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Introduction: Drug attrition in oncology clinical development is higher than in other therapeutic areas. In this context, pharmacometric modeling represents a useful tool to explore drug efficacy in earlier phases of clinical development, anticipating overall survival using quantitative model-based metrics. Furthermore, modeling approaches can be used to characterize earlier the safety and tolerability profile of drug candidates, and, thus, the risk-benefit ratio and the therapeutic index, supporting the design of optimal treatment regimens and accelerating the whole process of clinical drug development. Areas covered: Herein, the most relevant mathematical models used in clinical anticancer drug development during the last decade are described. Less recent models were considered in the review if they represent a standard for the analysis of certain types of efficacy or safety measures. Expert opinion: Several mathematical models have been proposed to predict overall survival from earlier endpoints and validate their surrogacy in demonstrating drug efficacy in place of overall survival. An increasing number of mathematical models have also been developed to describe the safety findings. Modeling has been extensively used in anticancer drug development to individualize dosing strategies based on patient characteristics, and design optimal dosing regimens balancing efficacy and safety.

Introduction: Pharmacometric models represent the most comprehensive approaches for extracting, summarizing and integrating information obtained in the often sparse, limited, and less-than-optimally designed experiments performed in the early phases of oncology drug discovery. Whilst empirical methodologies may be enough for screening and ranking candidate drugs, modeling approaches are needed for optimizing and making economically viable the learn-confirm cycles within an oncology research program and anticipating the dose regimens to be investigated in the subsequent clinical development. Areas covered: Papers appearing in the literature of approximately the last decade reporting modeling approaches applicable to anticancer drug discovery have been listed and commented. Papers were selected based on the interest in the proposed methodology or in its application. Expert opinion: The number of modeling approaches used in the discovery of anticancer drugs is consistently increasing and new models are developed based on the current directions of research of new candidate drugs. These approaches have contributed to a better understanding of new oncological targets and have allowed for the exploitation of the relatively sparse information generated by preclinical experiments. In addition, they are used in translational approaches for guiding and supporting the choice of dosing regimens in early clinical development.

Tumor growth inhibition (TGI) models are increasingly used during preclinical drug development in oncology for the in vivo evaluation of antitumor effect. Tumor sizes are measured in xenografted mice, often only during and shortly after treatment, thus preventing correct identification of some TGI model parameters. Our aims were (i) to evaluate the importance of including measurements during tumor regrowth and (ii) to investigate the proportions of mice included in each arm. For these purposes, optimal design theory based on the Fisher information matrix implemented in PFIM4.0 was applied. Published xenograft experiments, involving different drugs, schedules, and cell lines, were used to help optimize experimental settings and parameters using the Simeoni TGI model. For each experiment, a two-arm design, i.e., control versus treatment, was optimized with or without the constraint of not sampling during tumor regrowth, i.e., "short" and "long" studies, respectively. In long studies, measurements could be taken up to 6 g of tumor weight, whereas in short studies the experiment was stopped 3 days after the end of treatment. Predicted relative standard errors were smaller in long studies than in corresponding short studies. Some optimal measurement times were located in the regrowth phase, highlighting the importance of continuing the experiment after the end of treatment. In the four-arm designs, the results showed that the proportions of control and treated mice can differ. To conclude, making measurements during tumor regrowth should become a general rule for informative preclinical studies in oncology, especially when a delayed drug effect is suspected.

This paper presents TGI-Simulator, a software tool designed to show, through a 2-D graphical animation, the simulated time effect of an anticancer drug on a tumor mass by exploiting the well-known Tumor Growth Inhibition (TGI) model published by Simeoni et al. [1]. Simeoni TGI model is a mathematical model routinely used by pharma companies and researchers during the drug development process. The application is based on a Java graphical user interface (GUI) including a self installing differential equation solver implemented in Matlab together with an optimization algorithm that performs model identification via Weighted Least Squares (WLS). However, it can graphically show also the simulation results obtained within other scientific software tools, if they are preventively stored into a suitable ASCII file. The tool would be a valid support also for researchers with no specific skills in scientific calculations and in pharmacokinetic and pharmacodynamic modeling but daily involved in pharma companies drug development processes at different levels. The availability of a movie with a temporal varying 2-D iconographic representation is an original instrument to communicate results and learn Simeoni TGI model and its potential application in preclinical studies., (Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.)

