Simultaneous spectrophotometric determination of ethinylestradiol and levonorgestrel by partial least squares and principal component regression multivariate calibration

Two spectrophotometric methods for the determination of Ethinylestradiol (ETE) and Levonorgestrel (LEV) by using the multivariate calibration technique of partial least square (PLS) and principal component regression (PCR) are presented. In this study the PLS and PCR are successfully applied to quantify both hormones using the information contained in the absorption spectra of appropriate solutions. In order to do this, a calibration set of standard samples composed of different mixtures of both compounds has been designed. The results found by application of the PLS and PCR methods to the simultaneous determination of mixtures, containing 4–11 μg ml⁻¹ of ETE and 2–23 μg ml⁻¹ of LEV, are reported. Five different oral contraceptives were analyzed and the results were very similar to that obtained by a reference liquid Chromatographic method.     

Variable interaction network based variable selection for multivariate calibration

Multivariate calibration problems often involve the identification of a meaningful subset of variables, from a vast number of variables for better prediction of output variables. A new graph theoretic method based on partial correlations (variable interaction network—VIN) is proposed. Many well studied representative calibration datasets spanning different application domains are selected for investigating the performance. Partial least squares (PLS) regression models combined with variable selection techniques are employed for benchmarking the performance. Subsets of variables with different number of variables are retained for the final analysis after VIN selection and progressive prediction accuracies are used for comparison. VIN-PLS results show significant improvement in prediction efficiencies and variable subset optimization. Improvement of up to 45% over existing methods with significantly fewer variables is achieved using the new method. Advantages of VIN based variable selection are highlighted.     

Partial least squares-based multivariate spectral calibration method for simultaneous determination of beta-carboline derivatives in Peganum harmala seed extracts

The partial least squares regression method has been applied for simultaneous spectrophotometric determination of harmine, harmane, harmalol and harmaline in Peganum harmala L. (Zygophyllaceae) seeds. The effect of pH was optimized employing multivariate definition of selectivity and sensitivity and best results were obtained in basic media (pH > 9). The calibration models were optimized for number of latent variables by the cross-validation procedure. Determinations were made over the concentration range of 0.15-10 μg mL⁻¹. The proposed method was validated by applying it to the analysis of the β-carbolines in synthetic quaternary mixtures of media at pH 9 and 11. The relative standard errors of prediction were less than 4% in most cases. Analysis of P. harmala seeds by the proposed models for contents of the β-carboline derivatives resulted in 1.84%, 0.16%, 0.25% and 3.90% for harmine, harmane, harmaline and harmalol, respectively. The results were validated against an existing HPLC method and it no significant differences were observed between the results of two methods.     

A novel algorithm for linear multivariate calibration based on the mixed model of samples

We present a novel algorithm for linear multivariate calibration that can generate good prediction results. This is accomplished by the idea of that testing samples are mixed by the calibration samples in proper proportion. The algorithm is based on the mixed model of samples and is therefore called MMS algorithm. With both theoretical support and analysis of two data sets, it is demonstrated that MMS algorithm produces lower prediction errors than partial least squares (PLS2) model, has similar prediction performance to PLS1. In the anti-interference test of background, MMS algorithm performs better than PLS2. At the condition of the lack of some component information, MMS algorithm shows better robustness than PLS2.     

Near-infrared spectroscopy and multivariate calibration for the quantitative determination of certain properties in the petrochemical industry

Near-infrared (NIR) spectroscopy in conjunction with chemometric techniques allows on-line monitoring in real time, which can be of considerable use in industry. If it is to be correctly used in industrial applications, generally some basic considerations need to be taken into account, although this does not always apply. This study discusses some of the considerations that would help evaluate the possibility of applying multivariate calibration in combination with NIR to properties of industrial interest. Examples of these considerations are whether there is a relation between the NIR spectrum and the property of interest, what the calibration constraints are and how a sample-specific error of prediction can be quantified. Various strategies for maintaining a multivariate model after it has been installed are also presented and discussed.     

