Controlling coverage of D‐optimal onion designs and selections

Abstract

Statistical molecular design (SMD) is a powerful approach for selection of compound sets in medicinal chemistry and quantitative structure-activity relationships (QSARs) as well as other areas. Two techniques often used in SMD are space-filling and D-optimal designs. Both on occasions lead to unwanted redundancy and replication. To remedy such shortcomings, a generalization of D-optimal selection was recently developed. This new method divides the compound candidate set into a number of subsets ('layers' or 'shells'), and a D-optimal selection is made from each layer. This improves the possibility to select representative molecular structures throughout any property space independently of requested sample size. This is important in complex situations where any given model is unlikely to be valid over the whole investigated domain of experimental conditions. The number of selected molecules can be controlled by varying the number of subsets or by altering the complexity of the model equation in each layer and/or the dependency of previous layers. The new method, called D-optimal onion design (DOOD), will allow the user to choose the model equation complexity independently of sample size while still avoiding unwarranted redundancy. The focus of the present work is algorithmic improvements of DOOD in comparison with classical D-optimal design. As illustrations, extended DOODs have been generated for two applications by in-house programming, including some modifications of the D-optimal algorithm. The performances of the investigated approaches are expected to differ depending on the number of principal properties of the compounds in the design, sample sizes and the investigated model, i.e. the aim of the design. QSAR models have been generated from the selected compound sets, and root mean squared error of prediction (RMSEP) values have been used as measures of performance of the different designs.

ChemGPS-NP: Tuned for Navigation in Biologically Relevant Chemical Space

“…If there were less than 20 interesting outliers in a data set, they were all added to the training set. If the prediction set contained more than 20 interesting outliers, a subset was selected via the D-optimal design, or, if they were more than 100, via D-optimal onion design. , D-optimal designs select the most extreme points of the candidate set and give a minimal set of selected compounds with maximum diversity. D-optimal onion designs divide the set into a number of selected layers where one separate D-optimal design is made in each layer.…”

“…33 DModXPS was calculated for all compounds predicted with the evolving ChemGPS-NP using SIMCA-P+ 10.5. 33 D-optimal (onion) designs 36 were generated with the software MODDE 7. 41 Design factors were scaled to unit variance and centered by default prior to the design.…”

Solvent subset selection for polymorph screening

“…Alternative solutions to subset selection could be achieved by modifying the operation of one single algorithm. In addition to the D-optimality presented here a so-called D-optimal Onion Design (DOOD) has been proposed [17]. This method cleverly divides the sample space into layers followed by a D-optimal selection from within each layer, forcing the selected sample candidates to be evenly distributed in the design space, thus 'spanning the chemical space' .…”

ChemGPS-NPWeb: chemical space navigation online

“…Compound libraries could be positioned with ChemGPS-NP, and those compounds residing outside the 'active area' could be excluded for the benefit of compounds located closer to the active compounds. To demonstrate this we selected a subset of 42 confirmed active compounds using D-optimal onion design [12][13][14]. D-optimal designs select the most extreme points of the candidate set and give a minimal set of selected compounds with maximum diversity.…”