Statistical validation overview

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

Table 4.28. Overview of Key Statistical Indicators Obtained from Three Different Laboratories that Validated the... 

In this chapter, we will provide a statistical overview of some important concepts, performance characteristics, and acceptance criteria related to analytical validation. We will also attempt to resolve the inconsistencies noted above and clarify the link between the performance criteria established during analytical validation and the required performance of the measurements during the routine use of the analytical method during the in-study phase. 

A different approach to mathematical analysis of the solid-state C NMR spectra of celluloses was introduced by the group at the Swedish Forest Products Laboratory (STFI). They took advantage of statistical multivariate data analysis techniques that had been adapted for use with spectroscopic methods. Principal component analyses (PCA) were used to derive a suitable set of subspectra from the CP/MAS spectra of a set of well-characterized cellulosic samples. The relative amounts of the I and I/3 forms and the crystallinity index for these well-characterized samples were defined in terms of the integrals of specific features in the spectra. These were then used to derive the subspectra of the principal components, which in turn were used as the basis for a partial least squares analysis of the experimental spectra. Once the subspectra of the principal components are validated by relating their features to the known measures of variability, they become the basis for analysis of the spectra of other cellulosic samples that were not included in the initial analysis. Here again the interested reader can refer to the original publications or the overview presented earlier. ... 

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. 

This chapter gives an overview of relevant statistical methods for the analysis of bioimpedance measurements, with an aim to answer questions such as How do I begin with planning an experiment How many measurements do I need to take How do I deal with large amounts of frequency sweep data Which statistical test should I use How do I validate my results ... 

The fact that the number of simulated events is limited leads to a systematic uncertainty on the measured -quark production cross-section. The extent of this effect can be estimated by considering the results of the validation of the fitting procedure (Fig. 4.15). An overview of the relative error of the fitted -fraction is presented in Appendix B. The error of the fitted -fraction takes into account the limited MC statistics as well as the limited data statistics. 

In this paper we address this issue and show that the results attained by the DCI method are valid in general and do not depend upon the homogeneous system instances generated. We first briefly recall the basic notions and provide an overview of the DCI method in Sect. 2. In Sect. 3 we succinctly illustrate the sieving procedure used for identifying the RSs and their exchange of information. The robustness of the results is discussed in Sect. 4, where we present the results of a thorough statistical analysis. Finally, we discuss further improvements of the method and we conclude with Sect. 6. 

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