Optimum prediction space

TOPKA T Toxicity Prediction by Komputer Assisted Technology (TOPKAT) (http //www.accelrys.com/products/topkat/index.html) uses QSAR models for prediction of various toxicological properties such as mutagenicity, developmental toxicity potential, carcinogenicity, and skin/eye irritancy (see also Chapter 18). It employs the Optimum Prediction Space (OPS) technology to assess whether the query compound is well represented in its QSAR models and provides a confidence level on its prediction [85],... 

Shown in Figure 10 is the chromatogram acquired at the optimum predicted by CRF-4. Baseline resolution of all 8 components was achieved in about 27 minutes, except for components 2-4 which were almost baseline resolved. Additional evidence for the accuracy of the retention model (equation 9 and Table VI) employed for this window diagram optimization is evident in Table VIII, where predicted and measured retention factors differed by less than 15%. The slight positive bias observed for all solutes at the optimum conditions in Table VIII was coincidental averaged over the entire parameter space the bias was almost completely random. 

The importance of performing a simultaneous optimization of the three variables, pH, and concentrations of micelles and modifier, is illustrated by the separation of a mixture of amino acids and small peptides (Fig. 8.12) [19]. Apparently, a good separation is given at pH 2.5 for 0.1 M SDS and 4% (v/v) 2-propanol. The resolution is more than adequate, but the analysis time is relatively long ca. 40 min). The same applies to the optimum predicted at pH 3.5, where similar resolution and andysis time are observed at 0.14 M SDS and 1% 2-propanol. However, when the full variable space is taken into consideration, an even better separation is obtained. At pH 3.1,... 

When we examine the plots in Figure 56 we see that the PRESS decreases each time we add another factor to the basis space. When all of the factors are included, the PRESS drops all the way to zero. Thus, these fits cannot provide us with any information about the dimensionality of the data. The problem is that we are trying to use the same data for both the training and validation data. We lose the ability to assess the optimum rank for the basis space because we do not have independent validation samples that contain independent noise. So, the more factors we add, the better the calibration is able to model the particular noise in these samples. When we use all of the factors, we are able to model the noise completely. Thus, when we predict the concentrations for... 

Predictive models make it possible to perform true process scale-up, which consists of the use of a predictive model to find quantitative criteria for establishing process similarity across scales. The model is also used to determine the changes in both the design space and the target function across scales, and to predict optimum conditions of manufacturing facilities yet to be built. 

Although CRF-5 appears to be quite complex, it is highly successful in predicting the optimum separation for equal spacing of all peaks in the shortest amount of time. The importance of the spacing, however, is secondary when Smin (equations 10 and 13) is used. Once the optimum is predicted, column length can be altered based on the value of Smin at the optimum to provide the desired resolution. The number of theoretical plates needed, Nne, can then be calculated as... 

New experiments may not be required if, for instance, the optimum is located at a position in the parameter space where an experiment has already been performed. If this is not the case, then the location of one or more additional experiments will be the result of the calculation step. Subsequently, a new set of experiments is run and added to the existing database. The model can then be refined using all the available data, and a new optimum can be predicted. 

The use of shifted compositions encourages a good distribution of the experimental data over the parameter space. The optimization procedure directs the search to a certain area in the parameter space (around the predicted optimum), but the use of shifted compositions ensures that the maximum amount of new information is obtained from each next data point. The shift in composition (for a one-parameter optimization problem) can be described by... 

Using the same estimates for S and A as before, we find that Ax 0.32. Hence, when A equals 1, a total of four data points (x = 0, 0.33, 0.67 and 1) is sufficient to describe the capacity factor within 2.5% (an error in In k of 5= 0.025 corresponds to an error of about 2.5% in fc). When more than two data points are available, a better estimate for A may of course be obtained from the data. For instance, when the verification of the first predicted optimum yields exactly the same capacity factors as were predicted, then apparently all A values are equal to zero and the confidence intervals extend over the entire parameter space. 

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