Robust methods

Over the years an abundance of outlier tests have been proposed that have some theoretical rationale at their roots. ° Such tests have to be carefully adjusted to the problem at hand because otherwise one would either not detect true outliers (false negatives) in every case, or then throw out up to 50% of the good measurements as well (false positivesj. o Robust methods have been put forward to overcome this. Three tests will be described ... 

The importance of the degree of esterification (%DE) to the gelation properties of pectins makes it desirable to obtain a fast and robust method to determine (predict) the %DE in pectin powders. Vibrational spectroscopy is a good candidate for the development of such fast methods as spectrometers and quantitative software algorithms (chemometric methods) becomes more reliable and sophisticated. Present poster is a preliminary report on the quantitative performance of different instrumentations, spectral regions, sampling techniques and software algorithms developed within the area of chemometrics. 

Further development of robust methods tailored for isochron data can be anticipated, with the ultimate goal being a method that yields the same errors as EWLS for well-behaved data (i.e., strictly Gaussian, with accurate estimates of data-point errors), and only modest loss of precision for increasingly dirty data (R. Powell, written commun. 2002). 

The use of the in vivo labeling methods described above is limited by the fact that the sample must be grown in the presence of the labeling isotopes. In many cases, it is not feasible to perform in vivo metabolic labeling. For example, for human clinical samples it is not possible to perform in vivo labeling and yet it is highly desirable to obtain accurate quantitative information on protein expression levels within these samples. Therefore, robust methods are needed for quantitation of protein levels in the absence of in vivo labeling with isotopes. 

Robust calibration. The GAussian OLS criterion according to Eq. (6.16) is strongly sensitive against outliers. Therefore, robust methods of fitting have been developed following two strategies (Rousseeuw and Leroy [1987]) ... 

The lifetime of the excited state of fluorophores may be altered by physical and biochemical properties of its environment. Fluorescence lifetime imaging microscopy (FLIM) is thus a powerful analytical tool for the quantitative mapping of fluorescent molecules that reports, for instance, on local ion concentration, pH, and viscosity, the fluorescence lifetime of a donor fluorophore, Forster resonance energy transfer can be also imaged by FLIM. This provides a robust method for mapping protein-protein interactions and for probing the complexity of molecular interaction networks. 

Equation (18.17) predicts values for A0 that are in reasonably good agreement with the values determined by more robust methods. In many instances, an approximate value for the ligand field splitting is all that is required, and this approach gives a useful approximation for A0 rapidly with a minimum of effort. 

For investigations with nuclei with low natural abundance, such as 29Si (4.7%), isotopic enrichment is often applied. This is accompanied with difficulties in the analysis of connectivities between selected pairs, because multiple site interactions become more pronounced. Cadars et al. have suggested incorporation of a z-filter that results in a robust method to select local site connectivities and remove complications from multiple site interactions [122]. 

There is a strong limitation in the concentration range due to the logarithmic relationship between transmission and concentration (optical densities reasonably to measure range from 0.1 to 1.5). Nevertheless, protein quantification by direct UV-measurement or after staining with dyes in the visible range is a very robust method and can be found, e.g., as a common detection mode in HPLC or other chromatographic techniques. 

The validity of the results is a central issue, and it is confirmed by comparing traditional methods with their robust counterparts. Robust statistical methods are less common in chemometrics, although they are easy to access and compute quickly. Thus, several robust methods are included. 

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 distance between object points is considered as an inverse similarity of the objects. This similarity depends on the variables used and on the distance measure applied. The distances between the objects can be collected in a distance matrk. Most used is the euclidean distance, which is the commonly used distance, extended to more than two or three dimensions. Other distance measures (city block distance, correlation coefficient) can be applied of special importance is the mahalanobis distance which considers the spatial distribution of the object points (the correlation between the variables). Based on the Mahalanobis distance, multivariate outliers can be identified. The Mahalanobis distance is based on the covariance matrix of X this matrix plays a central role in multivariate data analysis and should be estimated by appropriate methods—mostly robust methods are adequate. 

