Desirability Functions and Probabilistic Scoring

The desirabilities of the individual properties of a compound can then be combined to give an overall score or desirability index for the compound. The contributions of each property s desirability to the overall score can also be weighted to reflect the importance of each property to the overall objective of a project There are two general approaches for this additive and multiplicative  

Here Xi are the values of N compound properties, di are the desirability functions for the corresponding properties, and c,- are optional coefficients that can be used to define the importance of each individual property. These are sometimes normalized by the munber of properties by taking a weighted arithmetic or geometric mean. 

In an additive approach to combine the desirabilities of multiple properties, the impact of any individual property on the overall desirability index will be limited. It is not possible for an unacceptable value for a single, critical property, to kill a compoimd. Furthermore, unless it is appropriately normalized, the total score will increase with the total number of properties for which data are available, which may bias decision making toward compounds that have been 

3 Multiparameter Optimization Identifying High-Quality Compounds 433 

A compromise between additive and multiplicative approaches was proposed by Nissink and Degorce [30] who suggested using the distance from the ideal point in desirability space, (rfi, d2, d, df ) = (1, 1, 1. 1), scaled by the distance of the ideal point from the origin, as a desirability index  

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