The study investigated the effects of the dopamine-somatostatin chimeric compound BIM-23A760 on cell proliferation and apoptosis in cultured cells from human non-functioning pituitary tumors (NFPTs). Both BIM-23A760 and the dopaminergic agonist BIM-53097 induced a significant inhibition of cell proliferation associated with increased p27 expression, together with a significant increase in caspase-3 activity. Conversely, null or marginal effects were elicited by somatostatin analogs. Moreover, BIM-23A760 and BIM-53097 induced ERK1/2 and p38 phosphorylation and the blockade of these pathways prevented both the antiproliferative and the pro-apoptotic effects of these drugs. In conclusions the chimeric compound BIM-23A760 is able to exert cytostatic and cytotoxic effects in NFPTs, these phenomena being mainly mediated by DR2D and involving ERK1/2 and p38 pathways activation., (2009 Elsevier Ireland Ltd. All rights reserved.)

Purpose: The use of in vitro screening tests for characterizing the activity of anticancer agents is a standard practice in oncology research and development. In these studies, human A2780 ovarian carcinoma cells cultured in plates are exposed to different concentrations of the compounds for different periods of time. Their anticancer activity is then quantified in terms of EC(50) comparing the number of metabolically active cells present in the treated and the control arms at specified time points. The major concern of this methodology is the observed dependency of the EC(50) on the experimental design in terms of duration of exposure. This dependency could affect the efficacy ranking of the compounds, causing possible biases especially in the screening phase, when compound selection is the primary purpose of the in vitro analysis. To overcome this problem, the applicability of a modeling approach to these in vitro studies was evaluated., Methods: The model, consisting of a system of ordinary differential equations, represents the growth of tumor cells using a few identifiable and biologically relevant parameters related to cell proliferation dynamics and drug action. In particular, the potency of the compounds can be measured by a unique and drug-specific parameter that is essentially independent of drug concentration and exposure time. Parameter values were estimated using weighted nonlinear least squares., Results: The model was able to adequately describe the growth of tumor cells at different experimental conditions. The approach was validated both on commercial drugs and discovery candidate compounds. In addition, from this model the relationship between EC(50) and the exposure time was derived in an analytic form., Conclusions: The proposed approach provides a new tool for predicting and/or simulating cell responses to different treatments with useful indications for optimizing in vitro experimental designs. The estimated potency parameter values obtained from different compounds can be used for an immediate ranking of anticancer activity.

The preclinical development of antitumor drugs greatly benefits from the availability of models capable of predicting tumor growth as a function of the drug administration schedule. For being of practical use, such models should be simple enough to be identifiable from standard experiments conducted on animals. In the present paper, a stochastic model is derived from a set of minimal assumptions formulated at cellular level. Tumor cells are divided in two groups: proliferating and nonproliferating. The probability that a proliferating cell generates a new cell is a function of the tumor weight. The probability that a proliferating cell becomes nonproliferating is a function of the plasma drug concentration. The time-to-death of a nonproliferating cell is a random variable whose distribution reflects the nondeterministic delay between drug action and cell death. The evolution of the expected value of tumor weight obeys two differential equations (an ordinary and a partial differential one), whereas the variance is negligible. Therefore, the tumor growth dynamics can be well approximated by the deterministic evolution of its expected value. The tumor growth inhibition model, which is a lumped parameter model that in the last few years has been successfully applied to several antitumor drugs, is shown to be a special case of the minimal model presented here.

