Comparison QSAR equations

The next step is the validation process. Validation is simply an examination of the model with compounds for which toxicity data are available and which were estimated by the QSAR equation. This process provides an indication of how well the model predicts the toxicity of compounds similar to the unknown. In this estimate six compounds were used as comparisons. 

The chi indexes may be viewed as a basic set of variables from which useful combinations may be developed to emphasize certain structure features. With such transformed chi indexes, it is also possible to set up QSAR equations, often with fewer variables, which also permit structure comparisons among different classes of molecules. To assist in that comparison, we introduce a transformed set of chi indexes. The delta chi index is the difference between a simple index and the corresponding valence index. In this example, A % is used and defined as follows ... 

Equation 6 (Table XIV) indicates that lipophilicity and molar reffactivity of the substituents at position 6 are important determinants of activity against S. aureus. There is a parabolic relationship seen with these same descriptors for the substituents at position 7. Comparison of equation 6 for S. aureus with equation 7 (Table XV) for Ps. aeruginosa indicates a different QSAR. An ethyl substituent at position 1, minimiun width (Bl) of the substituent at position 6, and the appearance of a piperazinyl ring in position 7 all appear in equation 7. The parabolic relationship of lipophilicity and MR seen in equation 6 for substituents at position 7 is found also in equation 7 indicating that there are optimiun lipophilicity and molar refraction ranges for the 7-substituent. At the same time, it must be noted that many of the values for the parameters listed in Tables IV and V show clustering which can bias the results. 

These successes were by no means Isolated. Throughout the development of the series, intuition continued to play an important role In the selection of synthetic targets, and therefore It Is possible to make a rough overall comparison of the performances of the QSAR equations with the performance of Intuition. Of course, these two "rationale for synthesis would not necessarily conflict and almost half of the series seemed reasonable synthetic targets from either point of view. However, there were compounds which, because of either synthetic difficulty or simple obscurity, would not have been prepared without a specific QSAR-based recommendation, and there were other compounds which were synthesized despite unfavorable QSAR auguries. Finally, the compounds In Table lA of course predated any possible QSAR rationale. These considerations allow the 98 pyranenamines to be divided Into four classes, based on "rationale for synthesis" and the mean experimental potencies within each class to be computed ... 

Table 32. Comparison of the p coefficients in QSAR equations of the hydrolysis of X-C6H4OCOCH2NHCOC6H5 (I) and...

Partial Least Squares regression (PLS) is usually performed on a - data matrix to search for a correlation between the thousands of CoMFA descriptors and biological response. However, usually after - variable selection, the PLS model is transformed into and presented as a multiple regression equation to allow comparison with classical QSAR models. 

Another crucial aspect of the validation process is the test of how well described and represented the molecule is in the map of the chemical toxicity space that the regression equation represents. If the substructural key does not exist in the database used to build the model, then it is unlikely that the compound can be accurately estimated. In addition, if compounds similar to the test compound do not exist, then a comparison as was done above cannot be conducted and a measure of the performance of the model with compounds similar to the test material cannot be made. This type of validation requires a large database and a substructural search algorithm, and should be included in a QSAR estimate. 

A question that sometimes arises in QSAR analyses deals with the possibility of random correlations. In this study the regression equations were carefully and extensively analyzed for spurious effects due to random correlations. The regressions were repeated with randomly selected observations deleted, and no significant effects were observed in the regression equations. Further, the process of equation selection was repeated using random numbers in place of the chi indexes. No correlation obtained with the random numbers was found to be significant in comparison to that of Eq. [41]. These random number analyses have also been carried out for other QSAR investigations. ... 

This analysis raises a question. Does a comparison between the log k and log Poet equations justify a conclusion that log Poet is not a suitable predictor for human intestinal absorption Although both log k and log Poet constitute the identical dependent variables for equations (7.17) and (7.15), respectively, log k represents a biological activity while log Poet is a physicochemical property. In order to clarify this confusion, we developed the following QSAR (7.18), based on the same data used by Abraham et al ... 

The overall statistical qualities of Equations C, B, and A are much more alike than would be supposed from comparison of r values alone. The variance not explained by the respective equations has remained stable as the range of potency spanded by the pyranenamlne series expanded, the s values of. 48,. 40 and. 48 being somewhat less than the estimated experimental variability and therefore unlikely to be Improved upon In a meaningful way by adding more terms to the equations. The Improvement In r from. 48 to. 77 Is the result of the Increased spread In potency. In turn brought about by the success of the original QSAR Itself ... 

The concept of lateral validation was first formulated by Hansch for classical QSARs. In this approach, the choice of parameters, their sign, and the size of their coefficients are compared with those from other QSARs. A comparison is illustrated in Table 5 for the Hammett equation ... 

Data for the 24 compounds which exhibited no sickness or lethality up to the highest screening concentration (5 or 10 mg L ) are provided in TABLE 2. A comparison was made between the QSAR predictions based upon equations 1 to 3 and the highest no effect concentration reported. These data are represented graphically in the form of a histogram (FIGURE 1). TABLE 1 provides an illustration of the raw test data for 4-chloro-2-nitroaniline (compound 28, TABLE 2). 

Recently, Veith et al. (1985) developed a second toxicity QSAR from data on 29 industrial esters. This equation, log LC50 = -0.535 (log Kq ) -2.75 r2 = 0.828, or narcosis II model, predicted the activity of polar-narcotic chemicals. Interestingly, the slopes of our equation 3 and Veith s polar-narcotic equation are not different in absolute value, although they are different in sign. This difference is due to the reciprocal transformation of the Tetrahymena toxicity data. Further comparison of these two equations reveals strikingly similar coefficients of determination. Veith and co-workers (1985) note that the polar narcotics QSAR may be improved with the addition of an electronic descriptor. These studies with para-substituted phenols show the field or polar electronic parameter, F, to be the best currently available second descriptor. While being a substituent constant may limit its universality, its addition to the current data set, as seen with equation 4, markedly improves the coefficient of determination, and F becomes significant at the P = 0.05 level. 

Hansch recommended a lateral validation of QSAR results, i.e., the comparison of models of closely related series of compounds in one biological test system (cf. equations 16 and 17) or trie comparison of the QSAR models derived for one series of compounds in several related biological test models (e.g., serine and cysteine proteases). If all models are of comparable quality, and if they show similar regression coefficients of the physicochemical terms, the results can be accepted. However, in most cases the required effort will be too large to do this routinely. In addition, even closely related enzymes or receptors may have significantly different binding sites. 

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