Diversity score calculation

Step 3 Calculate Diversity Score. Calculate a diversity score for the portfolio based on the Moody s industry groupings assigned to each asset. The diversity score will provide the important simplifying assumption driving correlation analysis of the portfolio. 

An example of a final consensus list can be seen in Fig. 6. In this figure one can see the Q-score and B-score and the computed preliminary consensus score. On the basis of the preliminary consensus, NP-103930 was chosen as the best compound and selected to be the dissimilarity seed. After the maximum dissimilarity calculation, the diversity score was input and the final consensus score was calculated. As one can see from this figure, the first compound in the preliminary run remains the best. The second compound from the preliminary run does not appear in this list as it was very similar to the NP-103930 and was de-prioritized and moved down the list accordingly. Also the 155th compound in the preliminary ranking moved up the 14th rank because it was considered as a structurally novel compound. This, we feel, illustrates the power of this approach. Compounds with the most desirable properties move up the list and compounds with less desirable properties move down the list. 

Diversity score a statistical value that is calculated via a formula developed by the rating agencies and designed to measure the level of diversity in the asset portfolio, thus minimizing pairwise correlation in terms of each asset s probability of default. 

Effectively, in calculating the diversity score, credits within the same industry are assumed to have some correlation, whereas credits in different industries are assumed to be completely uncorrelated. Each additional member of the portfolio adds to the diversity score, but members that are within the same industry add less and less as the industry concentration grows. For example, 20 assets in 20 different industries might add 20 to the diversity score 20 assets within the same industry, however, might only add 5 to the diversity score. 

Fig. 4. Chemical diversity is calculated as the fraction of compounds in a library that singly occupy cells in chemical space, and is shown here for an optimized library of 2000 compounds (a 10 x 20 x 10 combinatorial library) selected by MapMaker (left bar), and for the average of three 2000-member combinatorial libraries formed by selecting reagents at random. The optimized library has a nearly optimal diversity score of 1, whereas picking reagents without optimization would result in about half the screening efficiency, or about half the information (about 50% of the compounds in the random libraries occupy redundant cells).

Fig. 15.18 Selected examples of the distribution of predicted PSA scores for diversity reagents within a 2400-member library built around a common core. Topological PSA scores were calculated according to the method published by ErtI and expressed in A. Significant number of predicted scores greater than 140 is sufficient criteria for deselection of that diversity reagent.

To select the optimal subset of compounds, that is, a set of compounds having the maximal chemical diversity, a probabilistic search algorithm is applied, which consists in selecting a subset of compounds based on a probability assigned to each compound. This algorithm optimizes the joint entropy (/H) of the subset of selected compounds. The task is performed iteratively, assigning each ith compound an initial uniform probability Pi = 1 fn, then calculating the score S that is added to the previous compound probability as... 

Another index for evaluating presence of activity cliffs is the SAR Index (or Structure-Activity Relationship Index), defined as a function of two separately calculated scores that assess intraclass diversity and activity differences of similar compounds [Peltason and Bajorath, 2007] ... 

The continuity score measures activity-weighted structural diversity within a class of active compounds to generate the continuity score first, the following quantity is calculated as... 

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