The prevalence of metabolic syndrome is increasing along with breast cancer incidence worldwide. Because fenretinide improves insulin action and glucose tolerance in insulin-resistant obese mice and because tamoxifen has shown to regulate several markers involved in metabolic syndrome, we sought to investigate the effect of fenretinide or tamoxifen at low dose on features linked to insulin resistance in premenopausal women at risk for breast cancer. We randomized 235 women to low-dose tamoxifen (5 mg/daily), fenretinide (200 mg/daily), or their combination or placebo for 2 years. We used the homeostasis model assessment (HOMA; fasting insulin x glucose/22.5) to estimate insulin sensitivity. Women were considered to improve insulin sensitivity when they shifted from a HOMA >/=2.8 to <2.8. There was no effect of fenretinide or tamoxifen on HOMA overall, but overweight women (body mass index, >or=25 kg/m(2)) had a 7-fold greater probability to normalize HOMA after 2 years of fenretinide treatment [odds ratio (OR), 7.0; 95% confidence interval (95% CI), 1.2-40.5], with 25% of women improving their insulin sensitivity, whereas tamoxifen decreased insulin sensitivity by almost 7 times compared with subjects not taking tamoxifen (OR, 0.15; 95% CI, 0.03-0.88). In this group only, 5% improved their insulin sensitivity. Interestingly, women with intraepithelial or microinvasive neoplasia had higher HOMA (3.0) than unaffected subjects (2.8; P = 0.07). Fenretinide can positively balance the metabolic profile in overweight premenopausal women and this may favorably affect breast cancer risk. Furthermore, features of the metabolic syndrome should be taken into consideration before proposing tamoxifen for breast cancer prevention. The clinical implications of these results require further investigations.

The available mathematical models describing tumor growth and the effect of anticancer treatments on tumors in animals are of limited use within the drug industry. A simple and effective model would allow applying quantitative thinking to the preclinical development of oncology drugs. In this article, a minimal pharmacokinetic-pharmacodynamic model is presented, based on a system of ordinary differential equations that link the dosing regimen of a compound to the tumor growth in animal models. The growth of tumors in nontreated animals is described by an exponential growth followed by a linear growth. In treated animals, the tumor growth rate is decreased by a factor proportional to both drug concentration and number of proliferating tumor cells. A transit compartmental system is used to model the process of cell death, which occurs at later times. The parameters of the pharmacodynamic model are related to the growth characteristics of the tumor, to the drug potency, and to the kinetics of the tumor cell death. Therefore, such parameters can be used for ranking compounds based on their potency and for evaluating potential differences in the tumor cell death process. The model was extensively tested on discovery candidates and known anticancer drugs. It fitted well the experimental data, providing reliable parameter estimates. On the basis of the parameters estimated in a first experiment, the model successfully predicted the response of tumors exposed to drugs given at different dose levels and/or schedules. It is, thus, possible to use the model prospectively, optimizing the design of new experiments.

Purpose: The effect of an anticancer treatment on tumor cell proliferation in vitro can be described as a three-dimensional surface where the inhibitory effect is related to drug concentration and treatment time. The analysis of this kind of response surface could provide critical information: for example, it could indicate whether a prolonged exposure to a low concentration of an anticancer agent will produce a different effect from exposure to higher concentrations for a shorter period of time. The parametric approach available in the literature was not flexible enough to accommodate the behavior of the response surface in some of the data sets collected as part of our research programs. Therefore, a new, general, nonparametric approach was developed., Methods: The response surface of the inhibition of cell-based tumor growth was described using a radial basis function neural network (RBF-NN). The RBF-NN was trained using regularization theory, which provided the initialization of a constrained quadratic optimization algorithm that imposes monotonicity of the surface with respect to both concentration and exposure time., Results: In the two analyzed cases (doxorubicin and flavopiridol), the proposed method was accurate and reliable in describing the inhibition surface of tumor cell growth as a function of drug concentration and exposure time. Residuals were small and unbiased. The new method improved on the parametric approach when the relative importance of drug concentration and exposure time in determining the overall effect was not constant across the experimental data., Conclusions: The proposed RBF-NN can be reliably applied for the analysis in cell-based tumor growth inhibition studies. This approach can be used for optimizing the administration regimens to be adopted in vivo. The use of this methodology can be easily extended to any cell-based experiment, in which the outcome can be seen as a function of two experimental variables.

