Cited by 3,735Computational Drug Discovery MethodsMachine Learning in Materials ScienceAdvanced Chemical Physics Studies

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Beware of q2!

Golbraikh, Alexander, Tropsha, Alexander·2002·Journal of Molecular Graphics and Modelling

DOI 10.1016/s1093-3263(01)00123-1

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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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Gandomi, A. H., Alavi, A. H., Gandomi, M., & Kazemi, S. (2016) · Measurement · doi:10.1016/j.measurement.2016.10.024 · Cited by 51
Improved Descriptors for the Quantitative Structure–Activity Relationship Modeling of Peptides and Proteins
Barley, M. H., Turner, N. J., & Goodacre, R. (2018) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.7b00488 · Cited by 51
QSAR analysis of coumarin-based benzamides as histone deacetylase inhibitors using CoMFA, CoMSIA and HQSAR methods
Abdizadeh, R., Hadizadeh, F., & Abdizadeh, T. (2019) · Journal of Molecular Structure · doi:10.1016/j.molstruc.2019.126961 · Cited by 50
Implementing the Fisher's Discriminant Ratio in a k-Means Clustering Algorithm for Feature Selection and Data Set Trimming
Lin, T., Li, H.-T., & Tsai, K. (2003) · Journal of Chemical Information and Computer Sciences · doi:10.1021/ci030295a · Cited by 51
Quantitative Structure-Pharmacokinetic Relationships for Drug Distribution Properties by Using General Regression Neural Network
Yap, C. W., & Chen, Y. (2004) · Journal of Pharmaceutical Sciences · doi:10.1002/jps.20232 · Cited by 51
QSAR, ADME-Tox, molecular docking and molecular dynamics simulations of novel selective glycine transporter type 1 inhibitors with memory enhancing properties
fadili, M. E., Er-rajy, M., Imtara, H., Noman, O. M., Mothana, R. A., Abdullah, S., Zerougui, S., & Elhallaoui, M. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e13706 · Cited by 52
“For this reason, the Y-Randomization test is necessary [6,51].”
Method
A (Comprehensive) Review of the Application of Quantitative Structure–Activity Relationship (QSAR) in the Prediction of New Compounds with Anti-Breast Cancer Activity
Vasilev, B., & Atanasova, M. (2025) · Applied Sciences · doi:10.3390/app15031206 · Cited by 57
Chemically Aware Model Builder (camb): an R package for property and bioactivity modelling of small molecules
Murrell, D. S., Cortés‐Ciriano, I., van Westen, G. J. P., Stott, I. P., Bender, A., Malliavin, T. E., & Glen, R. C. (2015) · Journal of Cheminformatics · doi:10.1186/s13321-015-0086-2 · Cited by 50
“The value of these metrics permits the assessment of model performance according to the criteria proposed by Tropsha and Golbraikh [37, 38], namely: q(2) CV > 0.”
Method
Synthesis, antimycobacterial, antiviral, antimicrobial activities, and QSAR studies of isonicotinic acid-1-(substituted phenyl)-ethylidene/cycloheptylidene hydrazides
Judge, V., Narasimhan, B., Ahuja, M., Sriram, D., Yogeeswari, P., Clercq, E. D., Pannecouque, C. C., & Balzarini, J. M. (2011) · Medicinal Chemistry Research · doi:10.1007/s00044-011-9705-2 · Cited by 50
“5 is the basic requirement for qualifying a QSAR model as the valid one (Golbraikh and Tropsha, 2002).”
Influential
An empirical model for shear capacity of RC deep beams using genetic-simulated annealing
Gandomi, A. H., Alavi, A. H., Danial Mohammadzadeh, S., & Sahab, M. G. (2013) · Archives of Civil and Mechanical Engineering · doi:10.1016/j.acme.2013.02.007 · Cited by 50
Novel approach to predicting hormetic effects of antibiotic mixtures on Vibrio fischeri
Zou, X., Lin, Z., Deng, Z., & Yin, D. (2012) · Chemosphere · doi:10.1016/j.chemosphere.2012.09.042 · Cited by 50
“The Q 2ðExtÞ of the external validation sets were also larger than 0.90, and the difference between Q2ðExtÞ and R 2 did not exceed 0.3, suggesting that the developed models have good predictive abilities and no danger of over-fitting or over-estimating the re- sults (Golbraikh and Tropsha, 2002).”