Note that the approximation by the chi-square distribution is only possible for multivariate normally distributed data which somehow is in conflict if outliers are present that should be identified with this measure. We recommend that robust PCA is used whenever diagnostics is done because robust methods tolerate deviations from multivariate normal distribution. 

Outliers may heavily influence the result of PCA. Diagnostic plots help to find outliers (leverage points and orthogonal outliers) falling outside the hyper-ellipsoid which defines the PCA model. Essential is the use of robust methods that are tolerant against deviations from multivariate normal distributions. 

Instead of the classical estimation of the standard deviation, SEP, robust methods can be applied as described in Section 1.6.4, for instance the spread measures, VjqR... 

Outliers or inhomogeneous data can affect traditional regression methods, hereby leading to models with poor prediction quality. Robust methods, like robust regression (Section 4.4) or robust PLS (Section 4.7.7), internally downweight outliers but give full weight to objects that support the (linear) model. Note that to all methods discussed in this chapter robust versions have been proposed in the literature. 

Hubert, M., Vanden Branden, K. J. Chemom. 17, 2003, 537-549. Robust methods for partial least squares regression. 

The official EPA method for monitoring carbamate pesticides (Method 531.1) has seldom been used in Europe, although it is a highly sensitive and robust method. 

The fourth category of protein assay is amino acid analysis. This method is the most accurate and robust method for determination of protein concentration, but is appropriate only for pure proteins. In addition, it is relatively slow and requires specialized instrumentation and knowledge of the target protein s theoretical amino acid composition. 

With capillary electrophoresis (CE), another modern primarily analytically oriented separation methodology has recently found its way into routine and research laboratories of the pharmaceutical industries. As the most beneficial characteristics over HPLC separations the extremely high efficiency leading to enhanced peak capacities and often better detectability of minor impurities, complementary selectivity profiles to HPLC due to a different separation mechanism as well as the capability to perform separations faster than by HPLC are frequently encountered as the most prominent advantages. On the negative side, there have to be mentioned detection sensitivity limitations due to the short path length of on-capillary UV detection, less robust methods, and occasionally problems with run-to-run repeatability. Nevertheless, CE assays have now been adopted by industrial labs as well and this holds in particular for enantiomer separations of chiral pharmaceuticals. While native cyclodextrins and their derivatives, respectively, are commonly employed as chiral additives to the BGEs to create mobility differences for the distinct enantiomers in the electric field, it could be demonstrated that cinchona alkaloids [128-130] and in particular their derivatives are applicable selectors for CE enantiomer separation of chiral acids [19,66,119,131-136]. 

The main drawback in chiral separation methods using derivatized CDs is that these selectors are mainly available as complex mixtures that contain a large number of isomers differing in their degree of substitution, which may result in batch-to-batch selectivity differences.The use of pure single enantiomers or very reproducible mixtures is thus required to obtain reproducible and robust methods. 

The current status and characteristics of the technology in CE may lead to difficulties that are frequently encountered during daily application in a QC environment. There are four important characteristics of CE technology that requires our attention when developing robust methods ... 

To develop robust methods, you have to keep in mind that simple methods are preferable. Also, if you have a chromatographic background, then the factors affecting CE precision (and to a lesser extent accuracy) are widely different to HPLC, which is currently the predominantly employed technique for drug assay. There is no general preference for the choice between techniques CE, LC, or other. The choice should be made on a scientific basis, supported by the relative merits of the techniques for the specific problem and factors such as the experience of the method-developing scientist. Robust CE methods have been successfully transferred to relatively inexperienced QC and Contract Research Organisation (CRO) labs. 

The method can be robust concerning its quantitative aspect, but non-robust regarding one or more qualitative aspects, i.e., significant effects are found on responses, such as, resolution. Then SST limits can be mathematically or experimentally derived, based on the results of the robustness test. These SST limits correspond to the interval in which a qualitative response is allowed to vary, to still obtain a quantitatively robust method. 

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