolution-alternating least squares and unfolded-partial least squares followed by residual bilinearization algorithms: II. Prediction and figures of merit

A new powerful algorithm (unfolded-partial least squares followed by residual bilinearization (U-PLS/RBL)) was applied for first time on second-order liquid chromatography with diode array detection (LC–DAD) data and compared with a well-known established method (multivariate curve resolution-alternating least squares (MCR-ALS)) for the simultaneous determination of eight tetracyclines (tetracycline, oxytetracycline, meclocycline, minocycline, metacycline, chlortetracycline, demeclocycline and doxycycline) in wastewaters. Tetracyclines were pre-concentrated using Oasis Max C 18 cartridges and then separated on a Thermo Aquasil C18 (150 mm × 4.6 mm, 5 μm) column. The whole method was validated using Milli-Q water samples and both univariate and multivariate analytical figures of merit were obtained. Additionally, two data pre-treatment were applied (baseline correction and piecewise direct standardization), which allowed to correct the effect of breakthrough and to reduce the total interferences retained after pre-concentration of wastewaters. The results showed that the eight tetracycline antibiotics can be successfully determined in wastewaters, the drawbacks due to matrix interferences being adequately handled and overcome by using U-PSL/RBL.

Mean centering and computation of scalar net analyte signal in multivariate calibration

Lorber has identified the net analyte signal (NAS) vector as the part of the gross signal which is orthogonal to the pure spectra of the interferents. For calculation of multivariate analytical figures of merit, such as sensitivity and signal-to-noise ratio, the NAS vector must be converted into a scalar NAS. The traditional methods for calculating the scalar NAS amount to taking the Euclidean norm of the NAS vector. For mean-centered data, straightforward implementation of this recipe leads to an artifact: one value for the scalar NAS corresponds to two values for analyte concentration, i.e. the conversion is not unique. This paper details the origin of the problem and proposes a simple solution. The improved calculation of scalar NAS is illustrated on the near-infrared prediction of weight per cent oxygen delivered by the oxygenate methyl tert-butyl ether in standard reference material gasoline ampoules. Copyright © 1998 John Wiley & Sons, Ltd.

Efficient Computation of Net Analyte Signal Vector in Inverse Multivariate Calibration Models

The net analyte signal vector has been defined by Lorber as the part of a mixture spectrum that is unique for the analyte of interest; i.e., it is orthogonal to the spectra of the interferences. It plays a key role in the development of multivariate analytical figures of merit. Applications have been reported that imply its utility for spectroscopic wavelength selection as well as calibration method comparison. Currently available methods for computing the net analyte signal vector in inverse multivariate calibration models are based on the evaluation of projection matrices. Due to the size of these matrices (p × p, with p the number of wavelengths) the computation may be highly memory- and time-consuming. This paper shows that the net analyte signal vector can be obtained in a highly efficient manner by a suitable scaling of the regression vector. Computing the scaling factor only requires the evaluation of an inner product (p multiplications and additions). The mathematical form of the newly derived expression is discussed, and the generalization to multiway calibration models is briefly outlined.