Our Research Projects

I. Simple Interval Calculation (SIC)
II. Nonlinear Regression (NLR)
III. Statistics
V. Successive Bayesian Estimation (SBE)
VI. Fitter Add-In
VII. Counterfeit Drug Detection
IX. Chemometrics in Excel


I. Simple Interval Calculation (SIC)

Simple Interval Calculation (SIC) is a method of linear modeling 

y = Xa + errors

that gives the result of prediction directly in the interval form. The SIC also approach provides wide possibilities for the Object Status Classification, i.e. leverage-type classification of relative importance of the calibration and test sets samples with respect to a model.

Click the icon   to open a PowerPoint file (= 870 kB) "Simple Interval Calculation (SIC) - Theory and Applications", presented at  the Second Winter School on Chemometrics (WSC-2), Barnaul, Russia, 2003.

Click here to ask for the file by e-mail

The SIC approach is based on the single assumption that all errors are limited (sampling errors, measurement errors, modelling errors), which would appear to be reasonable in many practical applications. For prediction modelling, this leads to results that are in a convenient interval form. The SIC approach assesses the uncertainty of predicted values in such a way that each point of the resulting interval has equal 'possibility'. The SIC-interval is in contrast to the traditional confidence interval estimators, which are based upon theoretical error distributional model assumptions, which rarely hold for practical data analysis of technological and natural systems. No probabilistic measure is introduced on the error domain, therefore one does not have to evaluate the likelihood of the values within the resulting prediction interval. 

The finiteness of the error helps to construct the Region of Possible Values (RPV) (Fig. I.1), a limited region in the parameter space that includes all possible parameter values that satisfy the data set & model under consideration.

Fig.I.1: Illustration of RPV in model parameter space. 
The initial data set contains 24 objects but only 12
 were necessary to form the RPV. 

The SIC-approach does not use an(y) objective function (e.g. sum of squares) for the parameter estimate search. In conventional regression analysis these estimates are the values of unknown parameters, which agree with the experimental data in the best way. In the SIC method any model parameter value that does not contradict experimental data, i.e. lies inside or on the border of RPV, is accepted as a feasible estimate. 

The RPV concept provides wide possibilities for selection the samples from calibration set that are of the most importance for model construction. This is because the RPV is formed not by all objects from the calibration set, but only by so-called boundary objects. Therefore, if we exclude all objects from the calibration set except boundary ones, the RPV will not change.

The position of a new objects (e.g. test set objects, or new X-data alone) in relation to the RPV helps to understand the object similarities/dissimilarities in comparison with those from the calibration set. The object status map (see Fig. I.2), or so called the SIC influence plot, can be constructed for any dimensionality of initial data set [X, y] and any number of estimated model parameters. 

Fig. I.2: The example of Object Status map for real world data.
Samples С1-С11 () are the calibration objects. 
Samples T1-T4 () are the test objects. 
Samples C2, C1, C6, and C11 are the boundary objects
Sample T1 is an insider, sample T2 is an outsider
Sample T3 is an absolute outsider. Sample T4 is an outlier.

SIC returns an object status classification which divides the SIC- residual vs. SIC - leverage plane into three categories: 'insiders' (new objects very similar to the calibration set) and 'outsiders' (all other objects in the rest of this plane. It is possible to establish a further distinction between 'absolute outsiders' and more extreme 'outliers'.

Description of the SIC-method and the Object Status Classification approach is published in  --

O. Ye. Rodionova, K. H. Esbensen, and A.L. Pomerantsev, "Application of SIC (Simple Interval Calculation) for object status classification and outlier detection - comparison with PLS/PCR", J. Chemometrics, 18 , 402-413 ( 2004)

Click here to ask for the file by e-mail

No doubt that multivariate problems where data matrix is rank- deficient are of great practical interest. To apply SIC-method to such kind of problems we join it with traditional projection methods (e.g., principal component analysis or partial least squares).

We consider that the criteria of quality of interval prediction used in SIC-procedure allow to look at the old problems of multivariate data analysis from a new point of view. These problems are optimum number of PCs, outlier detection, missing data, and insignificant observations. The roots of the method are in the old ideas of Kantorovich to apply the linear programming to the data analysis. The calculation aspects of SIC-method are rather simple since they founded on the well-designed Simplex algorithm.

Now the  SIC method is implemented in MATLAB script-language. The software description is presented here. The program may be downloaded as zip file.

An examples of the SIC-method are published in -- 

A.L. Pomerantsev, O.Ye. Rodionova, "Hard and soft methods for prediction of antioxidants' activity based on the DSC measurements", Chemom. Intell. Lab.Syst., 79 (1-2), 73-83 (2005)  
Click here to ask for the file by e-mail
A.L. Pomerantsev, O.Ye. Rodionova, A. Höskuldsson, "Process control and optimization with simple interval calculation method",  Chemom. Intell. Lab.Syst., 81 (2), 165-179 (2006)
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A.L. Pomerantsev and O.Ye. Rodionova, "Prediction of antioxidants activity using DSC measurements. A feasibility study", In Aging of Polymers, Polymer Blends and Polymer Composites, 2, Nova science Publishers, NY, 2002, pp. 19-29 (ISBN 1-59033-256-3).