In the last decades three-dimensional (3D) in vitro cancer models have been proposed as a bridge between bidimensional (2D) cell cultures and in vivo animal models, the gold standards in the preclinical assessment of anticancer drug efficacy. 3D in vitro cancer models can be generated through a multitude of techniques, from both immortalized cancer cell lines and primary patient-derived tumor tissue. Among them, spheroids and organoids represent the most versatile and promising models, as they faithfully recapitulate the complexity and heterogeneity of human cancers. Although their recent applications include drug screening programs and personalized medicine, 3D in vitro cancer models have not yet been established as preclinical tools for studying anticancer drug efficacy and supporting preclinical-to-clinical translation, which remains mainly based on animal experimentation. In this review, we describe the state-of-the-art of 3D in vitro cancer models for the efficacy evaluation of anticancer agents, focusing on their potential contribution to replace, reduce and refine animal experimentations, highlighting their strength and weakness, and discussing possible perspectives to overcome current challenges. [ABSTRACT FROM AUTHOR]

The aim of this work is to build a mechanistic multiscale pharmacokinetic model for the anticancer drug 2',2'‐difluorodeoxycytidine (gemcitabine, dFdC), able to describe the concentrations of dFdC metabolites in the pancreatic tumor tissue in dependence of physiological and genetic patient characteristics, and, more in general, to explore the capabilities and limitations of this kind of modeling strategy. A mechanistic model characterizing dFdC metabolic pathway (metabolic network) was developed using in vitro literature data from two pancreatic cancer cell lines. The network was able to describe the time course of extracellular and intracellular dFdC metabolites concentrations. Moreover, a physiologically‐based pharmacokinetic model was developed to describe clinical dFdC profiles by using enzymatic and physiological information available in the literature. This model was then coupled with the metabolic network to describe the dFdC active metabolite profile in the pancreatic tumor tissue. Finally, global sensitivity analysis was performed to identify the parameters that mainly drive the interindividual variability for the area under the curve (AUC) of dFdC in plasma and of its active metabolite (dFdCTP) in tumor tissue. From this analysis, cytidine deaminase (CDA) concentration was identified as the main driver of plasma dFdC AUC interindividual variability, whereas CDA and deoxycytidine kinase concentration mainly explained the tumor dFdCTP AUC variability. However, the lack of in vitro and in vivo information needed to characterize key model parameters hampers the development of this kind of mechanistic approach. Further studies to better characterize pancreatic cell lines and patient enzymes polymorphisms are encouraged to refine and validate the current model. [ABSTRACT FROM AUTHOR]

Purpose: In clinical oncology, combination treatments are widely used and increasingly preferred over single drug administrations. A better characterization of the interaction between drug effects and the selection of synergistic combinations represent an open challenge in drug development process. To this aim, preclinical studies are routinely performed, even if they are only qualitatively analyzed due to the lack of generally applicable mathematical models. Methods: This paper presents a new pharmacokinetic-pharmacodynamic model that, starting from the well-known single agent Simeoni TGI model, is able to describe tumor growth in xenograft mice after the co-administration of two anticancer agents. Due to the drug action, tumor cells are divided in two groups: damaged and not damaged ones. The damaging rate has two terms proportional to drug concentrations (as in the single drug administration model) and one interaction term proportional to their product. Six of the eight pharmacodynamic parameters assume the same value as in the corresponding single drug models. Only one parameter summarizes the interaction, and it can be used to compute two important indexes that are a clear way to score the synergistic/antagonistic interaction among drug effects. Results: The model was successfully applied to four new compounds co-administered with four drugs already available on the market for the treatment of three different tumor cell lines. It also provided reliable predictions of different combination regimens in which the same drugs were administered at different doses/schedules. Conclusions: A good and quantitative measurement of the intensity and nature of interaction between drug effects, as well as the capability to correctly predict new combination arms, suggest the use of this generally applicable model for supporting the experiment optimal design and the prioritization of different therapies. [ABSTRACT FROM AUTHOR]