Reproducibility,complementary measure of predictability for robustness improvement of multivariate calibration models via variable selections

In multivariate calibration with the spectral dataset, variable selection is often applied to identify relevant subset of variables, leading to improved prediction accuracy and easy interpretation of the selected fingerprint regions. Until now, numerous variable selection methods have been proposed, but a proper choice among them is not trivial. Furthermore, in many cases, a set of variables found by those methods might not be robust due to the irreproducibility and uncertainty issues, posing a great challenge in improving the reliability of the variable selection. In this study, the reproducibility of the 5 variable selection methods was investigated quantitatively for evaluating their performance. The reproducibility of variable selection was quantified by using Monte-Carlo sub-sampling (MCS) techniques together with the quantitative similarity measure designed for the highly collinear spectral dataset. The investigation of reproducibility and prediction accuracy of the several variable selection algorithms with two different near-infrared (NIR) datasets illustrated that the different variable selection methods exhibited wide variability in their performance, especially in their capabilities to identify the consistent subset of variables from the spectral datasets. Thus the thorough assessment of the reproducibility together with the predictive accuracy of the identified variables improved the statistical validity and confidence of the selection outcome, which cannot be addressed by the conventional evaluation schemes.     

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Most multivariate calibration methods require selection of tuning parameters, such as partial least squares (PLS) or the Tikhonov regularization variant ridge regression (RR). Tuning parameter values determine the direction and magnitude of respective model vectors thereby setting the resultant predication abilities of the model vectors. Simultaneously, tuning parameter values establish the corresponding bias/variance and the underlying selectivity/sensitivity tradeoffs. Selection of the final tuning parameter is often accomplished through some form of cross-validation and the resultant root mean square error of cross-validation (RMSECV) values are evaluated. However, selection of a “good” tuning parameter with this one model evaluation merit is almost impossible. Including additional model merits assists tuning parameter selection to provide better balanced models as well as allowing for a reasonable comparison between calibration methods. Using multiple merits requires decisions to be made on how to combine and weight the merits into an information criterion. An abundance of options are possible. Presented in this paper is the sum of ranking differences (SRD) to ensemble a collection of model evaluation merits varying across tuning parameters. It is shown that the SRD consensus ranking of model tuning parameters allows automatic selection of the final model, or a collection of models if so desired. Essentially, the user’s preference for the degree of balance between bias and variance ultimately decides the merits used in SRD and hence, the tuning parameter values ranked lowest by SRD for automatic selection. The SRD process is also shown to allow simultaneous comparison of different calibration methods for a particular data set in conjunction with tuning parameter selection. Because SRD evaluates consistency across multiple merits, decisions on how to combine and weight merits are avoided. To demonstrate the utility of SRD, a near infrared spectral data set and a quantitative structure activity relationship (QSAR) data set are evaluated using PLS and RR.     

New cut-off criterion for uninformative variable elimination in multivariate calibration of near-infrared spectra for the determination of heroin in illicit street drugs

A new cut-off criterion has been proposed for the selection of uninformative variables prior to chemometric partial least squares (PLS) modelling. After variable elimination, PLS regressions were made and assessed comparing the results with those obtained by PLS models based on the full spectral range. To assess the prediction capabilities, uninformative variable elimination (UVE)-PLS and PLS were applied to diffuse reflectance near-infrared spectra of heroin samples. The application of the proposed new cut-off criterion, based on the t-Students distribution, provided similar predictive capabilities of the PLS models than those obtained using the original criteria based on quantile value. However, the repeatability of the number of selected variables was improved significantly.     