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O.Ye. Rodionova, A.L. Pomerantsev, "Principles of Simple Interval Calculations" In: Progress In Chemometrics Research, Ed.: A.L. Pomerantsev, 43-64, NovaScience Publishers, NY, 2005,  (ISBN: 1-59454-257-0) Click here to ask for the file by e-mail
A.L. Pomerantsev and O.Ye. Rodionova, "Multivariate Statistical Process Control and Optimization", Ibid, 209-227 Click here to ask for the file by e-mail



II. Nonlinear Regression (NLR)

The main purpose of non-linear regression is to fit data with a non-linear model, to predict response for predictor values that are far from the observed ones, to estimate the uncertainties in prediction.

Click the icon   to open a PowerPoint file (=1290 kB) "“Introduction to non-linear regression analysis" (in Russian), presented at  the Second Winter School on Chemometrics (WSC-2), Barnaul, Russia, 2003.

Click here to ask for the file by e-mail

E.V. Bystritskaya, A.L. Pomerantsev, and O.Ye. Rodionova "Nonlinear Regression Analysis: New Approach to Traditional Implementations", J. Chemometrics, 14, 667-692 (2000)
DOI: 10.1002/1099-128X(200009/12)14:5/6<667::AID-CEM614>3.0.CO;2-T

Click here to ask for the file by e-mail

These ideas were implemented in the software FITTER, a new Excel Add-In.

Consider example of rubber aging prediction. Data of accelerated aging tests, performed at temperatures: T=140C, 125C and 110C, are presented in Fig II.1.

Fig II.1: Experimental data (left Y- and bottom X-axes)
and predicted kinetics (right Y-  and top X-axes)

The response ELB is the 'Elongation at break' property that is measured in accordance with ASTM D412-87. The data are fitted with the first order kinetics, which rate constant k depends on temperature by the Arrhenius law: 

ELB=ELB1+(ELB0-ELB1)*exp(-k*t),          k=k0*exp[-E/(RT)], 

where ELB0, ELB1, k0, and E are unknown parameters. Prediction is performed at normal temperature 20oC and the left (bottom) limits of confidence intervals are obtained. This example is presented in:

E.V. Bystritskaya, O.Ye. Rodionova, and A.L. Pomerantsev "Evolutionary Design of Experiment for Accelerated Aging Tests", Polymer Testing, 19, 221-229, (1999) 

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O. Y. Rodionova, A. L. Pomerantsev "Prediction of Rubber Stability by Accelerated Aging Test Modeling", J Appl Polym Sci, 95 (5) 1275-1284, (2005)
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Click here to know more about Evolutionary Design of Experiment (EDOE). 



III. Statistics

Theoretical statistics is an area of our interests.

Making the forecast, it is essential to find not only the point prediction value, but also to characterize the uncertainty, which firstly depends on the extrapolation distance. Certainly, the most convenient way is to present the result of prediction as a confidence interval.

Fig  III.1: Upper bounds of confidence intervals versus confidence 
probability P for various methods: F, A, M, B, L, S, and "exact" values T

We suggest a new method of confidence estimation for NLR, where, unlike bootstrap, we simulate parameter estimates, not initial data. The details are presented in

A.L. Pomerantsev "Confidence Intervals for Non-linear Regression Extrapolation", Chemom. Intell. Lab. Syst, 49, 41-48, (1999)

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The difference in the confidence intervals constructed for a nonlinear model by various methods can be very great (see Fig. III.1), but in some cases this difference could be negligible from the "engineering" point of view. To explain this, we suggest a new coefficient of nonlinearity, which is used for the decision-making about the method that can be utilized for a given task. It is calculated by the Monte Carlo procedure and accounts for the model structure as well as the experimental design features. More information about the coefficient of nonlinearity is published in

E.V. Bystritskaya, A.L. Pomerantsev, and O.Ye. Rodionova "Nonlinear Regression Analysis: New Approach to Traditional Implementations", J. Chemometrics, 14, 667-692 (2000)
DOI: 10.1002/1099-128X(200009/12)14:5/6<667::AID-CEM614>3.0.CO;2-T

Click here to ask for the file by e-mail

These ideas were implemented in the software FITTER, a new Excel Add-In.



In the projection methods (PCA, PLS) two distance measures are of importance. They are the score distance (SD, a.k.a. leverage, h) and the orthogonal distance (OD, a.k.a. the residual variance, v). This research shows that both distance measures can be modeled by the chi-squared distribution (Fig IV.1). Each model includes a scaling factor that can be described by an explicit equation. Moreover, the models depend on an unknown number of degrees of freedom (DoF), which have to be estimated using a training data set. Such modeling is further applied to classification within the SIMCA framework, and various acceptance areas are built for a given significance level. .


