Multivariate reference region

The use of multivariate reference regions usually requires the assistance of a computer program, which takes a set of results obtained by several laboratory tests on the same clinical specimen and calculates an index. The interpretation of a multivariate observation in relation to reference values is then the task of comparing the index with a critical value estimated from the reference values. This, obviously, is much simpler than comparing each result with its proper reference interval. 

Although the theory of multivariate reference regions has been known for a long time, surprisingly few applications of it have been reported in the Hterature. An important report reviews the topic and presents the results of a very careful study on the multivariate 95% region for a 20-test chemistry profile. Some of the findings can be summarized as follows ... 

By contrast, only 5% of the patterns were outside the multivariate reference region (as expected). 

The multivariate reference region could detect minor deviations of multiple analytes,... 

The sensitivity could be increased by defining multivariate reference regions for subsets of physiologically related tests. 

The offset a, and the multiplication constant bj are estimated by simple linear regression of the ith individual spectrum on the reference spectrum z. For the latter one may take the average of all spectra. The deviation e, from this fit carries the unique information. This deviation, after division by the multiplication constant, is used in the subsequent multivariate calibration. For the above correction it is not mandatory to use the entire spectral region. In fact, it is better to compute the offset and the slope from those parts of the wavelength range that contain no relevant chemical information. However, this requires spectroscopic knowledge that is not always available. 

The multivariate tools typically used for the NIR-CI analysis of pharmaceutical products fall into two main categories pattern recognition techniques and factor-based chemometric analysis methods. Pattern recognition algorithms such as spectral correlation or Euclidian distance calculations basically determine the similarity of a sample spectrum to a reference spectrum. These tools are especially useful for images where the individual pixels yield relatively unmixed spectra. These techniques can be used to quickly define spatial distributions of known materials based on external reference spectra. Alternatively, they can be used with internal references, to locate and classify regions with similar spectral response. 

Fig. 16.4. Three methods of obtaining Raman-based estimates of biofluid concentrations in vivo, a Confocal isolation of a subsurface volume occupied by a blood vessel, enabling direct measurement of a blood spectrum, b Difference measurement between tissue in two states, one with more blood in the sampling volume (in this case, due to pressure modulation by the subject [6]). Computing the difference removes the bulk tissue contributions to the spectral measurement and emphasizes the contribution from blood, c Statistical correlation approach of measuring many volunteers tissue in a region where sufficient blood is present (e.g., the forearm as shown here) and obtaining a correlated reference value from a blood sample drawn at the same time. Multivariate calibration is then used to find correlations between the reference value and the spectral data vector. Unlike the previous two methods, this does not intrinsically isolate the blood chemicals Raman signatures from those of the surrounding tissue volume...

Partial chemical information in the form of known pure response profiles, such as pure-component reference spectra or pure-component concentration profiles for one or more species, can also be introduced in the optimization problem as additional equality constraints [5, 42, 62, 63, 64], The known profiles can be set to be invariant along the iterative process. The known profile does not need to be complete to be used. When only selected regions of profiles are known, they can also be set to be invariant, whereas the unknown parts can be left loose. This opens up the possibility of using resolution methods for quantitative purposes, for instance. Thus, data sets analogous to those used in multivariate calibration problems, formed by signals recorded from a series of calibration and unknown samples, can be analyzed. Quantitative information is obtained by resolving the system by fixing the known concentration values of the analyte(s) in the calibration samples in the related concentration prohle(s) [65],... 

It is important to note that although multivariate techniques such as PCR and PLS appear to allow the development of more accurate calibrations, single-wavelength analysis also demonstrated acceptable results. Therefore, after having identified a wavelength region that correlates well with reference method results, it may be possible to employ less expensive filter type spectrometers for at-line applications. 

Figure 5 Verification of a fruit juice sample (rediluted apple juice from Poland). Left the 400 MHz H spectrum in the region near 2 ppm (black trace) is plotted over a quantiles plot (gray-scale) of the model spectra set (univariate analysis of apple juice at 2 ppm). Right influence plot of a multivariate analysis (circles reference samples star test sample green region representative of group red region not representative).

As far as the quantitative evaluation of vibrational spectra is concerned, IR and NIR spectroscopy follow Beer s law, whereas the Raman intensity JRaman is directly proportional to the concentration of the compound to be determined (Figure i),i iS Si To compensate laser fluctuations, in many cases, quantitative Raman spectroscopy is performed with an internal reference signal in the vicinity of the analytical band. For Raman and IR spectroscopy, quantitative analysis can be performed by either univariate evaluation of band heights/ areas or multivariate evaluation (e.g., partial least-squares (PLS) regression) of large spectral regions. Due to the overlap of many absorption bands for the quantitative analysis of NIR spectra, predominantly multivariate chemometric procedures are applied. For an in-depth study of the precautions, pitfalls, and limitations, which have to be observed or may be encountered in the measurement of vibrational spectra, the reader is referred to the pertinent literature. " ... 

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