Validation of a multivariate calibration method for the determination of chlorophyll a, b and c and their corresponding pheopigments

This work concerns the validation of a previously described multivariate method for determining chlorophylls and their corresponding pheopigments. The meaning of the term validation is discussed, and the work is divided into two parts, concerning model validation and method validation. The model validation showed that 40 standards are sufficient to ensure that the Y-domain is adequately spanned, and that differentiation of the data improves the models. The wavelength range was restricted to 510–770 nm, thus, eliminating interfering signals from carotenoids that had not been included in the calibration solutions. This restriction does not affect the predictive ability towards any analytes except pheophytin a. For accurate predictions of pheophytin a the wavelength region between 350 and 415 nm was included in the model. All model evaluations were based on partial least squares regression for one y-variable (PLS1). A criterion used to quantify the performance of the model was the deviation, which is an estimate of variance calculated for predictions of samples, taking into account the model’s predictive ability, the leverage and the x-residuals. In the method validation section, predictions of samples by the proposed method are compared with results obtained using an HPLC reference method. It was found for chlorophyll a that the root mean square error of cross validation (RMSECV) calculated from the model was several times higher than the corresponding root mean square error of prediction (RMSEP) calculated from the HPLC analysis. A likely explanation for this is that the RMSECV is determined in the presence of severely interfering compounds, a desired consequence of spanning the Y-space. Samples were extracted (then measured and predicted) from algal cultures, representing six different taxonomic divisions of phytoplankton. The pigment composition of these species is known, so the analyst knows in advance which chlorophylls are present. Predictions by the models are consistent with a priori knowledge of the pigment composition. To evaluate the potential of these models to deal with data recorded by different instruments, the absorption spectra for a set of samples were registered with two instruments. The results show that there is a minor and negligible bias between the predictions obtained using these instruments, probably due to a slight shift in the wavelengths recorded by them.     

Determination of quinolone antimicrobial agents in strongly overlapped peaks from capillary electrophoresis using multivariate calibration methods

This paper describes a new procedure for the determination of quinolones ciprofloxacin and sarafloxacin in chicken muscle samples. It is based on a previously developed capillary zone electrophoresis (CZE) separation, in which all the quinolones regulated by EU Council Regulation number 2377/90 could be separated. However, as ciprofloxacin and sarafloxacin coelute in the CZE run and they have strongly overlapped spectra, separation between them is not possible.To overcome this problem, we have used a multivariate calibration procedure (partial least square regression (PLS-2)), applied to the spectra obtained at the maximum of the electrophoretic peaks, by using a diode array detector. The method has been validated by a combination of pure standards and fortified blank chicken muscle extracts. The recoveries obtained in the validation set were 101±6 and 93±6% for sarafloxacin and ciprofloxacin, respectively. The method has been also applied to chicken muscle samples, fortified at concentration levels between 100 and 350 μg kg⁻, corresponding to values near the maximum residue level (MRL) regulated by the European Community.     

Multivariate calibration applied to the time-resolved chemiluminescence for the simultaneous determination of morphine and its antagonist naloxone

A novel alternative for the simultaneous determination of compounds with similar structure is described, using the whole chemiluminescence-time profiles, acquired by the stopped-flow technique, in combination with mathematical treatments of multivariate calibration. The proposed method is based on the chemiluminescent oxidation of morphine and naloxone by their reaction with potassium permanganate in an acidic medium, using formaldehyde as co-factor. The whole chemiluminescence-time profiles, acquired using the stopped-flow technique in a continuous-flow system, allowed the use of the time-resolved chemiluminescence (CL) data in combination with multivariate calibration techniques, as partial least squares (PLS), for the quantitative determination of both opiate narcotics in binary mixtures.In order to achieve overcoat the additivity of the CL profiles and beside to obtain CL profiles for each drug the most separated as possible in the time, the optimum chemical conditions for the CL emission were investigated. The effect of common emission enhancers on the CL emission obtained in the oxidation reaction of these compounds in different acidic media was studied. The parameters selected were sulphuric acid 1.0 mol L⁻¹, permanganate 0.2 mmol L⁻¹ and formaldehyde 0.8 mol L⁻¹. A calibration set of standard samples was designed by combination of a factorial design, with three levels for each factor and a central composite design. Finally, with the aim of validating the chemometric proposed method, a prediction set of binary samples was prepared. Using the multivariate calibration method proposed, the analytes were determined in synthetic samples, obtaining recoveries of 97-109%.     

