Topliss-Costello rule

It should here be noticed that we are bordering the Topliss-Costello rule for what concerns data/A indices > 5, and for this reason the training test is not considered (not enough data). The zero-level descriptor, even if it is quite good. 

Notice that the quality ofis r = 0.707, s = 0.1, q = 0.661. The zero-level description let us guess that giving up the Topliss-Costello rule (N° data / N° indices > 5) with a descriptor encompassing seven random indices it should be possible to reach a more than satisfactory random model, even at the q level, as it is the case with the following random descriptor, which, nevertheless, continue to have a lower q quality than the previous descriptor with four indices,... 

Table 3) with seven-, five-, three-, and two-index index super-descriptor to keep an eye to the importance of the Topliss-Costello rule. In the following lines are the results,... 

An optimal model for the 12 properties has here been achieved and for some properties the model is even outstanding. Other and more specific conclusions deserve out attention, and the first one follows from the use of random and semi-random descriptions of Tables 7.11-7.14, respectively. The zero-level descriptors show their main weakness at the s and level. The random tests of the EV property confirms in a clear way the importance of the Topliss-Costello rule. The very good model of EV by a semi-random descriptor with three random indices borders the limit of five for the ratio N°datalN°indices. The importance of this rule and of the q statistics is confirmed by the zero-level descriptors for... 

It is worth mentioning that the number of compounds is in relevant ratio with the number of descriptors used, according with the so-called Topliss-Costello rule (i.e., N/M>5), and that both chemical variability and congenericity are fulfilled since most of them reflect the phenolic toxicity. 

The best descriptor, which is normally chosen with a least-squares procedure, is characterized by the lowest standard deviation of the estimates, s, and highest correlation coefficient, r. The minimum requirement is that at least r > 0.84 for a ratio N° AstaJN° indices > 5 (TopUss-Costello rule, Topliss and Costello 911). The best descriptor usually has a high Fischer ratio, F, which is monotonically related tor for constant number (V of data points, and constant number of variables, v. 

The last model of eight randomized properties does not obey the Topliss-Costello mle anymore, while the model with N = 16 borders this rule (r > 0.84 for N° dataJN° indices > 5). The model of A = 8 compounds with just an index is quite negative. The reader should remind that the values of the properties are... 

Although there is a strong negative correlation between partition coefficient and aqueous solubility (Hansch et al., 1968 Chiou et al., 1977), and a strong positive correlation between % and molecular volume (Dearden et al., 1988), the use of the partial least squares (PLS) method in this study allows the simultaneous use of intercorrelated descriptors. Nevertheless, the use of four descriptors to model the bioconcentration factor of only 11 compounds contravenes the Topliss and Costello (1972) rule, and renders the QSAR of dubious validity. 

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