Analyzing the distribution of progression-free survival for combination therapies: A study of model-based translational predictive methods in oncology.

Progression-free survival (PFS) is an important clinical metric in oncology and is typically illustrated and evaluated using a survival function. The survival function is often estimated post-hoc using the Kaplan-Meier estimator but more sophisticated techniques, such as population modeling using the nonlinear mixed-effects framework, also exist and are used for predictions. However, depending on the choice of population model PFS will follow different distributions both quantitatively and qualitatively. Hence the choice of model will also affect the predictions of the survival curves. In this paper, we analyze the distribution of PFS for a frequently used tumor growth inhibition model with and without drug-resistance and highlight the translational implications of this. Moreover, we explore and compare how the PFS distribution for combination therapy differs under the hypotheses of additive and independent-drug action. Furthermore, we calibrate the model to preclinical data and use a previously calibrated clinical model to show that our analytical conclusions are applicable to real-world setting. Finally, we demonstrate that independent-drug action can effectively describe the tumor dynamics of patient-derived xenografts (PDXs) given certain drug combinations.

Plasma Pharmacokinetics of N-Acetylgalactosamine-Conjugated Small-Interfering Ribonucleic Acids (GalNAc-Conjugated siRNAs).

Small-interfering ribonucleic acids (siRNAs) with N-acetylgalactosamine (GalNAc) conjugation for improved liver uptake represent an emerging class of drugs that modulate liver-expressed therapeutic targets. The pharmacokinetics of GalNAc-siRNAs are characterized by a rapid distribution from plasma to tissue (hours) and a long terminal plasma half-life, analyzed in the form of the antisense strand, driven by redistribution from tissue (weeks). Understanding how clinical pharmacokinetics relate to the dose and type of siRNA chemical stabilizing method used is critical, e.g., to design studies, to investigate safety windows, and to predict the pharmacokinetics of new preclinical assets. To this end, we collected and analyzed pharmacokinetic data from the literature regarding nine GalNAc-siRNAs. Based on this analysis, we showed that the clinical plasma pharmacokinetics of GalNAc-siRNAs are approximately dose proportional and similar between chemical stabilizing methods. This holds for both the area under the concentration-time curve (AUC) and the maximum plasma concentration (Cmax). Corresponding rat and monkey pharmacokinetic data for a subset of the nine GalNAc-siRNAs show dose-proportional Cmax, supra-dose-proportional AUC, and similar pharmacokinetics between chemical stabilizing methods​. Together, the animal and human pharmacokinetic data indicate that plasma clearance divided by bioavailability follows allometric principles and scales between species with an exponent of 0.75. Finally, the clinical plasma concentration-time profiles can be empirically described by standard one-compartment kinetics with first-order absorption up to 24 h after subcutaneous dosing, and by three-compartment kinetics with first-order absorption in general. To describe the system more mechanistically, we report a corrected and unambiguously defined version of a previously published physiologically based pharmacokinetic model.

Model-based prediction of progression-free survival for combination therapies in oncology.

Progression-free survival (PFS) is an important clinical metric for comparing and evaluating similar treatments for the same disease within oncology. After the completion of a clinical trial, a descriptive analysis of the patients' PFS is often performed post hoc using the Kaplan-Meier estimator. However, to perform predictions, more sophisticated quantitative methods are needed. Tumor growth inhibition models are commonly used to describe and predict the dynamics of preclinical and clinical tumor size data. Moreover, frameworks also exist for describing the probability of different types of events, such as tumor metastasis or patient dropout. Combining these two types of models into a so-called joint model enables model-based prediction of PFS. In this paper, we have constructed a joint model from clinical data comparing the efficacy of FOLFOX against FOLFOX + panitumumab in patients with metastatic colorectal cancer. The nonlinear mixed effects framework was used to quantify interindividual variability (IIV). The model describes tumor size and PFS data well, and showed good predictive capabilities using truncated as well as external data. A machine-learning guided analysis was performed to reduce unexplained IIV by incorporating patient covariates. The model-based approach illustrated in this paper could be useful to help design clinical trials or to determine new promising drug candidates for combination therapy trials.