Fig. IV.1: Example of the SD and OD distributions. I=1440, A=6, Nh=5, Nv=1

The SD and OD distributions are similar. Each of them depends on a single unknown parameter, Nh and Nv that are the effective DOFs. In our opinion, the estimation of DoF is a key challenge in the projection modeling. In case of SD, DoF should be close to the number of PCs used, i.e., NhA; and, in case of OD, DoF is undoubtedly linked to the unknown rank of the data matrix, K=rank(X), e.g. NvKA. However, such evaluations are valid only under an assumption that either data, or scores, are normally distributed, which is always a dubious conjecture. Therefore, we believe that a data-driven estimator of DoF, rather than a theory-driven one should be used. The conventional method of moments is sensitive to outliers, therefore other techniques have to be applied. The first approach is the robust estimation via IQR estimator. The second way is the statistical simulation technique, such as bootstrap and jackknife.


Fig. IV.2: SIMCA classification with the conventional (left) and new (right) acceptance areas

It is clear that any classification problem within the projection approach should be solved with respect to a given significance level, α, i.e. the type I error. At the same time, the SD-OD, a.k.a. influence plot is a valuable exploratory tool for the identification of the influential, typical, extreme, and other interesting objects in data. In this plot different acceptance areas can be constructed. They are the regions where a given share, 1–α, of the class members belongs to. Two of such areas are presented in Fig. IV.2.

All of them are valid, i.e. they comply with the type I error requirement, but not all of them are practical. Left panel shows the  conventional rectangle area, and the right panel represents the acceptance area, which follows from the modified Wilson-Hilferty approximation of the chi-squared distribution.

Click the icon   to open a PowerPoint file (=3.3 MB) "Critical levels in projection techniques ", presented at the Six Winter Symposium on Chemometrics (WSC-6), Kazan, Russia, 2008.

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A. Pomerantsev  "Acceptance areas for multivariate classification derived by projection methods", J. Chemometrics, 22, 601-609 (2008)
DOI: 10.1002/cem.1147

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Fig. IV.3 : Extreme plots: observed number of extreme objects vs. the expected number. Grey area represents the 0.95 tolerance limits.

For the construction of a reliable decision area in the SIMCA method, it is necessary to analyze calibration data revealing the objects of special types such as extremes and outliers. For this purpose a thorough statistical analysis of the scores and orthogonal distances is necessary. The distance values should be considered as any data acquired in the experiment, and their distributions are estimated by a data driven method, such as a method of moments or similar. The scaled chi-squared distribution seems to be the first candidate among the others in such an assessment. This provides the possibility of constructing a two-level decision area, with the extreme and outlier thresholds, both in case of regular dataset and in the presence of outliers. We suggest application of classical PCA with further use of enhanced robust estimators both for the scaling factor and for the number of degrees of freedom. A special diagnostic tool called Extreme plot is proposed for the analyses of calibration objects (see Fig IV.3). Extreme objects play an important role in data analysis. These objects are a mandatory attribute of any data set. The advocated Dual Data Driven PCA/SIMCA (DD-SIMCA) approach has demonstrated a proper performance in the analysis of simulated and real world data for both regular and contaminated cases. DD-SIMCA has also been compared to ROBPCA, which is a fully robust method

Click the icon   to open a PowerPoint file (=3.2 MB) "Dual data driven SIMCA as a one-class classifier", presented at the Nineth Winter Symposium on Chemometrics (WSC-9), Tomsk, Russia, 2014.

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A.L. Pomerantsev, O.Ye. Rodionova, "Concept and role of extreme objects in PCA/SIMCA",  J. Chemometrics, 28, 429–438 (2014)
DOI: 10.1002/cem.2506

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Y.V. Zontov, O.Ye. Rodionova, S.V. Kucheryavskiy, A.L. Pomerantsev, "DD-SIMCA – A MATLAB GUI tool for data driven SIMCA approach",  Chemom. Intell. Lab. Syst. 167, 23-28 (2017) 
DOI: 10.1016/j.chemolab.2017.05.010 
Click here to ask for the file by e-mail
Implementation of the Data-Driven SIMCA method for MATLAB can be downloaded from GitHub

A novel method for theoretical calculation of the type II (β) error in soft independent modeling by class analogy (SIMCA) is proposed. It can be used to compare tentatively predicted and empirically observed results of classification. Such an approach can better characterize model quality, and thus improve its validation.

Fig IV.4: Fisher's Iris. Probability density distributions of statistics c and c' in case
Versicolor (1) is the target class, while Virginica (2) and Setosa (3) are the alternative classes.
Line 4 represents the critical cut-off value.

None of classification models are complete without validation of the model quality, which is primarily associated with the expected errors of misclassification. The type I error, α, is the rate of false rejections (false alarm), i.e. the share of objects from the target class that are misclassified as aliens. The type II error β is the rate of false acceptances (miss),  i.e. the share of alien objects that are misclassified as the members of the target class. When alternative classes are presented, the  β-error can be calculated for a given α-error as shown in  Fig. IV.4. The α-error is equal to the area under curve 1 to the right of line 4. The β-error is equal to the area under curve 2 to the left of line 4. Moving critical level 4 we can change the risks of wrong rejection (α) and wrong acceptance (β) decisions.

A.L. Pomerantsev, O.Ye. Rodionova, "On the type II error in SIMCA method",  J. Chemometrics, 28, 518-522 (2014)

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Fig. IV.5 : Amlodipine, producer A4 is used as the target class. PCA model with two PCs.
Acceptance areas: regular at
α= 0.01 (1); extended at  β = 0.005 (2). Left panel: training set; right panel: test set.  

