Toxics 2023, 11, 419. htps://doi.org/10.3390/toxics11050419 www.mdpi.com/journal/toxics Article The System of Self-Consistent Models: QSAR Analysis of Drug-Induced Liver Toxicity Alla P. Toropova *, Andrey A. Toropov, Alessandra Roncaglioni and Emilio Benfenati * Istituto di Ricerche Farmacologiche Mario Negri IRCCS, Via Mario Negri 2, 20156 Milano, Italy; andrey.toropov@marionegri.it (A.A.T.); alessandra.roncaglioni@marionegri.it (A.R.) * Correspondence: alla.toropova@marionegri.it (A.P.T.); emilio.benfenati@marionegri.it (E.B.); Tel.: +39-02-3901-4595 (E.B.); Fax: +39-02-3901-4735 (E.B.) Abstract: Removing a drug-like substance that can cause drug-induced liver injury from the drug discovery process is a significant task for medicinal chemistry. In silico models can facilitate this process. Semi-correlation is an approach to building in silico models representing the prediction in the active (1)—inactive (0) format. The so-called system of self-consistent models has been suggested as an approach for two tasks: (i) building up a model and (ii) estimating its predictive potential. However, this approach has been tested so far for regression models. Here, the approach is applied to building up and estimating a categorical hepatotoxicity model using the CORAL software. This new process yields good results: sensitivity = 0.77, specificity = 0.75, accuracy = 0.76, and Mathew correlation coefficient = 0.51 (all compounds) and sensitivity = 0.83, specificity = 0.81, accuracy = 0.83 and Mathew correlation coefficient = 0.63 (validation set). Keywords: drug-induced liver injuries; hepatotoxicity; Monte Carlo method; index of ideality of correlation (IIC); CORAL software 1. Introduction The liver is highly susceptible to drug insults: around 5–10% of adverse drug reac- tions result in liver injuries [1]. Naturally, this stimulates the search for reliable models to anticipate and avoid this dangerous toxicity [2]. More than 1100 chemical substances ap- plied daily have been identified as potentially causing liver injuries [3–5]. The clinical im- pact may be vary, provoking oxidative stress, an increase in the level of liver enzymes (cytochromes P450), and a dangerous impact on metabolism [5–7]. In silico models can help predict adverse effects and plan safer drugs before their complete development. Of course, these models have limits. This is a general issue since experimental studies also have limits of different types, such as the time and costs needed and ethical concerns regarding the use of animals. “The idea of approximation dominates all exact science” (Bertrand Russell). Quanti- tative structure–activity relationships (QSARs) are an example of science where approxi- mation is relevant. QSAR should be considered a surrogate of a real experiment with some limits. Even though “all models are wrong” [8], “some of them are useful” [9]. Therefore, the point is to develop “useful models”. This refers to purpose and ambition, and how far we go with a model. For screening purposes, for instance, models for an initial evaluation are acceptable even if they have greater uncertainty. However, models for the final eval- uation require much less uncertainty. We aim to develop some simple, fast models for the first evaluation of large collec- tions of substances. This is suitable for the endpoint we are addressing in the present case: drug-induced liver injuries (DILI). This relates to many toxicological mechanisms involv- ing complexity. At the basis of our model, as with QSAR models in general, there are data collections with experimental values. These data serve to extract the correct information, Citation: Toropova, A.P.; Toropov, A.A.; Roncaglioni, A.; Benfenati, E. The System of Self-Consistent Models: QSAR Analysis of Drug-Induced Liver Toxicity. Toxics 2023, 11, 419. htps://doi.org/10.3390/ toxics11050419 Academic Editor: Jong-Choon Kim Received: 15 March 2023 Revised: 11 April 2023 Accepted: 25 April 2023 Published: 29 April 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Atribution (CC BY) license (htps://creativecommons.org/license s/by/4.0/).