A study of robustness with multivariate calibration. Application to the polarographic determination of benzaldehyde

A procedure to evaluate the robustness of an analytical method when there are changes in some experimental variables, when using multivariate calibration, is proposed. The procedure consists of analysing the root mean square error of prediction (RMSEP) as a response to a Plackett–Burman experimental design, through which the influence of several experimental factors on the prediction capability of the multivariate partial least squares (PLS) models built is studied. Two different ways of analysing the experimental design response are considered: establishing the residual variance with replicates and using Lenth's method. The proposed methodology has been applied to estimate the robustness of the polarographic determination of benzaldehyde when PLS calibration is used.     

Using variable combination population analysis for variable selection in multivariate calibration

Variable (wavelength or feature) selection techniques have become a critical step for the analysis of datasets with high number of variables and relatively few samples. In this study, a novel variable selection strategy, variable combination population analysis (VCPA), was proposed. This strategy consists of two crucial procedures. First, the exponentially decreasing function (EDF), which is the simple and effective principle of ‘survival of the fittest’ from Darwin’s natural evolution theory, is employed to determine the number of variables to keep and continuously shrink the variable space. Second, in each EDF run, binary matrix sampling (BMS) strategy that gives each variable the same chance to be selected and generates different variable combinations, is used to produce a population of subsets to construct a population of sub-models. Then, model population analysis (MPA) is employed to find the variable subsets with the lower root mean squares error of cross validation (RMSECV). The frequency of each variable appearing in the best 10% sub-models is computed. The higher the frequency is, the more important the variable is. The performance of the proposed procedure was investigated using three real NIR datasets. The results indicate that VCPA is a good variable selection strategy when compared with four high performing variable selection methods: genetic algorithm–partial least squares (GA–PLS), Monte Carlo uninformative variable elimination by PLS (MC-UVE-PLS), competitive adaptive reweighted sampling (CARS) and iteratively retains informative variables (IRIV). The MATLAB source code of VCPA is available for academic research on the website: http://www.mathworks.com/matlabcentral/fileexchange/authors/498750.     

Gran电位滴定法测定乳酸环丙沙星

介绍了乳酸环丙沙星测定的Gran电位滴定法。采用Gran线性函数进行电位滴定,经图解外推或线性回归处理求出计量点,可直接用于测定乳酸环丙沙星原料药的含量。该法用于多批原料药的测定,结果与药典法基本一致。     

Analysis of amino acids in complex samples by using voltammetry and multivariate calibration methods

A voltammetric method is proposed for the simultaneous determination of tryptophan, cysteine, and tyrosine using multivariate calibration techniques. Various electrodes and voltammetric techniques were explored to ascertain the optimum measurement strategy. Among them, differential pulse voltammetry (DPV) with a Pt electrode was selected as analytical technique since it provided a suitable compromise between sensitivity and reproducibility while allowing the oxidation peaks of the three compounds to be reasonably discriminated. The sensitivity of DPV with Pt electrode for Trp standards was 8.4×10⁻² A l mol⁻¹, the repeatability 3.7% and the detection limit below 10⁻⁷ M. The lack of full selectivity of the voltammetric data was overcome using multivariate calibration methods on the basis of the differences in the voltammetric waves of each compound. The accuracy of predictions was evaluated preliminarily from the analysis of three-component synthetic mixtures. Subsequently, this method was applied to the analysis of oxidizable amino acids in feed samples. Results obtained were in good concordance with those given by the standard method using an amino acid analyzer.     

Bayesian linear regression and variable selection for spectroscopic calibration

This paper presents a Bayesian approach to the development of spectroscopic calibration models. By formulating the linear regression in a probabilistic framework, a Bayesian linear regression model is derived, and a specific optimization method, i.e. Bayesian evidence approximation, is utilized to estimate the model “hyper-parameters”. The relation of the proposed approach to the calibration models in the literature is discussed, including ridge regression and Gaussian process model. The Bayesian model may be modified for the calibration of multivariate response variables. Furthermore, a variable selection strategy is implemented within the Bayesian framework, the motivation being that the predictive performance may be improved by selecting a subset of the most informative spectral variables. The Bayesian calibration models are applied to two spectroscopic data sets, and they demonstrate improved prediction results in comparison with the benchmark method of partial least squares.     