In counterfeit combating it is equally important to recognize fakes and to avoid misclassification of genuine samples. This study presents a general approach to the problem using a newly-developed method called Data Driven Soft Independent Modeling of Class Analogy. In classification modeling the possibility to collect representative data both for training and validation is of great importance. In case no fakes are available, it is proposed to compose the test set using the legitimate drug's analogues manufactured by various producers. These analogues should have the identical API and similar composition of excipients. The approach shows satisfactory results both in revealing counterfeits and in accounting for the future variability of the target class drugs. The presented in Fig. IV.5 a case study demonstrates that theoretically predicted misclassification errors can be successfully employed for the science-based risk assessment in drug identification.

O.Ye. Rodionova, K.S. Balyklova, A.V. Titova, A.L. Pomerantsev "Quantitative risk assessment in classification of drugs with identical API content",  J. Pharm. Biomed. Anal. 98, 186-192 (2014)
DOI: 10.1016/j.jpba.2014.05.033

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V. Successive Bayesian Estimation

The successive Bayesian estimation (SBE) of regression parameters is an effective technique applied in nonlinear regression analysis. The main concept of SBE is to split the whole data set into several parts. Afterwards, estimation of parameters is performed successively - fraction by fraction - with Maximum Likelihood Method. It is important, that results obtained on the previous step are used as a priori values (in the Bayesian form) for the next part. During this procedure, the sequence of the parameter estimates is produced and its last term is the ultimate estimate. Description of SBE is published in

G.A. Maksimova, A.L. Pomerantsev, "Successive Bayesian Estimation of Regression Parameters", Zavod. Lab., 61, 432-435, (1995)


It was shown that this technique is correct and it gives the same values of estimates for linear regression as the traditional OLS approach. Moreover, in that case, the result does not depend on the order of the series. In non-linear regression case, the situation becomes more difficult but we can pose that all these properties are asymptotically the same.

Click the icon   to open a PowerPoint file (=1890 kB)  "Successive Bayesian estimation for linear and non-linear modeling", presented at the Second Winter School on Chemometrics (WSC-2), Barnaul, Russia, 2003 )

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This method is used for obtaining kinetic information from spectral data without any pure component spectra (Fig. V.1, left). With the help of real-world example, this approach is compared with known methods of kinetic modeling (Fig V.1, right). 


Fig. V.1: Successive estimates of kinetic parameters (left panel) and  
ultimate estimates with various methods presented by the 0.95 confidence ellipses (right panel)

This example is presented in

A.L. Pomerantsev "Successive Bayesian estimation of reaction rate constants from spectral data", Chemom. Intell. Lab. Syst, 66 (2), 127-139 (2003)

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O.Ye Rodionova, A.L Pomerantsev "On One Method of Parameter Estimation in Chemical Kinetics Using Spectra with Unknown Spectral Components", Kinetics and Catalysis, 45 (4): 455-466, (2004)
DOI: 10.1023/B:KICA.0000038071.51067.d5
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VI. Fitter Add-In

FITTER is an Add-In procedure for Excel. If you are under Excel you can open FITTER as any add-in file using Tools/Add-Ins menu command. It will add the new menu item Fitter into Tools menu. Clicking it, the main Fitter dialog for starting FITTER is activated.

Fig. VI.1: Main Fitter dialog

FITTER is a powerful instrument of statistical analysis. Using it you may solve multivariate nonlinear regression problems. Much of the power of FITTER comes from its ability to estimate parameter values of complicated user-defined functions that may be entered in ordinary algebraic notation as a set of explicit, implicit and ordinary differential equations. FITTER uses the unique procedure for analytic calculation of derivatives and special optimization algorithm which provides the high accuracy even for significantly nonlinear models. All complicated calculations are performed in the special DLL library created using C++ compiler, which provides high speed processing. FITTER allows to include prior knowledge about parameters and accuracy of measurement in addition to experimental data. Using Bayesian estimation, you can process both unlimited arrays of single-response data, and data referring to different responses.

Click the icon   to open a PowerPoint file (=1290 kB) "Non-linear Regression Analysis with Fitter Software Application", presented at  the First Winter School on Chemometrics (WSC-1), Kostroma, Russia, 2002.

Click here to ask for the file by e-mail

With the help of FITTER you can obtain a lot of additional statistical information concerning the input data and the quality of fitting. Parameter estimates, variances, covariance matrix, correlation matrix and F-matrix; the starting and final values of the sum of squares and objective function, error variance, and spread in eigenvalues of the Hessian matrix; error variance for each observation point calculated by fit and by population. Moreover, there are hypotheses testing for: Student's test for outliers, test of series for residual correlation, Bartlett's test for homoscedastisity, Fisher's test for goodness of fit. Also, you can calculate confidence intervals for each observation point by linearization method or with the help of modified bootstrap technique. Detailed description of Fitter application is presented in

E.V. Bystritskaya, A.L. Pomerantsev, and O.Ye. Rodionova "Nonlinear Regression Analysis: New Approach to Traditional Implementations", J. Chemometrics, 14, 667-692 (2000)
DOI: 10.1002/1099-128X(200009/12)14:5/6<667::AID-CEM614>3.0.CO;2-T

Click here to ask for the file by e-mail

FITTER takes all information from open Excel workbook. Information should be placed directly on a worksheets (Data and Parameters) or written in a text box (Model). All results are also output as tables on the worksheets. In purpose to explain what information you want to use, you need to register it with the help of FITTER wizards. There are DATA, MODEL and BAYES registration wizards. While working with different FITTER wizards you only register the required information, change options and look through process of registration. You may change data only on the worksheets but not inside the wizards. Since your information (Data, Model, ...) has been registered it is kept in memory till you replace it by another registration. 

