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Beware of q2

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TLDR
It is argued that the high value of LOO q2 appears to be the necessary but not the sufficient condition for the model to have a high predictive power, which is the general property of QSAR models developed using LOO cross-validation.
Abstract
Validation is a crucial aspect of any quantitative structure-activity relationship (QSAR) modeling. This paper examines one of the most popular validation criteria, leave-one-out cross-validated R2 (LOO q2). Often, a high value of this statistical characteristic (q2 > 0.5) is considered as a proof of the high predictive ability of the model. In this paper, we show that this assumption is generally incorrect. In the case of 3D QSAR, the lack of the correlation between the high LOO q2 and the high predictive ability of a QSAR model has been established earlier [Pharm. Acta Helv. 70 (1995) 149; J. Chemomet. 10(1996)95; J. Med. Chem. 41 (1998) 2553]. In this paper, we use two-dimensional (2D) molecular descriptors and k nearest neighbors (kNN) QSAR method for the analysis of several datasets. No correlation between the values of q2 for the training set and predictive ability for the test set was found for any of the datasets. Thus, the high value of LOO q2 appears to be the necessary but not the sufficient condition for the model to have a high predictive power. We argue that this is the general property of QSAR models developed using LOO cross-validation. We emphasize that the external validation is the only way to establish a reliable QSAR model. We formulate a set of criteria for evaluation of predictive ability of QSAR models.

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Citations
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References
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Book

Graph theory

Frank Harary
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Comparative molecular field analysis (CoMFA). 1. Effect of shape on binding of steroids to carrier proteins.

TL;DR: The main features of the CoMFA approach, exemplified by analyses of the affinities of 21 varied steroids to corticosteroid and testosterone-binding globulins, and a number of advances in the methodology of molecular graphics are described.
Book

Substituent constants for correlation analysis in chemistry and biology

TL;DR: In this paper, the book is the window to get in the world and you can open the world easily, and these wise words are really familiar with you, so bring home now the book enPDFd substituent constants for correlation analysis in chemistry and biology to be your sources when going to read.
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