Purpose: Pharmacokinetic-pharmacodynamic (PK-PD) models able to predict the action of anticancer compounds in tumor xenografts have an important impact on drug development. In case of anti-angiogenic compounds, many of the available models show difficulties in their applications, as they are based on a cell kill hypothesis, while these drugs act on the tumor vascularization, without a direct tumor cell kill effect. For this reason, a PK-PD model able to describe the tumor growth modulation following treatment with a cytostatic therapy, as opposed to a cytotoxic treatment, is proposed here. Methods: Untreated tumor growth was described using an exponential growth phase followed by a linear one. The effect of anti-angiogenic compounds was implemented using an inhibitory effect on the growth function. The model was tested on a number of experiments in tumor-bearing mice given the anti-angiogenic drug bevacizumab either alone or in combination with another investigational compound. Nonlinear regression techniques were used for estimating the model parameters. Results: The model successfully captured the tumor growth data following different bevacizumab dosing regimens, allowing to estimate experiment-independent parameters. A combination model was also developed under a 'no-interaction' assumption to assess the effect of the combination of bevacizumab with a target-oriented agent. The observation of a significant difference between model-predicted and observed tumor growth curves was suggestive of the presence of a pharmacological interaction that was further accommodated into the model. Conclusions: This approach can be used for optimizing the design of preclinical experiments. With all the inherent limitations, the estimated experiment-independent model parameters can be used to provide useful indications for the single-agent and combination regimens to be explored in the subsequent development phases. [ABSTRACT FROM AUTHOR]

One important issue in the preclinical development of an anticancer drug is the assessment of the compound under investigation when administered in combination with other drugs. Several experiments are routinely conducted in xenograft mice to evaluate if drugs interact or not. Experimental data are generally qualitatively analyzed on empirical basis. The ability of deriving from single drug experiments a reference response to the joint administrations, assuming no interaction, and comparing it to real responses would be key to recognize synergic and antagonist compounds. Therefore, in this paper, the minimal model of tumor growth inhibition (TGI), previously developed for a single drug, is reformulated to account for the effects of noninteracting drugs and simulate, under this hypothesis, combination regimens. The model is derived from a minimal set of basic assumptions that include and extend those formulated at cellular level for the single drug administration. The tumor growth dynamics is well approximated by the deterministic evolution of its expected value that is obtained through the solution of an ordinary and several partial differential equations. Under suitable assumptions on the cell death process, the model reduces to a lumped parameter model that represents the extension of the very popular Simeoni TGI model to the combined administration of noninteracting drugs. [ABSTRACT FROM PUBLISHER]

Xenograft models are commonly used in oncology drug development. Although there are discussions about their ability to generate meaningful data for the translation from animal to humans, it appears that better data quality and better design of the preclinical experiments, together with appropriate data analysis approaches could make these data more informative for clinical development. An approach based on mathematical modeling is necessary to derive experiment-independent parameters which can be linked with clinically relevant endpoints. Moreover, the inclusion of biomarkers as predictors of efficacy is a key step towards a more general mechanism-based strategy. [Copyright &y& Elsevier]

The purpose of this study was to establish a population pharmacokinetic/pharmacodynamic (PK/PD) model linking etoposide free tumor and total plasma concentrations to the inhibition of solid tumor growth in rats. Walker-256 tumor cells were inoculated subcutaneously in the right flank of Wistar rats, which were randomly divided in control and two treated groups that received etoposide 5 or 10 mg/kg i.v. bolus every day for 8 and 4 days, respectively, and tumor volume was monitored daily for 30 days. The plasma and intratumoral concentrations-time profiles were obtained from a previous study and were modeled by a four-compartment population pharmacokinetic (popPK) model. PK/PD analysis was conducted using MONOLIX v.4.3.3 on average data and by mean of a nonlinear mixed-effect model. PK/PD data were analyzed using a modification of Simeoni Tumor Growth Inhibition (TGI) model by introduction of an E max function to take into account the concentration dependency of k 2variable parameter (variable potency). The Simeoni TGI-E max model was capable to fit schedule-dependent antitumor effects using the tumor growth curves from the control and two different administered schedules. The PK/PD model was capable of describing the tumor growth inhibition using total plasma or free tumor concentrations, resulting in higher k 2max (maximal potency) for free concentrations (25.8 mL·μg − 1 ·day − 1 - intratumoral vs. 12.6 mL·μg − 1 ·day − 1 total plasma). These findings indicate that the plasma concentration may not be a good surrogate for pharmacologically active free tumor concentrations, emphasizing the importance of knowing drug tumor penetration to choose the best antitumor therapy. [ABSTRACT FROM AUTHOR]