An example of Fitter application to the diffusion problems solution is published in 

A. L. Pomerantsev "Phenomenological modeling of anomalous diffusion in polymers", J Appl Polym Sci, 96(4) 1102 - 1114, (2005)

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Estimation of the parameters of the Arrhenius equation often leads to multicollinearity, or, in other words, a degenerate set of equations in the least-squares procedure. This circumstance makes it difficult to estimate the unknown parameters. Simple expedients for model modification are considered that reduce multicollinearity.

O. E. Rodionova, A. L. Pomerantsev "Estimating the Parameters of the Arrhenius Equation", Kinetics and Catalysis, 46, 305–308, (2005).
DOI: 10.1007/s10975-005-0077-9

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Click here to know more about Fitter software.



VII. Counterfeit Drug Detection

The problem of counterfeit drugs is important all over the world. For the first time the World Health Organization (WHO) obtained information about forgeries in 1982. At that time counterfeit drugs were mainly found in the developing countries. The definition for “counterfeit drug” by WHO is as follows: “A counterfeit medicine is one which is deliberately and fraudulently mislabeled with respect to identity and/or source. Counterfeiting can apply to both branded and generic products and counterfeit products may include products with the correct ingredients or with the wrong ingredients, without active ingredients, with insufficient active ingredient or with fake packaging”

Nowadays, there are “high quality” counterfeit drugs that are very difficult to detect. It is worth mentioning that fake drugs include dietary supplements too. In such medicine non-declared substances such as hormones, ephedrine, etc., may be found. According to WHO information the spread of counterfeit drugs in different countries are as follows: 70% of turnover is in developing countries and 30% is in market-economy countries. The distribution of fake drugs with respect to different therapeutic groups is as follows: (1) antimicrobial drugs 28%; (2) hormone-containing drugs 22% (including 10% of steroids); (3) antihistamine medicines 17%; (4) vasodilators 7%; (5) drugs used for treatment of sexual disorders 5%; (6) anticonvulsants 2%; (7) others 19%. Visual control, disintegration tests or simple color reaction tests reveal only very rough forgeries. More complicated chemical methods are also used  but all these methods try to prove or disprove the content and concentration of an active ingredient. But the main goal is to discriminate genuine and counterfeit drug, even in cases where the counterfeit drug contains the sufficient concentration of active ingredient and as a result to answer the question: “Does given drug correspond to the original as it is marked on the package?” 

Express-methods for detection of counterfeit drugs are of vital necessity. In many cases dosage forms contain not only active substances but also excipients. The exact content of excipients could differ for the genuine and fake drugs. It is proposed to apply near infra-red (NIR) spectroscopy  that could be used both for identification of pharmaceutical substances and dosage forms independently of contents of an active ingredient. NIR also could give information about the excipients in a pharmaceutical preparation and thereby be able to detect counterfeit drugs even with proper active substance. A feasibility study has been published in

O.Ye. Rodionova, L.P. Houmøller, A.L. Pomerantsev, P. Geladi, J. Burger, V.L. Dorofeyev, A.P. Arzamastsev "NIR spectrometry for counterfeit drug detection", Anal. Chim. Acta, 549, 151-158 (2005)

 Click here to ask for the file by e-mail

Two grades of tablets (antispasmodic drug, uncoated tablets, 40 mg) are investigated. Ten genuine tablets, subset N1, and 10 forgeries, subset N2 were measured using the InAs detector. After that one tablet from set N1 was cut in half and a spectrum of the interior of a cut tablet was measured; this was named N1Cut. The same procedure was done for one tablet from set N2. As a result, in total 22 spectra were obtained. These spectra were pre-treated by MSC and are shown in Fig. VII.1.

Fig VII.1: MSC pre-treated spectra . Blue lines (N1) are 11 genuine tablets spectra 
and red lines (N2) are 11 counterfeit tablets spectra.

The data are subjected to a principal component analysis. Taking into account two principal components (PCs) we come to the following results (Fig. VII.2, left). Two manifest clusters in the PC1–PC2 plane are seen. Thus, the subsets N1 and N2 may easily be discriminated. The object variance in subset N2 (counterfeit drug) is significantly greater than the variance between objects in subset N1 (genuine tablets). This may be explained by better manufacturing control for genuine tablets. Spectra for the cut tablets are similar to the spectra of the whole tablets (compare open dots). 


Fig. VII.2: PCA scores plot (left panel) and SIMCA plot (right panel). Blue dots represent genuine tablets  (N1)
 and red squares represent counterfeit tablets (N2). Open dots and squares show cut tablets.

