Linking Drug or Phytochemical Exposure to Toxicity


aAdjunct Associate Professor of Pharmaceutical Sciences, The University of Michigan, Ann Arbor, Mi, uSA; bAdjunct professor of pharmaceutics and Medicinal Chemistry, university of the pacific, Stockton, CA, uSA; cVice president of Scientific training and director of Strategic Consulting, Certara, princeton, NJ, uSA; dprofessor of pharmaceutics and Medicinal Chemistry, Associate provost of research, and interim dean of graduate Studies, university of the pacific, Stockton, CA, uSA ?e-mail: This email address is being protected from spam bots, you need Javascript enabled to view it


Toxicokinetic studies are an integral part of the overall evaluation of the toxicity of a new chemical entity. By definition,1 these studies are designed to generate pharmacokinetic data that may be used in the interpretation of toxicology findings and their relevance in clinical safety. At a very minimum, toxicokinetic data includes measurements of the systemic exposure in different animals at various dose levels to attempt a correlation between these exposure measurements and toxicology findings. In a typical toxicology study with toxicokinetic support, serial measurements of plasma concentrations of parent drug or metabolites (whether total or unbound) at specific time points yield exposure pharmacokinetic parameters (for example, Cmax, AuC, Css, C at some time t), that quantify the magnitude of the exposure in

Issues in Toxicology No. 31

Computational Systems Pharmacology and Toxicology Edited by Dale E. Johnson and Rudy J. Richardson © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, that particular study. The collection of toxicokinetic data from multiple toxicology studies allows for the determination of exposures associated with the absence of toxicological findings, and as such, provide a margin of safety based on concentrations when clinical studies are planned.2

the predictive value of toxicokinetic data is enhanced when a suitable statistical model can be used to summarize the collective findings from different studies (and in some cases, even different compounds). these pharmacostatis- tical models contain two parts: a structural (or systematic) component which describes the exact mathematical relationship between different exposure and toxicity parameters, and a variance (or stochastic) component, which attempts to explain the statistical variability in the observed data. In general, biological data tend to have more noise than models found in the physical sciences. For that reason, pharmacostatistical models tend to be more complex.

the general approach to developing pharmacostatistical models is no different to other areas of science. First, the modeler scientist studies and identifies the problem at hand. In this process, some exposure or toxicity measurements may have already been collected. the modeler determines which variables are relevant, and make plans to measure additional variables if necessary. the relevant experiments are performed and the data are collected as planned. part of data collection involves a documentation of the procedures followed in these experiments, a check in the quality of the data in which uncertainties in the measurements are assessed, and a data preparation step in which the data are placed in a suitable format for modeling. At this stage, the data are examined for trends, and a base model relating the toxicokinetic (or toxicology) parameters and the observations is postulated. An interactive process starts in which the base model gets refined with the addition of other parameters, helping to explain more of the variability observed in the data. these additional models are compared to the original base model, and only those models which statistically explain more of the observed data are subsequently retained, until the addition of more parameters does not significantly change the predictive value of the model. at this stage, a final model is chosen based on statistical goodness-of-fit criteria (such as residual analysis, coefficients of determination, and others), and among competing models with similar goodness-of-fit measures, the simplest one is chosen (occam’s razor). the predictive ability of the final model is checked by generating simulated predictions based on the model and comparing these predictions to the experimental observations. the result of this visual predictive check not only support the appropriateness of the final model, but can also suggest model improvements.

the final step in the model building process is the communication of the results by the modeler. the results of the model should be presented in relation to the original problem that was sought to be answered by the modeler. However, the message needs to be tailored to the intended recipient of the information. the level of detail in the communication of the results will be greater if the recipient is a regulatory agency or another scientist modeler; whereas if the recipient is a project team, the results of the modeling process and the impact of the model in future decisions are more important than the details of the model. Regardless of the level of detail, the results should be presented in a clear and succinct manner. This will aid in understanding the science behind the modeling, its implications, and will avoid rejection of the model based on a lack of knowledge. this is assuming, of course, that the features and benefits of pharmacostatistical modeling are recognized by all who are the intended recipients. If not, models that are scientifically sound will be discarded, and considerable time would be spent on convincing others that the whole modeling approach is worthwhile.

Computing advances in the late 20th century have led to an increase in the use of pharmacostatistical models, not only in the traditional areas of drug development (that is, those related to human pharmacokinetics and approval of drugs), but also in other areas, such as toxicokinetics3 and in veterinary medicine.4 regulatory agencies have recognized the value of pharmacostatistical modeling and have required the presentation of such data, not only as an integral part of a submission,5^ but also during the drug development process.7 in fact, the united States Food and Drug Administration (FDA) encourages sponsors “to discuss the use of quantitative drug development methods (e.g. trial simulation using disease, drug, placebo, and dropout models) before conducting phase 2B and phase 3 clinical trials”.7 For that reason alone, an understanding of these models is important for any drug development scientist, and, as the use of these models increases in toxicology areas, it is relevant for toxicologists to understand them as well. the following sections present an overview of the models used in drug development related to pharmacokinetic/toxicokinetic (pk/TK) measurements, pK/tK responses, and drug interactions.

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