Robust multivariate statistics

Robust multivariate statistics has been used to relate variations in... 

Filzmoser P, Todorov V. Review of robust multivariate statistical methods in high dimension. Anal Chim Acta 2011 705 2-14. 

Chen, J., Bandoni, A., and Romagnoli, J. A. (1996). Robust PCA and normal region in multivariable statistical process monitoring. AIChE J. 42, 3563-3566. 

Peter Filzmoser was bom in 1968 in Weis, Austria. He studied applied mathematics at the Vienna University of Technology, Austria, where he wrote his doctoral thesis and habilitation, devoted to the field of multivariate statistics. His research led him to the area of robust statistics, resulting in many international collaborations and various scientific papers in this area. His interest in applications of robust methods resulted in the development of R software packages. J ( He was and is involved in the organization of several y scientific events devoted to robust statistics. Since... 

The focus is on multivariate statistical methods typically needed in chemo-metrics. In addition to classical statistical methods, also robust alternatives are introduced which are important for dealing with noisy data or with data including outliers. Practical examples are used to demonstrate how the methods can be applied and results can be interpreted however, in general the methodical part is separated from application examples. 

A bioprocess system has been monitored using a multi-analyzer system with the multivariate data used to model the process.27 The fed-batch E. coli bioprocess was monitored using an electronic nose, NIR, HPLC and quadrupole mass spectrometer in addition to the standard univariate probes such as a pH, temperature and dissolved oxygen electrode. The output of the various analyzers was used to develop a multivariate statistical process control (SPC) model for use on-line. The robustness and suitability of multivariate SPC were demonstrated with a tryptophan fermentation. 

Data analysis and sensibly applied statistical tools are of crucial importance for metabolomics. Good experimental design is of course a fundamental first requirement. There have been a number of books and research papers written recently discussing statistics use and models for data analysis of metabolomics.100-104 Statistical and experimental robustness have been the focus of metabolomics and demonstrated in a study of NMR protocols and multivariate statistical batch processing, which were examined for consistency over six different centers. The data were shown to be sufficiently robust to generate comparable results across each center.105... 

Quantitative metabolomics, on the other hand, can be described as a targeted approach focused on the analysis of specific metabolite species. In this method, multivariate statistical analysis follows metabolite identification and quantitation. Because of the reliable peak identification and measurement of metabolite integrals, quantitative metabolomics promises greater insights into the dynamics and fluxes of metabolites, as well as robust statistical models for distinguishing classes with better classification accuracy. A major requirement for quantitative metabolomics is good-quality spectral analysis to provide reliable peak assignments and metabolite identification. 

It is commonly the case that a wide variety of properties can be included in a QSAR analysis and a decision must be made on whether to include all possibilities or limit the number of descriptors. This decision depends on the size of the data set and the correlation matrix between the properties. Farge sets of property data contain a lot of redundancy of information. For example, molecular weight, surface area and molar refraction are always highly correlated, therefore a decision to nse only molecular weight could be made. Some multivariate statistical analysis methods are tolerant of data sets which contain more properties than compounds, for example, PFS, while others are not, for example, linear discriminant analysis (FDA). Ideally, a set of uncorrelated properties is desirable as this is most likely to give a robust, interpretable model. 

Spectroscopic methods can provide fast, non-destructive analytical measurements that can replace conventional analytical methods in many cases. The non-destructive nature of optical measurements makes them very attractive for stability testing. In the future, spectroscopic methods will be increasingly used for pharmaceutical stability analysis. This chapter will focus on quantitative analysis of pharmaceutical products. The second section of the chapter will provide an overview of basic vibrational spectroscopy and modern spectroscopic technology. The third section of this chapter is an introduction to multivariate analysis (MVA) and chemometrics. MVA is essential for the quantitative analysis of NIR and in many cases Raman spectral data. Growth in MVA has been aided by the availability of high quality software and powerful personal computers. Section 11.4 is a review of the qualification of NIR and Raman spectrometers. The criteria for NIR and Raman equipment qualification are described in USP chapters <1119> and < 1120>. The relevant highlights of the new USP chapter on analytical instrument qualification <1058> are also covered. Section 11.5 is a discussion of method validation for quantitative analytical methods based on multivariate statistics. Based on the USP chapter for NIR <1119>, the discussion of method validation for chemometric-based methods is also appropriate for Raman spectroscopy. The criteria for these MVA-based methods are the same as traditional analytical methods accuracy, precision, linearity, specificity, and robustness however, the ways they are described and evaluated can be different. 

Wise, B.M. and Ricker, N.L., (1991), Recent advances in multivariate statistical process control improving robustness and sensitivity. Proceedings of IFAC ADCHEM Symposium, 125. 

Traditionally, data was a single numerical result from a procedure or assay for example, the concentration of the active component in a tablet. However, with modem analytical equipment, these results are more often a spectrum, such as a mid-infrared spectrum for example, and so the use of multivariate calibration models has flourished. This has led to more complex statistical treatments because the result from a calibration needs to be validated rather than just a single value recorded. The quality of calibration models needs to be tested, as does the robustness, all adding to the complexity of the data analysis. In the same way that the spectroscopist relies on the spectra obtained from an instrument, the analyst must rely on the results obtained from the calibration model (which may be based on spectral data) therefore, the rigor of testing must be at the same high standard as that of the instrument... 

The great majority of statistical procedures are based on the assumption of normality of variables, and it is well known that the central limit theorem protects against failures of normality of the univariate algorithms. Univariate normality does not guarantee multivariate normality, though the latter is increased if all the variables have normal distributions in any case, it avoids the deleterious consequences of skewness and outliers upon the robustness of many statistical procedures. Numerous transformations are also able to reduce skewness or the influence of outlying objects. 

It is essential for the clinical implementation of the MRS technology that high sensitivity and specificity are available reproducibly. This requirement was the driving force in the development of the statistical classification strategy (SCS)-based multivariate analysis methods that form the focus of this review. This review aims to summarize the clinical MRS studies reported to date that have included clinical outcomes and/or histopathological assessment of the entire biopsy specimen examined by MRS and where the data have been analysed in recognition of the criteria essential for robust data classification. 

To simplify hardness determination, Kirsch and Drennen [67] presented a new approach to tablet hardness determination that relies on simpler, more understandable statistical methods and provides the essence of the full spectral multivariate methods, but does not depend upon individual wavelengths of observation. Specifically, the previous hypotheses regarding the spectroscopic phenomena that permit NIR-based hardness determinations were examined in greater detail. Additionally, a robust method employing simple statistics based upon the calculation of a spectral best fit was developed to permit NIR tablet hardness prediction across a range of drug concentrations. 

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