SIMCA method is applied to discriminate class N1 (genuine tablets) from any other counterfeit tablets .The “membership plot” that presents the distance to model si  versus leverage hi is shown in Fig. 10, right panel. The limits are shown as white lines: horizontal for the distance to model and vertical for the leverage. It may be easily seen that the N1Cut object has a low leverage, but its distance to the model  is greater than the limit though it lies not far from the model. Samples from set N2 are very far from the model and undoubtedly can be classified as non-members of this class. 

In general, there is one class of genuine drug samples and there may be plenty of forgeries of different degrees of similarity. Due to the production quality demands in the large pharmaceutical plants, the differences between the genuine items are rather small. Nevertheless, we consider this investigation as a feasibility study that yields promising results. For more trustworthy modeling it is necessary to collect a representative set of genuine samples of the drug produced at different times, with different shelf life, etc. On the other hand, the diversity inside the counterfeit samples is essentially large. Sometimes the difference between the genuine and counterfeit drugs could be seen visually in the NIR spectra, but in other situations the answer is not so evident. To claim that a sample is a forgery, it is not necessary to compare the concentrations of active ingredients. All that is needed is to check whether a given sample is identical to the genuine drug or not. The above analysis shows that the NIR approach together with PCA has the good prospects and may efficiently substitute wet chemistry.  

This a common opinion that the NIR spectroscopy is a low sensitive method. However, being combined with a proper chemometric analysis, this method demonstrates excellent results, which often are even better (or compatible) than conventional "wet chemistry" approach. This study confirms this claim. The research is based on the case study of injection of Dexamethasone, which is a glucocorticosteroid remedy. The manufacturer detected a batch of forgery medicine in the pharmaceutical market by revealing the lack of several printing marks, which are hidden in the package for security reasons. At the same time the standard pharmacopoeia tests (GC-MS) held at the manufacturer facility did not confirm the counterfeiting since the quality and quantity of the active substance was within the standards. Later the suspicious drug (labeled F2) and genuine samples (labeled G1 and G2) with identical batch numbers (G2 and F2) were subjected to the NIR based analysis.


Fig. VII.3: Raw NIR spectra (left panel). 30 genuine samples G1 & G2 (blue) and 15 fakes F2 (red).
PCA plot (right panel). Blue and yellow dots represent G1 & G2, red ones stand for F2.

NIR spectra (Fig VII.3, left) were obtained through the closed ampoules. PCA (Fig  VII.3, right) confirmed that genuine series G1 and G2 are very similar, but suspicious sample F2 differs. 

To compare the chemometrics based solution with the conventional analytical methods the ampoules were opened and the drug was subjected to the GC-MS, HPLC-DAD-MS, and CE-UV techniques. HPLC-DAD chromatograms of the suspicious F2 and the genuine (G2 and G1) samples are shown in Fig. VII.4.  

Fig VII.4: Comparison of the HPLC-DAD chromatograms of the fake (F2) and original (G2 and G1) samples. UV detection at 254 nm.
Mind peak (10) for suspicious sample F2. This peak is absented for genuine samples G1 & G2

The results of the NIR tests have been completely confirmed by the intensive chemical studies. Samples from batches G1 and G2 similar in their impurity composition but differ in the quantity of the impurities. Difference in impurity composition reflects in NIR spectra and helps easily to disclosure the counterfeited samples.

Click the icon   to open a PowerPoint presentation (=1.1 MB) "Another proof that chemometrics is usable: NIR confirmed by HPLC-DAD-MS and CE-UV ", presented at the Seventh Winter Symposium  on Chemometrics (WSC-7), St Petersburg, Russia, 2010 )

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O.Ye. Rodionova, A.L. Pomerantsev, L. Houmuller, A.V.Shpak, O.A. Shpigun " Noninvasive detection of counterfeited ampoules of dexamethasone using NIR with confirmation by HPLC-DAD-MS and CE-UV methods " Anal Bioanal Chem  397, 1927–1935 (2010)
DOI: 10.1007/s00216-010-3711-y

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There is no simple solution to the problem of counterfeit drug detection. The so-called 'high quality fakes' with proper composition are the most difficult to reveal. The methods based only on quantitative determination of active ingredients are sometimes insufficient. A more general approach is to consider a remedy as a whole object, taking into account a complex composition of active ingredients, excipients, as well as manufacturing conditions, such as degree of drying, etc. The application of NIR measurements combined with chemometric data processing is an effective method but its superficial application simplicity may lead to wrong conclusions that undermine confidence in the technique. The main drawback of the NIR-based approach is the necessity to apply multivariate/chemometric data analysis in order to extract useful information from the acquired spectra.


Fig. VII.5: Spectra after pre-processing: blue (green) lines G are genuine samples, red  lines F are counterfeit samples
Left. Sildenafil. The whole spectra and the range selected by a program
Right Metronidazole. The whole spectra and the range with high water influence 

We've  published an overview of the experience of different research groups in NIR drug detection and highlights the main issues that should be taken into account. The common problems to be dealt with are the following:
            (1) each medical product should be carefully tested for a batch-to-batch variability;
            (2) the selection of a specific spectral region and the data pre-processing method should be done for each type of medicine individually;
            (3) it is crucial to recognize counterfeits as well as to avoid misclassification of the genuine samples.