Influential
Predicting antitrichomonal activity: A computational screening using atom-based bilinear indices and experimental proofs
Marrero‐Ponce, Y., Meneses‐Marcel, A., Castillo‐Garit, J. A., Tugores, Y. M., Escario, J. A., Gómez‐Barrio, A., Pereira, D. M., Nogal‐Ruiz, J. J., Arán, V. J., Martínez‐Fernández, A. R., et al. (2006) · Bioorganic & Medicinal Chemistry · doi:10.1016/j.bmc.2006.06.016 · Cited by 50
Building energy consumption forecast using multi-objective genetic programming
Tahmassebi, A., & Gandomi, A. H. (2018) · Measurement · doi:10.1016/j.measurement.2018.01.032 · Cited by 50
3D-quantitative structure–activity relationship and antiviral effects of curcumin derivatives as potent inhibitors of influenza H1N1 neuraminidase
Lai, Y., Yan, Y., Liao, S.-H., Li, Y., Ye, Y., Liu, N., Zhao, F., & Xu, P. (2020) · Archives of Pharmacal Research · doi:10.1007/s12272-020-01230-5 · Cited by 52
“It is generally accepted that Total Score is > 6 for better activity, and ≥ 9 for very good activity (Golbraikh and Tropsha 2002) .”
Influential
Machine Learning‐Based Modeling with Optimization Algorithm for Predicting Mechanical Properties of Sustainable Concrete
Shah, M. I., Memon, S. A., Niazi, M. S. K., Amin, M. N., Aslam, F., & Javed, M. F. (2021) · Advances in Civil Engineering · doi:10.1155/2021/6682283 · Cited by 50
“, k and k′, passing through the origin should be nearly equal to 1 [86].”
Background
Larvicidal activities of some organotin compounds on mosquito larvae: A QSAR study
Hansch, C. H., & Verma, R. P. (2008) · European Journal of Medicinal Chemistry · doi:10.1016/j.ejmech.2008.02.040 · Cited by 49
Design, synthesis, antibacterial, and QSAR studies of myristic acid derivatives
Narasimhan, B., Mourya, V. K., & Dhake, A. S. (2006) · Bioorganic & Medicinal Chemistry Letters · doi:10.1016/j.bmcl.2006.02.056 · Cited by 50
Quantitative and qualitative models for carcinogenicity prediction for non-congeneric chemicals using CP ANN method for regulatory uses
Fjodorova, N., Vračko, M., Tušar, M., Jezierska, A., Novič, M., Kühne, R., & Schüürmann, G. (2009) · Molecular Diversity · doi:10.1007/s11030-009-9190-4 · Cited by 50
“[88] should be considered to confirm that proposed QSAR models have both, robustness and predictive power.”
