St. Petersburg State University, St. Petersburg, Russia March 1st 2016 Three-point calibration models by correlation constrained MCR-ALS: A feasibility study B. Debus, D. Kirsanov, V.V Panchuk, A.A.Goydenko, V.G Semenov, A. Legin St. Petersburg State University, St. Petersburg, Russia March 1st 2016

Background First order multivariate analysis … and eventually get evidence of the possible interferent species Quantitative analysis of complex mixtures in the presence of unknown interfering species Recovery of pure individual spectral components of the target analyte

Validation / Prediction Background Partial Least Squares (PLS) Xcal Ycal β R2 R2 RMSEC RMSEP Calibration Validation / Prediction RE (%) RE (%) Strongly collinear variables / Noisy data / Prediction of more than one Y variable For this presentation we will focus mainly on the fist part that is calibration

Background Calibration set design Evaluation of the number of samples Selection of a set of uniformly distributed samples Kennard-stone Xcal? k-mean X D-optimal design 1) Large calibration set = if the number of calibration sample is too small, the predictive performance of the PLS model tends to decrease and provide biased estimates for future predictive errors. 2) Representative set of samples. 3) Kennard-stone maximum distance between pair of samples / D-optimal design = maximize the determinant of the information matrix X’X 4) k-mean and Kohonen maping = clustering techniques 5) Say that we have interest in decreasing the number of calibration samples Xtest? Human decision Reference data Complex algorithms

Sample selection criterion? Raised issues Can we save time and efforts on calibration by using a limited number of samples? Now the question we will try to answer today is the following. In our case we will use 3 points for the calibration. Sample selection criterion? Robustness / accuracy?

Correlation constrained MCR-ALS (CC-MCR1) k k = bx +b0 y = bp +b0 Select profile Update profile C profile is divided into calibration (x) and test set prediction (p) Build a local univariate calibration model with known concentrations (k) Prediction of the test set concentrations based on regression coefficients (b, b0) Everything is done in a single loop Calibration and test set prediction are performed iteratively until convergence All information of the dataset is used to optimize the model 1Antunes, M. C.; J. Simao, J. E.; Duarte, A. C.; Tauler, R. Analyst 2002, 127, 809-817

Correlation constrained MCR-ALS (CC-MCR1) Advantages of CC-MCR No influence on the number of samples Possibility to recover “pure” spectral contributions Get evidence of potential interfering species Advantages (if we compare with standard PLS method) Number of sample: because in PLS 3 pts = 2 LVs / for CC-MCR we work on the full C profile + (directly in concentration unit) 2) Comparison MCR components Vs PLS regression coefficients

Datasets Simulated datasets D1 D2 35 samples 40 samples Uniformly distributed concentration profiles D2 40 samples

Datasets Real datasets 6 lanthanides mixture2 (Ce, Pr, Nd, Sm, Eu, Gd) DTXRF 38 samples Ternary alcohol mixture (propanol, butanol, pentanol) Total reflection X-ray fluorescence (TXRF) DNMR http://www.models.life.ku.dk 225 samples

Results Simulated data D1 PLS CC-MCR Simulated profiles R2 RMSEP Explain how the points are selected (min, max and average) Simulated profiles R2 RMSEP RE (%) PLS 0.66 2.3 × 10-1 24.42 CC -MCR 0.99 6.3 × 10-3 0.73

Results Simulated data D2 PLS CC-MCR Simulated profiles R2 RMSEP Do not talk about the recovery of spectra profiles because we will see it in details in the case of real samples Simulated profiles R2 RMSEP RE (%) PLS 0.05 3.2 × 100 91.83 CC -MCR 0.89 4.4 × 10-1 12.43

Results Simulated datasets RMSEP RE (%) Ncal PLS 0.99 5.4 × 10-3 0.64 20pts CC-MCR 5.3 × 10-3 0.62 0.66 2.3 × 10-1 24.42 3 pts 6.3 × 10-3 0.73 D2 R2 RMSEP RE (%) Ncal PLS 0.98 2.0 × 10-1 6.24 30pts CC-MCR 2.3 × 10-1 7.17 0.05 3.2 × 100 91.83 3 pts 0.89 4.4 × 10-1 12.43 Similar prediction performance when the number of calibration samples is significant Strong increase of the prediction error for 3-pts PLS regression models Moderate increase of the prediction error for 3-pts CC-MCR regression models

Results TXRF dataset

Results TXRF dataset CC-MCR gives better performance than OLS and PLS Parameters Analyte Method R2 RMSEP (mol/L) RE (%) Nd OLS 0.825 1.3 × 10-4 34.87 PLS 0.835 1.6 × 10-4 42.10 CC-MCR 0.985 4.8 × 10-5 13.02 Sm 0.645 1.7 × 10-4 54.71 0.430 3.1 × 10-4 98.99 0.982 5.8 × 10-5 14.88 - 7.21 % + 30.8 % + 4.5 % + 22.5 % + 81.8 % + 1.1 % Say the order of magnitude is the same PLS : CC-MCR for large calibration set Introduce the case of Sm for which PLS cannot build a predicted model (overlap)  show the slide before CC-MCR gives better performance than OLS and PLS Moderate increase of the relative error in predicted concentration for CC-MCR PLS fails to build a predictive model for Sm

Results Reliable estimate of the signal for the target analyte Pure spectra Reliable estimate of the signal for the target analyte Selectivity of the PLS model can be questioned CC-MCR enable the estimation of possible interfering species PLS CC-MCR

Results NMR3 dataset Low S/N ratio (< 40 %) Here we arbitrary selected Propanol and Butanol for quantitative analyse whereas Pentanol was considered as an interferent Low S/N ratio (< 40 %) 3Winning and als. Journal of Magnetic Resonance,2008

Results NMR dataset Similar performance reported for PLS and CC-MCR Parameters Analyte Method R2 RMSEP (%) RE (%) Propanol PLS 0.993 2.362 5.72 CC-MCR 0.997 1.479 3.58 Butanol 2.343 5.60 0.998 1.248 2.98 + 3.1 % + 0.5 % + 3.3 % + 0.6 % Similar performance reported for PLS and CC-MCR Lower error in predicted concentration for CC-MCR Possibility to accommodate low S/N ratio with CC-MCR

Results Interpretation Interfering species “Pure spectra” PLS Interfering species “Pure spectra” CC-MCR Interfering species

Perspectives CC-MCR can be extended to 3-pts calibration models with reasonable relative error in predicted concentrations (4 – 15 %) Simple selection criterion for calibration samples Simple choice for calibration samples (min, max, average) To a certain extend it is possible so save time, money and effort on calibration Conclusion about NIR data (not very well appropriate) Both qualitative and quantitative information can be derivate from CC-MCR regression models

Thank you for your attention Acknowledgments A. Legin D. Kirsanov VV. Panchuk M. Khaydukova A.A Goydenko V.G Semenov Thank you for your attention Signaler que les resultats seront publies prochainement dans ACA