Qualitative Regression Analysis

Let us consider a pair of regression equations to illustrate the qualitative nature of them. The selected equation, which represents the Hansch-type QSAR, is 

This equation relates to the antiadrenergic activity of 3,4-disubstituted N-dimethyl-a-bromophenemethylamines 

WID is the identification number based on weighted walks [10], and x is the connectivity index. 

Molecular identification numbers (ID) were introduced in 1984 [10] and have been used as molecular descriptors in QSAR [11] although they were constructed initially as a tool for identification of highly similar molecules. We should add that the problem of identification of highly similar molecules is different and distinct from the problem of graph isomorphism in the sense that for the former occasional occurrence of identical ID numbers for distinct structures is acceptable (as it may point to very similar structures), and in the latter, the occurrence of identical numerical values for different structures points to a failure of the approach. In the following section, we give more information on molecular ID numbers and their properties. 

Coming to the second regression equation involving WID, a way to improve the regression is to consider variable molecular descriptors. Thus, instead of x. one 

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Partitioning into the CNS will be important for hallucinogens, as for any drug that acts centrally. Correlation between 1-octanol/water partition coefficients and human activity has been reported (13). Regression analysis of log human activity on log P yielded a parabolic fit with an optimum at log P 3.14. The derived equation accounted for only 62% of the variance but included compounds with a variety of substitution patterns and, presumably, qualitative differences in activity. 

In reference 88, response surfaces from optimization were used to obtain an initial idea about the method robustness and about the interval of the factors to be examined in a later robustness test. In the latter, regression analysis was applied and a full quadratic model was fitted to the data for each response. The method was considered robust concerning its quantitative aspect, since no statistically significant coefficients occurred. However, for qualitative responses, e.g., resolution, significant factors were found and the results were further used to calculate system suitability values. In reference 89, first a second-order polynomial model was fitted to the data and validated. Then response surfaces were drawn for... 

Blair et al. (1998) performed a retrospective cohort mortality study of 14 457 workers employed for at least one year between 1952 and 1956 at an aircraft maintenance facility in the United States. Among this cohort were 6737 workers who had been exposed to carbon tetrachloride (Stewart et al., 1991). The methods used for this study are described in greater detail in the monograph on dichloromethane. An extensive exposure assessment was performed to classify exposure to trichloroethylene quantitatively and to classify exposure (ever/never) to other chemicals qualitatively (Stewart et al., 1991). Risks from chemicals other than trichloroethylene w ere examined in a Poisson regression analysis of cancer incidence data. Among women, exposure to carbon tetrachloride was associated with an increased risk of non-Hodgkin lymphoma (relative risk (RR), 3.3 95% CI,... 

Using the LTF scheme, the study of effluent discharge situations at 16 Ontario pulp and paper mills has illustrated predominantly moderate to strong qualitative relationships between toxicity tests and ecosystem indicators (fish populations and benthic invertebrate communities). Ceriodaphnia- to-benthos, Selenastrum-to-benthos and fathead-to-fish survey relationships were qualitatively rated strong or moderate in 94%, 75% and 60% of the sixteen studies, respectively. Regression analysis of LTF scores has revealed that the relationship between the Ceriodaphnia reproduction test and benthic invertebrate field survey measurements was significant (p < 0.001, r = 0.79). However, there were not sufficient data to determine if this can be used as a predictive tool (Borgmann et al., 2004). 

The use and benefits of regression analysis can be appreciable, particularly in the evaluation of process data. In these applications, processes having as many as fifty variables, which are continuously changing over months of operation, can be evaluated by this technique. For these, the daily log records for say 400 to 500 data points are analyzed through the selected model (usually linear as a first approximation) to determine the relative effects of each variable on the response. This analysis in many cases has led to qualitative and often to quantitative determination of key operating variables whose effect had been masked on individual data point comparisons by the simultaneous changes in other less important, but unknown, variables. 

The methods used to correlate suspensibility may be used with other response variables — such as biological activity, stability, or yield value — that are important in the development of pesticides. Also, formulations of greater complexity, which have more components, can be studied with the same correlational techniques. There are, however, many important response variables that are qualitative or semiquantitative and are not usually estimated with the precision necessary for reliable regression analysis. These include, freeze-thaw stability, bloom, compatibility, and... 

Dispersion and correlation analyses are used to process the data obtained in the preliminary experiments. The goal of these statistical analyses is to have qualitative or quantitative answers to points 2 and 3 mentioned above. Finally, when all the statistical data have been collected, a correlation and regression analysis will be used to obtain the inter-dependence relationships between the dependent and the independent variables of the process (see relation (5.1)). 

Therefore no longer qualitative statements are cast into a numerical framework but easily measurable values are linked to obtain information on complex stability or bond energies. Thus, by linear regression analysis, two new parameters are obtained which -once they are known for sufficiently many different metal ions, both essential and non-essential ones - in turn can be linked to this biochemical property of essentiality. Electrochemical ligand parameters for different complexes of the same metal ion are correlated... 

Lastly, the quality of a statistical correlation alone cannot be taken as an indication of correctness of the assumptions. For example, a model with slightly larger, but random error is more likely correct than its rival with smaller, but systematic error, and primitive statistics programs do not take this into account. As Connors puts it, "the human eye, in combination with chemical knowledge, is a more subtle qualitative judge of data than is regression analysis" [57]. 

Some methods aim at obtaining structural features that are common for all the active (or inactive) compounds of the analyzed series and formulating prognostic rules for biological activity. There are also efforts to find empirical functional relationships between physicochemical (and other) parameters of the systems and the level of biological activity by means of multiparameter regression analysis. An adequate combination of the qualitative and quantitative approaches seems to be most efficient. 

Chemometrics is an essential part of NIR and Vis/NIR spectroscopy in food sector. NIR and Vis/NIR instrumentation in fact must always be complemented with chemometiic analysis to enable to extract useful information present in the sp>ectra separating it both from not useful information to solve the problem and from sp>ectral noise. Chemometric techniques most used are the princip)al component analysis (PCA) as a technique of qualitative analysis of the data and PLS regression analysis as a technique to obtain quantitative prediction of the parameters of interest (Naes et al., 2002 Wold et al., 2001 Nicolai et al., 2007 Cen He, 200 . ... 

Part V will cover several techniques for working on prevention that apply multiple factor models. Multiple factor models may use quantitative or qualitative analysis. Statistical techniques, such as factor analysis, multiple regression analysis and other multivariate methods may be useful. Fault tree analysis, failure mode and effects analysis and other approaches help identify characteristics that together can lead to undesired events. 

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