Background
2D‐QSAR and molecular docking studies of carbamate derivatives to discover novel potent anti‐butyrylcholinesterase agents for Alzheimer's disease treatment
Nour, H., Abchır, O., Belaıdı, S., Qais, F. A., Chtita, S., & Belaaouad, S. (2021) · Bulletin of the Korean Chemical Society · doi:10.1002/bkcs.12449 · Cited by 49
Prioritization of the ecotoxicological hazard of PAHs towards aquatic species spanning three trophic levels using 2D-QSTR, read-across and machine learning-driven modelling approaches
Li, F., Wang, P., Fan, T., Zhang, N., Zhao, L., Zhong, R., & Sun, G. (2024) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2023.133410 · Cited by 49
Applications of conceptual density functional theory in reference to quantitative structure–activity / property relationship
Sharma, P., Ranjan, P., & Chakraborty, T. (2024) · Molecular Physics · doi:10.1080/00268976.2024.2331620 · Cited by 54
Comparative analysis of various machine learning algorithms to predict strength properties of sustainable green concrete containing waste foundry sand
Javed, M. F., Khan, M., Fawad, M., Alabduljabbar, H., Najeh, T., & Gamil, Y. (2024) · Scientific Reports · doi:10.1038/s41598-024-65255-2 · Cited by 53
Development, Validation, and Use of Quantitative Structure−Activity Relationship Models of 5-Hydroxytryptamine (2B) Receptor Ligands to Identify Novel Receptor Binders and Putative Valvulopathic Compounds among Common Drugs
Hajjo, R., Grulke, C., Golbraikh, A., Setola, V., Huang, X., Roth, B. L., & Tropsha, A. (2010) · Journal of Medicinal Chemistry · doi:10.1021/jm100600y · Cited by 49
Self-citation
4-Thiazolidinone derivatives: synthesis, antimicrobial, anticancer evaluation and QSAR studies
Deep, A., Narasimhan, B., Lim, S. M., Ramasamy, K., Mishra, R. K., & Mani, V. (2016) · RSC Advances · doi:10.1039/c6ra23006g · Cited by 49
“2-4) are valid ones (Golbraikh and Tropsha, 2002).”
Error measures in quantitative structure-retention relationships studies
Taraji, M., Haddad, P. R., Amos, R. I. J., Talebi, M., Szücs, R., Dolan, J. W., & Pohl, C. A. (2017) · Journal of Chromatography A · doi:10.1016/j.chroma.2017.09.050 · Cited by 49
A novel non-stochastic quadratic fingerprints-based approach for the ‘in silico’ discovery of new antitrypanosomal compounds
Montero, A., Vega, C., Marrero‐Ponce, Y., Rolón, M. S., Gómez‐Barrio, A., Escario, J. A., Arán, V. J., Martínez‐Fernández, A. R., & Meneses‐Marcel, A. (2005) · Bioorganic & Medicinal Chemistry · doi:10.1016/j.bmc.2005.06.049 · Cited by 49
Nucleic Acid Quadratic Indices of the “Macromolecular Graph’s Nucleotides Adjacency Matrix”. Modeling of Footprints after the Interaction of Paromomycin with the HIV-1 Ψ-RNA Packaging Region
Marrero‐Ponce, Y., Nodarse, D., González‐Díaz, H., de Armas, R. R., Zaldívar, V. R., Torrens, F., & Castro, E. A. (2004) · International Journal of Molecular Sciences · doi:10.3390/i5110276 · Cited by 49
Development of a Sigma-2 Receptor affinity filter through a Monte Carlo based QSAR analysis
Rescifina, A., Floresta, G., Marrazzo, A., Parenti, C., Prezzavento, O., Nastasi, G., Dichiara, M., & Amata, E. (2017) · European Journal of Pharmaceutical Sciences · doi:10.1016/j.ejps.2017.05.061 · Cited by 48
Prediction of dielectric constants and glass transition temperatures of polymers by quantitative structure property relationships
Liu, A., Wang, X., Wang, L., Wang, H., & Wang, H. (2006) · European Polymer Journal · doi:10.1016/j.eurpolymj.2006.12.029 · Cited by 48
In Silico Predictions of Human Skin Permeability using Nonlinear Quantitative Structure–Property Relationship Models
Baba, H., Takahara, J.-I., & Mamitsuka, H. (2015) · Pharmaceutical Research · doi:10.1007/s11095-015-1629-y · Cited by 49
“Golbraikh and Tropsha (47) and Roy (48) suggested the following criteria to validate QSPR models: A model is highly predictive if its statistical characteristics satisfy the following conditions in external validation:”
BackgroundMethod
Towards interoperable and reproducible QSAR analyses: Exchange of datasets
Spjuth, O., Willighagen, E., Guha, R., Eklund, M., & Wikberg, J. E. S. (2010) · Journal of Cheminformatics · doi:10.1186/1758-2946-2-5 · Cited by 48
“There exist many examples of investigations regarding the resulting statistical models with respect to validity and applicability in QSAR and similar fields [9,10].”
