Data evaluation multivariate analysis

A homogeneity index or significance coefficienf has been proposed to describe area or spatial homogeneity characteristics of solids based on data evaluation using chemometrical tools, such as analysis of variance, regression models, statistics of stochastic processes (time series analysis) and multivariate data analysis (Singer and... 

Similar data evaluation problems exist in other scientific fields and can also be treated by multivariate statistical data analysis, for instance, in economics (econometrics), sociology, psychology (psychometrics), medicine, biology (chemotaxonomy),... 

The initial multivariate analysis consisted of a principal component analysis on the raw data to determine if any obvious relationships were overlooked by univariate statistical analysis. The data base was reviewed and records containing missing data elements were deleted. The data was run through the Statistical Analysis System (SAS) procedure PRINCOMP and the results were evaluated. 

Multivariate statistical analysis is considered a useful tool for evaluating the significance of geochemical anomalies in relation to both any individual variable and the mutual influence of variables on each other. In basic terms, when applied to geochemistry, multivariate analysis aims to identify spatial correlations between groups of elements—lithological characteristics, enrichment phenomena, anthropogenic pollution, etc.—in a complex system and reduce a multidimensional data set to more basic components. 

Statistical analyses were performed using the change scores from the NBAS evaluation (Time 2-Time 1). Multivariate analysis of covariance (MANCOVA) was performed for each of the NBAS clusters with group membership (high, low, and no fish consumption) as the independent variable and the 24 components representing potential confounders as covariates. Approximately 75% of each fish consumption group was included in the analysis (n=416). The loss of subjects occurred because only subjects with data for all variables were included. Multiple regression was also performed for each of the NBAS clusters with inclusion of component covariates for confounder control. 

Multivariate analysis techniques were applied to peak areas obtained by CE to evaluate the ripening time of the cheese. Data were autoscaled prior to model calculations. This normalization involved the subtraction of the mean and then the division of each value of a given variable by the standard deviation of all the values for this variable over the entire sample collection period (48). After normalization, all variables had the same weight because they had a mean of zero and unitary variance. 

The basic principle of experimental design is to vary all factors concomitantly according to a randomised and balanced design, and to evaluate the results by multivariate analysis techniques, such as multiple linear regression or partial least squares. It is essential to check by diagnostic methods that the applied statistical model appropriately describes the experimental data. Unacceptably poor fit indicates experimental errors or that another model should be applied. If a more complicated model is needed, it is often necessary to add further experimental runs to correctly resolve such a model. 

Schlich et al. (1987) proposed a new approach to selecting variables in principal component analysis (PCA) and getting correlations between sensory and instrumental data. Among other studies, Wada et al. (1987a,b) evaluated 39 trade varieties of coffee by coupling gas chromatographic data with two kinds of multivariate analysis. The objective classification was compared with the sensory data (cup test), directly or after statistical treatment. The results were concordant. Murota (1993) used qualitative sensory data to interpret further the results of GC data and canonical discriminant analysis. He could thus suggest which were the components responsible for the flavor characteristics in different coffee cultivars. 

In addition to the usual statistical methods based on univariate descriptors (mean, median, and standard deviation) and analysis of variance, multivariate techniques of statistics and chemometrics are increasingly being used in data evaluation. Whereas the former are more rigorous in theoretical background and assumptions, the latter are useful in the presentation of the data, pattern recognition, and multivariate calibrations. Several good monographs on chemometrics are available (see for example [58-61]). 

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. 

The hydrocarbon ("oil") fraction of a coal pyrolysis tar prepared by open column liquid chromatography (LC) was separated into 16 subfractions by a second LC procedure. Low voltage mass spectrometry (MS), infrared spectroscopy (IR), and proton (PMR) as well as carbon-13 nuclear magnetic resonance spectrometry (CMR) were performed on the first 13 subfractions. Computerized multivariate analysis procedures such as factor analysis followed by canonical correlation techniques were used to extract the overlapping information from the analytical data. Subsequent evaluation of the integrated analytical data revealed chemical information which could not have been obtained readily from the individual spectroscopic techniques. The approach described is generally applicable to multisource analytical data on pyrolysis oils and other complex mixtures. 

Factor Analysis. Several choices had to be made in preparing the data for factor analysis as well as in choosing criteria for selecting the number of factors needed to describe the data space (e.g. eigenvalue > 1.0, ratio adjacent eigenvalues > 2.0, etc.) and the number of factor scores to be used as input into the canonical correlation analysis. These choices may have affected subsequent interpretation of the multivariate spaces and evaluation of the chemometric analysis methods. Table II shows the types of spectral data input into factor analyses of the first 13 subfractions. 

A class comprises a collection of objects that have similar features. The pattern of an object is its collection of characteristic features. For multivariate data evaluation, not all objects and features are necessarily used. On the other hand, some of the available data cannot be used as they are reported. Therefore, pretreatment of data is a prerequisite for efficient multivariate data analysis. 

Electrolyte balance In a retrospective analysis of data obtained from 84 patients with lupus nephritis or non-Hodgkin s lymphoma, 112 treatment episodes with low-dose intravenous pulse cyclophosphamide (500-750 mg/m ) were evaluated [28. All received 0.45% saline as hydration to prevent hemorrhagic cystitis. There was cyclophosphamide-induced hyponatremia during 15 treatment episodes in 12 patients. Patients with hyponatremia were significantly older than those without, although no factors independently predicted hyponatremia in a multivariate analysis, including cyclophosphamide dose. Cyclophosphamide potentiates the renal action of vasopressin, thereby reducing the ability of the kidney to excrete water, which should warrant the use of hypotonic solutions for prophylactic hydration to prevent hyponatremia. 

Christophersen J, Menne T, Tanghoj P, et al. (1989) Clinical patch test data evaluated by multivariate analysis. Contact Dermatitis 21 291-299... 

In order to use multivariate calibration methods the training set must have at least as many samples as there are constituents of interest and usually many more. How many samples are required to build a good model Unfortunately, there is no hard answer such as use at least 10 samples for one constituent, 20 samples for two constituents, etc. The real answer is use as many samples as it takes. A statistically significant number of samples is critical in both evaluating the analysis and obtaining a robust calibration model. The more data, the higher the confidence in the analysis and in the statistics. 

In order to adequately evaluate these complex systems, multivariate data analysis techniques must be used. The examples previously discussed highlight only a few approaches to multivariate data acquisition and analysis. There are many approaches for using these tools to obtain an increased understanding of granulation, and to elicit critical process/material attributes, as well as their relationship with final product quality attributes, for controlling the manufacturing process. 

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