The real-world examples presented in the paper illustrate these statements.  

O.Ye. Rodionova, A.L. Pomerantsev,"NIR based approach to counterfeit-drug detection"
Trends Anal. Chem
., 29 (8), 781-938 (2010)
DOI: 10.1016/j.trac.2010.05.004

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Process Analytical Technology (PAT) and Quality by Design (QbD) are the novel approaches for designing, analyzing, and controlling manufacturing through timely measurements (i.e., during processing) of critical quality and performance attributes of raw and in-process materials and processes, with the goal of ensuring final product quality. Several studies in this area have been performed in the group.

Methods of process control and optimization are presented and illustrated with a real world example. We considered a multi-stage technological process that is represented by 25 process variables and one output variable, y, which is the final quality of the end-product. The production cycle (see Fig. VIII.1) is divided into seven stages numbered by the Roman numerals. Each stage may be described by the input, current, and further variables. Variables used in all previous stages are fixed input variables, current variables are the controlled ones, and the variables that characterize the following production stages are out of scope at the moment. Moving along the process, variables change their roles.

Fig. VIII.1: Production cycle

The optimization methods are based on the PLS block modeling as well as on the Simple Interval Calculation methods of interval prediction and object status classification. It is proposed to employ the series of expanding PLS/SIC models in order to support the on-line process improvements. This method helps to predict the effect of planned actions on the product quality, and thus enables passive quality control. We have also considered an optimization approach that proposes the correcting actions for the quality improvement in the course of production. The latter is an active quality optimization, which takes into account the actual history of the process. The advocate approach is allied to the conventional method of multivariate statistical process control (MSPC) as it also employs the historical process data as a basis for modeling. On the other hand, the presented concept aims more at the process optimization than at the process control. Therefore, it is proposed to call such an approach as multivariate statistical process optimization (MSPO).

Fig. VIII.2: Process optimization. SIC intervals (green bars), PLS prediction (red dots) for sample 52.
Blue rhombus shows the historical quality value, y, that was actually obtained in the production.
White dots represent the PLS predictions for the control set.

Click the icon   to open a PowerPoint file (=1MB)  "Multivariate Statistical Process Optimization ", presented at the Third Winter School on Chemometrics (WSC-3), PushGory , Russia, 2004 

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A.L. Pomerantsev, O.Ye. Rodionova, A. Höskuldsson, "Process control and optimization with simple interval calculation method",  Chemom. Intell. Lab.Syst., 81 (2), 165-179 (2006)

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The possibility of routine testing of pharmaceutical substances directly in warehouses is of great importance for manufactures, especially taking into account the demands of PAT. The application of NIR instruments with remote fiber optic probe makes these measurements simple and rapid. On the other hand carrying out measurements through closed polyethylene bags is a real challenge. To make the whole procedure reliable we propose the special trichotomy classification procedure. The approach is illustrated by a real-world example.

Fig. VIII.3: Spectrum S1 obtained from sample 1 without PE bag (substance), P is a spectrum of PE bag,
A1 is a spectrum of sample 1 in PE bag, A2 is a spectrum of sample 2 in PE bag

The substance under investigation is Taurine, a non-essential sulfur-containing amino acid. The NIR spectra were recorded with a hand held diffuse reflectance fiber optic probe. The spectra were measured through closed polyethylene (PE) bags in the 4000 – 10000 cm-1 region. The explorative PCA of the dataset shows an essential difference between the samples (Fig. VIII.3). More than 60 objects (out of 246) may be treated as doubtless outliers. The source of such variations was found after comparing the spectra of the substance in a bag, the spectra of unpacked substance (S1), and the spectra of empty polyethylene bags (P). 

Samples that are measured successfully (through a single PE layer) belong to Class 1. Other samples that are not measured carefully (through the several PE layer) are attributed to Class 2. Two corresponding SIMCA models participate in the following routine testing procedure.

The flowchart of the routine testing is shown in Fig. VIII.4  

Fig. VIII.4: The flowchart of the sample routine testing

.Ye. Rodionova, Ya.V. Sokovikov, A.L. Pomerantsev " Quality control of packed raw materials in pharmaceutical industry" Anal. Chim. Acta , 642(1-2), 222-227 (2009)
DOI: 10.1016/j.aca.2008.08.004

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This QbD research is aimed at optimization of a hybrid binder formulation that includes water solution of sodium silicate (water glass) and polyisocyanate. Optimization is performed with respect to twelve output quality characteristics. Calibration modeling is done as a two-step NPCR procedure. At first, PCA is applied to the X- block for variable reduction. Then nonlinear regression is used to predict a particular quality characteristic as a function of score vectors. The input variables reduction enables to choose an optimal binder formulation that meets the predefined quality requirements.  


Fig. VIII.5: Conversion level predicted by NPCR. Color intensity reflects the property value.
Contour map. Black dots are the calibration points, red squares are optimized test points (Left);
3-D surface model (Right) .

The study demonstrates the benefits of chemometric approach in application to chemical engineering. The non-linear PCR solves a complex nonlinear multivariate optimization problem employing a simple projection approach and graphical representation of the models. The input variables' reduction gives an opportunity to choose the optimal binder formulations visually without complicated numerical procedures.