Simultaneous spectrophotometric determination of four preservatives in foodstuffs by multivariate calibration and artificial neural networks

Benzoic acid(BA),methylparaben(MP),propylparaben(PP)and sorbic acid(SA)are food preservatives,and they have well defined UV spectra.However,their spectra overlap seriously,and it is difficult to determine them individually from their mixtures without preseparation.In this paper,seven different chemometric approaches were applied to resolve the overlapping spectra and to determine these compounds simultaneously.With respect to the criteria of%relative prediction error(RPE)and%recovery, principal component...     

Simultaneous determination of albumin and immunoglobulin G with fluorescence spectroscopy and multivariate calibration

A method is proposed for the simultaneous determination of albumin and immunoglobulin G (IgG1) with fluorescence spectroscopy and multivariate calibration with partial least squares regression (PLS). The influence of some instrumental parameters were investigated with two experimental designs comprising 19 and 11 experiments, respectively. The investigated parameters were excitation and emission slit, detection voltage and scan rate. When a suitable instrumental setting had been found, a minor calibration and test set were analysed and evaluated. Thereafter, a larger calibration of albumin and IgG1 was made out of 26 samples (0-42 μg ml⁻¹ albumin and 0-12.7 μg ml⁻¹ IgG1). This calibration was validated with a test set consisting of 14 samples in the same concentration range. The precision of the method was estimated by analysing two test set samples for six times each. The scan modes tested were emission scan and synchronous scan Δ60 nm. The results showed that the method could be used for determination of albumin and IgG1 (albumin, root mean square error of prediction (RMSEP) <2, relative standard error of prediction (RSEP) <6% and IgG1, RMSEP <1, RSEP <8%) in spite of the overlapping fluorescence of the two compounds. The estimated precision was relative standard deviation (R.S.D.) <1.7%. The method was finally applied for the analysis of some sample fractions from an albumin standard used in affinity chromatography.     

Simultaneous voltammetric determination of levodopa, carbidopa and benserazide in pharmaceuticals using multivariate calibration

An analytical methodology based on differential pulse voltammetry (DPV) on a glassy carbon electrode and the partial least-squares (PLS-1) algorithm for the simultaneous determination of levodopa, carbidopa and benserazide in pharmaceutical formulations was developed and validated. Some sources of bi-linearity deviation for electrochemical data are discussed and analyzed. The multivariate model was developed as a ternary calibration model and it was built and validated with an independent set of drug mixtures in presence of excipients, according with manufacturer specifications. The proposed method was applied to both the assay and the uniformity content of two commercial formulations containing mixtures of levodopa-carbidopa (10:1) and levodopa-benserazide (4:1). The results were satisfactory and statistically comparable to those obtained by applying the reference Pharmacopoeia method based on high performance liquid chromatography. In conclusion, the methodology proposed based on DPV data processed with the PLS-1 algorithm was able to quantify simultaneously levodopa, carbidopa and benserazide in its pharmaceuticals formulations using a ternary calibration model for these drugs in presence of excipients. Furthermore, the model appears to be successful even in the presence of slight potential shifts in the processed data, which have been taken into account by the flexible chemometric PLS-1 approach.     

Multicomponent flow injection based analysis with diode array detection and partial least squares multivariate calibration evaluation. Rapid determination of Ca(II) and Mg(II) in waters and dialysis liquids

Flow injection analysis (FIA) with multiwavelength scanning of the FIA peaks using a diode array detector (DAD) has been combined with a multivariate calibration approach applying the partial least squares (PLS) method for the data evaluation. In this way, various side effects like dilution of the reagent, high blank, absorbance changes due to the pH gradient throughout the peak and/or the other interferences can be accounted for. Thus, even with a simple FIA manifold instrumentation the satisfactory results of multicomponent analysis are obtained. The method described has been checked on analysis of binary (Ca and Mg) and ternary (Ca, Mg and Cu) mixtures with pyridylazo resorcinol (PAR) as reagent and applied for rapid determination of calcium and magnesium in dialysis liquids and waters.