Method development outliers

Analytical methods are not ordinarily associated with the Neyman-Pearson theory of hypothesis testing. Yet, statistical hypothesis tests are an indispensable part of method development, validation, and use Such testa are used to construct analytical curves, to decide the "minimum significant measured" quantity, and the "minimum detectable true" quantity (33.34) of a method, and in handling the "outlier value problem"(35.36). 

The results of the SLV should be fully reported. Generally, rather basic summaries of data (means, RSDs) will be adequate and testing for outliers should not be necessary. Statistical analyses established for ILS precision data can also be useful to separate within-lab repeatability and reproducibility. Significance tests may be required for some key robustness experiments, but method development should have eliminated most perturbations that could adversely affect reproducibility. 

Cropley made general recommendations to develop kinetic models for compUcated rate expressions. His approach includes first formulating a hyperbolic non-linear model in dimensionless form by linear statistical methods. This way, essential terms are identified and others are rejected, to reduce the number of unknown parameters. Only toward the end when model is reduced to the essential parts is non-linear estimation of parameters involved. His ten steps are summarized below. Their basis is a set of rate data measured in a recycle reactor using a sixteen experiment fractional factorial experimental design at two levels in five variables, with additional three repeated centerpoints. To these are added two outlier... 

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]) ... 

Only a few publications in the literature have dealt with this problem. Almasy and Mah (1984) presented a method for estimating the covariance matrix of measured errors by using the constraint residuals calculated from available process data. Darouach et al. (1989) and Keller et al. (1992) have extended this approach to deal with correlated measurements. Chen et al. (1997) extended the procedure further, developing a robust strategy for covariance estimation, which is insensitive to the presence of outliers in the data set. 

The method assumes that the data are independent and normally distributed, and it is sensitive to outliers. The Y-axis (or horizontal) component plays an extremely important part in developing the least square fit. All points have equal weight in determining the height of a regression line, but extreme x-axis values unduly influence the slope of the line. 

Kaznessis et al. [24] used Monte Carlo simulations on a data set of 85 molecules collected from various sources, to calculate physically significant descriptors such as solvent accessible surface area (SASA), solute dipole, number of hydrogen-bond acceptors (HBAC) and donors (HBDN), molecular volume (MVOL), and the hydrophilic, hydrophobic, and amphiphilic components of SASA and related them with BBB permeability using the MLR method. After removing nine strong outliers, the following relationship was developed (Eq. 37) ... 

Accommodation. The philosophy of this strategy is to include the outlying observations in the analysis. Methods are then used to define the final actions which are only slightly influenced by the presence of outliers (Figure le). Such statistical methods are developed under the name of "robust statistics. ... 

Methods for robust statistics have been developed that deliver good results (i.e. estimation of the population mean) even with a relatively large number of outliers or with a skewed distributiom For more detailed descriptions of these methods please refer to the relevant textbooks. 

To obtain a robust PRESS value, we can apply the following procedure. For each PCA model under investigation (k = 1,. .., km,dJ), the outliers are marked. As discussed in Section 6.5.5, these are the observations that exceed the horizontal or vertical cutoff value on the outlier map. Next, all the outliers are collected (over all k) and removed from the sum in Equation 6.21. By doing this, the robust PRESS, value is based on the same set of observations for each k. Moreover, fast methods to compute x j have been developed [62],... 

An important extension of our large validation studies involves the use of data bases from field studies in the development of improved statistical methods for a variety of problems in quantitative applications of immunoassays. These problems include the preparation and analysis of calibration curves, treatment of "outliers" and values below detection limits, and the optimization of resource allocation in the analytical procedure. This last area is a difficult one because of the multiple level nested designs frequently used in large studies such as ours (22.). We have developed collaborations with David Rocke and Davis Bunch (statisticians and numerical analysts at Davis) in order to address these problems within the context of working assays. Hopefully we also can address the mathematical basis of using multiple immunoassays as biochemical "tasters" to approach multianalyte situations. 

In anal3rtical chemistry, developii a calibration curve or modelling a phenomenon often requires the use of a mathematical fitting procedure. Probably the most familiar of these procedures is linear least-squares fitting [1]. Criteria other than least-squares for defining the best fit have been developed for linear parameters when the data possibly contain outliers [2,3]. Sometimes, the model equation to be fit is nonlinear in the parameters. This requires appeal to other fitting methods [4]. 

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