I.A. Starovoitova, V.G. Khozin, L.A. Abdrakhmanova, O.Ye. Rodionova, A.L. Pomerantsev "Application of nonlinear PCR for optimization of hybrid binder used in construction materials", Chemom. Intell. Lab.Syst., 97 (1), 46-51 (2009)
DOI: 10.1016/j.chemolab.2008.07.008

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A new method for prediction of the drug release profiles during a running pellet coating process from in-line near infrared (NIR) measurements has been developed. The NIR spectra were acquired during a manufacturing process through an immersion probe. These spectra reflect the coating thickness that is inherently connected with the drug release. Pellets sampled at nine process time points from thirteen designed laboratory-scale coating batches were subjected to the dissolution testing. In the case of the pH-sensitive Acryl-EZE coating the drug release kinetics for the acidic medium has a sigmoid form with a pronounced induction period that tends to grow along with the coating thickness. In this work the autocatalytic model adopted from the chemical kinetics has been successfully applied to describe the drug release. A generalized interpretation of the kinetic constants in terms of the process and product parameters has been suggested. A combination of the kinetic model with the multivariate Partial Least Squares (PLS) regression enabled prediction of the release profiles from the process NIR data. The method can be used to monitor the final pellet quality in the course of a coating process  

Fig. VIII.6: Research goal

A valuable theoretical result is the solution of the “curve-to-curve” calibration problem and in the particular case considered here, the prediction of the drug release profiles from NIR spectra. This method differs from the conventional approach, where a curve is restored from the individually calibrated and predicted points. The advocated approach extracts new features as the parameters of a function approximating the drug release profile. Such a function can be selected on a purely empirical basis, or derived from the fundamental process knowledge. Additionally, successful approximation results in a considerable data reduction. The main merit however is the ability to predict the whole curve smoothly.


Fig. VII.7: Predicted API release curves

It has been found that the autocatalytic model perfectly fits the drug release kinetics of the pellets coated by a pH-sensitive polymer. Moreover, two underlying kinetic constants have a reasonable physical interpretation. The first parameter, m, is responsible for the coating material grade and this parameter varies neither within a batch nor between the similar batches. The second parameter, k, is closely related to the coating thickness and this dependence is individual for every batch. Subsequently, the autocatalysis is a mechanical rather than a purely empirical model. A preliminary explanation of the mechanism's nature has been suggested.  

Click the icon   to open presentation (=1.3 MB) "In-line prediction of drug release profile for pH-sensitive coated pellets", 12- th International Conference on Chemometrics in Analytical Chemistry (CAC-2010), Antwerp, Belgium, 2010

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IX. Chemometrics in Excel

Chemometrics is a very practical discipline. To learn it one should not only understand the numerous chemometric methods, but also adopt their practical application. This book can assist you in this difficult task. It is aimed primarily at those who are interested in the analysis of experimental data: chemists, physicists, biologists, and others. It can also serve as an introduction for beginners who start learning about multivariate data analysis.


Fig. IX.1: Russian & English editions of the book

A.L. Pomerantsev, Chemometrics in Excel, Wiley, 336 pages, 2014 , ISBN: 978-1-118-60535-6

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Померанцев А.Л. Хемометрика в Excel: учебное пособие, Томск, Из-во ТПУ,  435 стр.,2014, ISBN 978-5-4387-0374-7    

The conventional way of chemometrics training utilizes either specialized programs (the Unscrambler, SIMCA, etc.), or the MatLab. We suggest our own method that employs the abilities of the world’s most popular program, Microsoft Excel®. However, the main chemometric algorithms, e.g. projection methods (PCA, PLS) are difficult to implement using basic Excel facilities. Therefore, we have developed a special supplement to the standard Excel version called Chemometrics AddIn, which can be used to perform such calculations. In this case all calculations are carried out in the open Excel books. Moreover all regular Excel capacities can be applied for additional calculations, graphical presentations, export and import of data and results, customizing individual templates, etc. Excel 2007 gives additional incentive to this idea as now very large arrays (1,048,576 rows by 16,384 columns) can be input and processed directly in the worksheets. We have designed the core functions for the PCA/PLS decompositions and ensured that calculations are performed very quickly even for rather large data sets (200 samples by 4500 variables). These functions are programmed in C++ language and linked to Excel as an Add-In tool named Chemometrics Add-in.


Fig  IX.2: Software flow-chart

We designed "Chemometrics" as an Add-In procedure for Excel. This add-in file is opened by a Tools/Add-Ins menu command. After that, main projection functions can be applied as ordinary user-defined functions in Excel. 

Fig IX.3: Common worksheet layout for application of Chemometrics Add-In

List of user-defined functions 

PCA Decomposition 

PLS Decomposition 

PLS2 Decomposition 

Click the icon   to open a PowerPoint file (=2335 kB) "Chemometric functions in Excel", presented at the First Symposium of South African Chemometrics Society (Stellenbosch University, South Africa). Click here to ask for the file by e-mail

Click here to know more about Chemometrics Add-In. 

Click here to read about the project "Distance Learning Course in Chemometrics  for Technological and Natural-Science Mastership Education" 


 Last update 27.07.17