Algorithm of Activity Spectrum Estimation

The algorithm of activity spectrum estimation is based on the above-mentioned Bayesian approach, but dilfers in several details. For each kind of activity A, which can be predicted by PASS, on the basis of a molecule s structure represented by the set of MNA descriptors [D D2- -D the following values 

In PASS version 1.703 and later the estimations of probabilities P Ak), P Ak Di) are calculated as  

The estimations Equations (6.17a, b) of probabilities P Ak), P Ak D not only increase the algorithm s prediction accuracy but also open up new possibilities. For example, function fn A in the range [0,1] can be considered as a measure of molecule n belonging to a fuzzy set of molecules that reveal activity Ak- The descriptor weight gn Dd can be considered in the same manner, and then the molecule structure descriptors can be of arbitrary nature, e.g., such as in the refs. 51 and 52. 

The main purpose of PASS is the prediction of activity spectra for new, possibly not yet synthesized compounds. Therefore, the general principle of the PASS algorithm is the exclusion from SAR Base of substances that is equivalent to the substance under prediction. So, if molecule n is equivalent to the molecule under prediction then this substance is excluded from sums in (Equations 6.17a,b). 

To obtain the qualitative ( Yes/No ) results of prediction, it is necessary to define the threshold Bk values for each kind of activity Ak- On the basis of statistical decision theory (Section 6.3.4) it is possible using the risk functions minimization, but nobody can a priori determine such functions for all kinds of activity and for all possible real-world problems. Therefore the predicted activity spectrum is presented in PASS by the list of activities with probabilities to be active Pa and to be inactive Pi calculated for each activity. The list is arranged in descending order of Pa—Pi, thus, the more probable activities are at the top of the list. The list can be shortened at any desirable cutoff value, but Pa Pi is used by default. If the user chooses a rather high value of Pa as a cutoff for selection of probable activities, the chance to confirm the predicted activities by the experiment is high too, but many activities will be lost. For instance, if Pq 80% is used as a threshold, about 80% of real activities will be lost for Pq 70%, the portion of lost activities is 70%, etc. 

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