Hansch chance correlations

Calculated descriptors have generally fallen into two broad categories those that seek to model an experimentally determined or physical descriptor (such as ClogP or CpKJ and those that are purely mathematical [such as the Kier and Hall connectivity indices (4)]. Not surprisingly, the latter category has been heavily populated over the years, so much so that QSAR/QSPR practitioners have had to rely on model validation procedures (such as leave-k-out cross-validation) to avoid models built upon chance correlation. Of course, such procedures are far less critical when very few descriptors are used (such as with the Hansch, Leo, and Abraham descriptors) it can even be argued that they are unnecessary. 

Hansch and Fujita found that Eq. (42) is a chance correlation, resulting from the fact that 7t and a are closely interrelated in this series (r = 0.91, without the 4-nitro analog). All analogs could be correlated with n (Eq. (43)) [16] ... 

Topliss was the first to investigate the risk of chance correlations in Hansch analyses in a systematic manner. Several simulations, using random numbers instead of real parameter values, revealed that for a given number of compounds the chance of obtaining correlation coefficients r larger than 0.9 not only drastically increases with the number of variables included in the equation, but also with the number of variables from which the different combinations are being selected [400, 401],... 

Another major reason for plotting factors is the possibility that an optimum will be observed. This is illustrated genetically in Figure 16. It is clear that optimal behavior occurs often in the relationship of tr or log P to activity (Hansch and Fujita Takemoto et al. ). It is thus reasonable to include a term as a faaor in an analysis of biodata. However, the inclusion of squared terms for all factors in a design would be a problem relative to the probability of chance correlations. Since examples of optimal behavior for other faaors have been reported (e.g., for or a ), this possibility must be considered. 

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