Model-based assessment of combination therapies - ranking of radiosensitizing agents in oncology.

BACKGROUND: To increase the chances of finding efficacious anticancer drugs, improve development times and reduce costs, it is of interest to rank test compounds based on their potential for human use as early as possible in the drug development process. In this paper, we present a method for ranking radiosensitizers using preclinical data. METHODS: We used data from three xenograft mice studies to calibrate a model that accounts for radiation treatment combined with radiosensitizers. A nonlinear mixed effects approach was utilized where between-subject variability and inter-study variability were considered. Using the calibrated model, we ranked three different Ataxia telangiectasia-mutated inhibitors in terms of anticancer activity. The ranking was based on the Tumor Static Exposure (TSE) concept and primarily illustrated through TSE-curves. RESULTS: The model described data well and the predicted number of eradicated tumors was in good agreement with experimental data. The efficacy of the radiosensitizers was evaluated for the median individual and the 95% population percentile. Simulations predicted that a total dose of 220 Gy (5 radiation sessions a week for 6 weeks) was required for 95% of tumors to be eradicated when radiation was given alone. When radiation was combined with doses that achieved at least 8 [Formula: see text] of each radiosensitizer in mouse blood, it was predicted that the radiation dose could be decreased to 50, 65, and 100 Gy, respectively, while maintaining 95% eradication. CONCLUSIONS: A simulation-based method for calculating TSE-curves was developed, which provides more accurate predictions of tumor eradication than earlier, analytically derived, TSE-curves. The tool we present can potentially be used for radiosensitizer selection before proceeding to subsequent phases of the drug discovery and development process.

Optimized scaling of translational factors in oncology: from xenografts to RECIST.

PURPOSE: Tumor growth inhibition (TGI) models are regularly used to quantify the PK-PD relationship between drug concentration and in vivo efficacy in oncology. These models are typically calibrated with data from xenograft mice and before being used for clinical predictions, translational methods have to be applied. Currently, such methods are commonly based on replacing model components or scaling of model parameters. However, difficulties remain in how to accurately account for inter-species differences. Therefore, more research must be done before xenograft data can fully be utilized to predict clinical response. METHOD: To contribute to this research, we have calibrated TGI models to xenograft data for three drug combinations using the nonlinear mixed effects framework. The models were translated by replacing mice exposure with human exposure and used to make predictions of clinical response. Furthermore, in search of a better way of translating these models, we estimated an optimal way of scaling model parameters given the available clinical data. RESULTS: The predictions were compared with clinical data and we found that clinical efficacy was overestimated. The estimated optimal scaling factors were similar to a standard allometric scaling exponent of - 0.25. CONCLUSIONS: We believe that given more data, our methodology could contribute to increasing the translational capabilities of TGI models. More specifically, an appropriate translational method could be developed for drugs with the same mechanism of action, which would allow for all preclinical data to be leveraged for new drugs of the same class. This would ensure that fewer clinically inefficacious drugs are tested in clinical trials.

Exposure-response modeling improves selection of radiation and radiosensitizer combinations.

A central question in drug discovery is how to select drug candidates from a large number of available compounds. This analysis presents a model-based approach for comparing and ranking combinations of radiation and radiosensitizers. The approach is quantitative and based on the previously-derived Tumor Static Exposure (TSE) concept. Combinations of radiation and radiosensitizers are evaluated based on their ability to induce tumor regression relative to toxicity and other potential costs. The approach is presented in the form of a case study where the objective is to find the most promising candidate out of three radiosensitizing agents. Data from a xenograft study is described using a nonlinear mixed-effects modeling approach and a previously-published tumor model for radiation and radiosensitizing agents. First, the most promising candidate is chosen under the assumption that all compounds are equally toxic. The impact of toxicity in compound selection is then illustrated by assuming that one compound is more toxic than the others, leading to a different choice of candidate.

Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures.

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.

Modeling long-term tumor growth and kill after combinations of radiation and radiosensitizing agents.

PURPOSE: Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology. We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. The model also describes long-term treatment effects including tumor regrowth and eradication. METHODS: We challenge the model with data from a xenograft study using a clinically relevant administration schedule and use a mixed-effects approach for model-fitting. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE). RESULTS: The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. Using TSE, we predict the total radiation dose necessary for tumor eradication to be 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg kg-1 of a radiosensitizer. TSE is also explored via a heat map of different growth and shrinkage rates. Finally, we discuss the translational potential of the model and TSE concept to humans. CONCLUSIONS: The new model is capable of describing different tumor dynamics including tumor eradication and tumor regrowth with different rates, and can be calibrated using data from standard xenograft experiments. TSE and related concepts can be used to predict tumor shrinkage and eradication, and have the potential to guide new experiments and support translations from animals to humans.

Evaluation and translation of combination therapies in oncology - A quantitative approach.

Quantitative techniques improve our understanding of tumor volume data for combination treatments and its translation across in vivo models and species. The focus of this paper is therefore on understanding in vivo data, highlighting key structural elements of pharmacodynamic tumor models, and challenging these methods from a translational point of view. We introduce the concept of Tumor Static Exposure (TSE) both for single and multiple combined anticancer agents. The TSE curve separates all possible exposure combinations into regions of tumor growth and tumor shrinkage. Moreover, the degree of curvature of the TSE curve indicates the degree of synergy or antagonism. We demonstrate the TSE approach by two case studies. The first examines a combination of the drugs cetuximab and cisplatin. The TSE curve associated with this combination reveals a weak synergistic effect, suggesting only modest gains from combination therapy. The second case study examines combinations of ionizing radiation and a radiosensitizing agent. In this case, the TSE curve exhibits a pronounced curvature, indicating a strong synergistic effect; tumor regression can be achieved at significantly lower exposure levels and/or radiation doses. Finally, an allometric approach to human dose prediction demonstrates the translational power of the model and the TSE concept. We conclude that the TSE approach, which embodies model-based measures of both drug (potency) and target properties (tumor growth rate), has a strong potential for ranking of compounds, supporting compound selection, and translating preclinical findings to humans.

Model-Based Evaluation of Radiation and Radiosensitizing Agents in Oncology.

Radiotherapy is one of the major therapy forms in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Moreover, we extend previous analyses of drug combinations by introducing the tumor static exposure (TSE) curve. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. The model and TSE analysis are then tested on xenograft data. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth 10-fold. The TSE curve shows that with an average radiosensitizer concentration of 1.0 µg/mL the radiation dose can be decreased from 2.2 Gy to 0.7 Gy. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept.

Tumor Static Concentration Curves in Combination Therapy.

Combination therapies are widely accepted as a cornerstone for treatment of different cancer types. A tumor growth inhibition (TGI) model is developed for combinations of cetuximab and cisplatin obtained from xenograft mice. Unlike traditional TGI models, both natural cell growth and cell death are considered explicitly. The growth rate was estimated to 0.006 h-1 and the natural cell death to 0.0039 h-1 resulting in a tumor doubling time of 14 days. The tumor static concentrations (TSC) are predicted for each individual compound. When the compounds are given as single-agents, the required concentrations were computed to be 506 µg · mL-1 and 56 ng · mL-1 for cetuximab and cisplatin, respectively. A TSC curve is constructed for different combinations of the two drugs, which separates concentration combinations into regions of tumor shrinkage and tumor growth. The more concave the TSC curve is, the lower is the total exposure to test compounds necessary to achieve tumor regression. The TSC curve for cetuximab and cisplatin showed weak concavity. TSC values and TSC curves were estimated that predict tumor regression for 95% of the population by taking between-subject variability into account. The TSC concept is further discussed for different concentration-effect relationships and for combinations of three or more compounds.