Background
Structure-based prediction of protein–protein binding affinity with consideration of allosteric effect
Tian, F., Lv, Y., & Li, Y. (2011) · Amino Acids · doi:10.1007/s00726-011-1101-1 · Cited by 50
“However, Golbraikh and Tropsha (2002) pointed out that a more reliable result should be obtained by dividing external test set.”
Background
Prediction of refractive index of vinyl polymers by using density functional theory
Yu, X., Yi, B., & Wang, X. (2007) · Journal of Computational Chemistry · doi:10.1002/jcc.20752 · Cited by 48
Significantly Improved HIV Inhibitor Efficacy Prediction Employing Proteochemometric Models Generated From Antivirogram Data
van Westen, G. J. P., Hendriks, A., Wegner, J. K., IJzerman, A. P., van Vlijmen, H., & Bender, A. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002899 · Cited by 48
“[ 36,62] Density based applicability domain As our models are trained on a database of different HIV mutants, applicability domains based on a single wild type sequence are expected to perform sub optimal.”
Method
Development of linear and nonlinear predictive QSAR models and their external validation using molecular similarity principle for anti-HIV indolyl aryl sulfones
Roy, K., & Mandal, A. S. (2008) · Journal of Enzyme Inhibition and Medicinal Chemistry · doi:10.1080/14756360701811379 · Cited by 48
“All the models have satisfied the requirement of the value of (r2 2 r20)/r 2 being less than 0.1 as recommended by Golbraikh and Tropsha [52].”
MethodInfluential
QSPR study of Setschenow constants of organic compounds using MLR, ANN, and SVM analyses
Xu, J., Wang, L., Wang, L., Shen, X., & Xu, W. (2011) · Journal of Computational Chemistry · doi:10.1002/jcc.21907 · Cited by 49
Development of a robust and validated 2D-QSPR model for sweetness potency of diverse functional organic molecules
Ojha, P. K., & Roy, K. (2017) · Food and Chemical Toxicology · doi:10.1016/j.fct.2017.03.043 · Cited by 48
“We have also validated the model using Golbraikh and Tropsha criteria and the results are given in Table 2.”
MethodInfluential
A QSAR-based mechanistic study on the combined toxicity of antibiotics and quorum sensing inhibitors against Escherichia coli
Wang, D., Shi, J., Xiong, Y., Hu, J., Lin, Z., Qiu, Y., & Cheng, J. (2017) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2017.07.059 · Cited by 48

Authors: Golbraikh, A., & Tropsha, A.
Affiliations: University of North Carolina at Chapel Hill (US)
Corresponding author: Tropsha, Alexander
ORCID: Golbraikh, Alexander
Tropsha, Alexander
Venue: Journal of Molecular Graphics and Modelling
Publisher: Elsevier BV
Published: 2002-01
Volume: 20
Issue: 4
Pages: 269-276
ISSN: 1093-3263 (ISSN-L)
DOI: 10.1016/s1093-3263(01)00123-1
OpenAlex: W2087661061
Cited by: 3,735
References: 39
Citations by year: 2026: 133 · 2025: 164 · 2024: 179 · 2023: 174 · 2022: 194 · 2021: 197 · 2020: 215 · 2019: 189 · 2018: 200 · 2017: 174 · 2016: 181 · 2015: 175 · 2014: 197 · 2013: 203 · 2012: 202
FWCI: 52.71
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: Journal of Molecular Graphics and Modelling (publishedVersion)
PubMed (publishedVersion)
Topics: Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Drug Discovery › Computational Drug Discovery Methods
Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Keywords: leave-one-out cross-validation, QSAR model validation, predictive power, external validation, 2D molecular descriptors, overfitting, model evaluation metrics
MeSH terms: Data Interpretation, Statistical, Ligands, Mathematical Computing, Models, Molecular, Receptors, Histamine H1, Steroids, Transcortin, Databases, Factual, Quantitative Structure-Activity Relationship, Ecdysteroids

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