Multivariate range modeling

Two class-modeling techniques have recently been introduced multivariate range modeling (MRM) and CAIMAN analogues modelling methods (CAMM). 

Forina, M., Oliveri, P., Casale, M., and Lanteri, S. (2008). Multivariate range modeling, a new technique for multivariate class modeling—The uncertainty of the estimates of sensitivity and specificity. Anal. Chim. Acta 622, 85-93. 

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

Problems like overlapping and interfering of fluorophores is overcome by the BioView sensor, which offers a comprehensive monitoring of the wide spectral range. Multivariate calibration models (e.g., partially least squares (PLS), principal component analysis (PCA), and neuronal networks) are used to filter information out of the huge data base, to combine different regions in the matrix, and to correlate different bioprocess variables with the courses of fluorescence intensities. 

A large variety of techniques are available to develop predictive models for toxicity. These range from relatively simple techniques to relate quantitative levels of potency with one or more descriptors to more multivariate techniques and ultimately the so-called expert systems that lead the user directly from an input of structure to a prediction. These are outlined briefly below. 

Generally, the multivariate data analysis attempts to find the best matrices C and A for a given measured Y. We discuss a wide range of methods for this task, in depth, in the two Chapters 4 and 5, Model-Based Analyses and Model-Free Analyses. 

Multivariate analysis of single point NIR spectra has become a mainstay for a wide range of pharmaceutical applications. Single point methods are generally based on a relatively small number of individually collected reference spectra, with the quahty of a method dependent on how well the reference spectra model the unknown sample. With a robust method, highly accurate concentration estimates of sample components can be extracted from unknown mixture spectra. 

It was mentioned earlier that empirical multivariate modeling often reqnires a very large amount of data. These data can contain a very large number of samples (IN), a very large number of variables (M) per sample, or both. In the case of PAT, where spectroscopic analytical methods are often used, the number of variables collected per process sample can range from the hundreds to the thonsands ... 

M. Alcala, J. Leon, J. Ropero, M. Blanco and R.J. Romanach, Analysis of low content drug tablets by transmission near infrared spectroscopy selection of calibration ranges according to multivariate detection and quantitation limits of PLS models, J. Pharm. Sci, 97(12), 5318-5327 (2007). 

In traditional method validation, assessment of the calibration has been discussed in terms of linear calibration models for univariate systems, with an emphasis on the range of concentrations that conform to a linear model (linearity and the linear range). With modern methods of analysis that may use nonlinear models or may be multivariate, it is better to look at the wider picture of calibration and decide what needs to be validated. Of course, if the analysis uses a method that does conform to a linear calibration model and is univariate, then describing the linearity and linear range is entirely appropriate. Below I describe the linear case, as this is still the most prevalent mode of calibration, but where different approaches are required this is indicated. 

Luo et al. [83] used an ANN to perform multivariate calibration in the XRF analysis of geological materials and compared its predictive performance with cross-validated PLS. The ANN model yielded the highest accuracy when a nonlinear relationship between the characteristic X-ray line intensity and the concentration existed. As expected, they also found that the prediction accuracy outside the range of the training set was bad. 

Savolainen et al. investigated the role of Raman spectroscopy for monitoring amorphous content and compared the performance with that of NIR spectroscopy [41], Partial least squares (PLS) models in combination with several data pre-processing methods were employed. The prediction error for an independent test set was in the range of 2-3% for both NIR and Raman spectroscopy for amorphous and crystalline a-lactose monohydrate. The authors concluded that both techniques are useful for quantifying amorphous content however, the performance depends on process unit operation. Rantanen et al. performed a similar study of anhydrate/hydrate powder mixtures of nitrofurantoin, theophyllin, caffeine and carbamazepine [42], They found that both NIR and Raman performed well and that multivariate evaluation not always improves the evaluation in the case of Raman data. Santesson et al. demonstrated in situ Raman monitoring of crystallisation in acoustically levitated nanolitre drops [43]. Indomethazine and benzamide were used as model... 

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