Hierarchical cluster analysis and nonlinear mixed-effects modelling for candidate biomarker detection in preclinical models of cancer.

BACKGROUND: Preclinical models of cancer can be of translational benefit when assessing how different biomarkers are regulated in response to particular treatments. Detection of molecular biomarkers in preclinical models of cancer is difficult due inter-animal variability in responses, combined with limited accessibility of longitudinal data. METHODS: Nonlinear mixed-effects modelling (NLME) was used to analyse tumour growth data based on expected tumour growth rates observed 7 days after initial doses (DD7) of Radiotherapy (RT) and Combination of RT with DNA Damage Response Inhibitors (DDRi). Cox regression was performed to confirm an association between DD7 and survival. Hierarchical Cluster Analysis (HCA) was then used to identify candidate biomarkers impacting responses to RT and RT/DDRi and these were validated using NLME. RESULTS: Cox regression confirmed significant associations between DD7 and survival. HCA of RT treated samples, combined with NLME confirmed significant associations between DD7 and Cluster specific CD8+ Ki67 MFI, as well as DD7 and cluster specific Natural Killer cell density in RT treated mice. CONCLUSION: Application of NLME, as well as HCA of candidate biomarkers may provide additional avenues to assess the effect of RT in MC38 syngeneic tumour models. Additional studies would need to be conducted to confirm association between DD7 and biomarkers in RT/DDRi treated mice.

Skipping a pillar does not make for strong foundations: Pharmacokinetic-pharmacodynamic reasoning behind the shape of dose-response relationships in oncology.

Dose-response analysis is often applied to the quantification of drug-effect especially for slowly responding disease end points where a comparison is made across dose levels after a particular period of treatment. It has long been recognized that exposure - response is more appropriate than dose-response. However, trials necessarily are designed as dose-response experiments. Second, a wide range of functional forms are used to express relationships between dose and response. These considerations are also important for clinical development because pharmacokinetic (PK; and variability) plus pharmacokinetic-pharmacodynamic modeling may allow one to anticipate the shape of the dose-response curve and so the trial design. Here, we describe how the location and steepness of the dose response is determined by the PKs of the compound being tested and its exposure-response relationship in terms of potency (location), efficacy (maximum effect) and Hill coefficient (steepness). Thus, the location (50% effective dose [ED50 ]) is dependent not only on the potency (half-maximal effective concentration) but also the compound's PKs. Similarly, the steepness of the dose response is shown to be a function of the half-life of the drug. It is also shown that the shape of relationship varies dependent on the assumed time course of the disease. This is important in the context of drug-discovery where the in vivo potencies of compounds are compared as well as when considering an analysis of summary data (for example, model-based meta-analysis) for clinical decision making.

Mixed effects modeling of radiotherapy in combination with immune checkpoint blockade or inhibitors of the DNA damage response pathway.

Dosage optimization to maximize efficacy and minimize toxicity is a potential issue when administering radiotherapy (RT) in combination with immune checkpoint blockade (ICB) or inhibitors of the DNA Damage Response Pathway (DDRi) in the clinic. Preclinical models and mathematical modeling can help identify ideal dosage schedules to observe beneficial effects of a tri-therapy. The aim of this study is to describe a mathematical model to capture the impact of RT in combination with inhibitors of the DNA Damage Response Pathway or blockade of the immune checkpoint protein - programmed death ligand 1 (PD-L1). This model describes how RT mediated activation of antigen presenting cells can induce an increase in cytolytic T cells capable of targeting tumor cells, and how combination drugs can potentiate the immune response by inhibiting the rate of T cell exhaustion. The model was fitted using preclinical data, where MC38 tumors were treated in vivo with RT alone or in combination with anti-PD-L1 as well as with either olaparib or the ataxia telangiectasia mutated (ATM) inhibitor-AZD0156. The model successfully described the observed data and goodness-of-fit, using visual predictive checks also confirmed a successful internal model validation for each treatment modality. The results demonstrated that the anti-PD-L1 effect in combination with RT was maximal in vivo and any additional benefit of DDRi at the given dosage and schedule used was undetectable. Model fit results indicated AZD0156 to be a more potent DDRi than olaparib. Simulations of alternative doses indicated that reducing efficacy of anti-PD-L1 by 68% would potentially provide evidence for a benefit of ATM inhibition in combination with ICB and increase the relative efficacy of tri-therapy.

Radiation in Combination with Immune Checkpoint Blockade and DNA Damage Response Inhibitors in Mice: Dosage Optimization in MC38 Syngeneic Tumors via Modelling and Simulation.

Clinical trials assessing the impact of radiotherapy (RT) in combination with DNA damage response pathway inhibitors (DDRis) and/or immune checkpoint blockade are currently ongoing. However, current methods for optimizing dosage and schedule are limited. A mathematical model was developed to capture the impacts of RT in combination with DDRi and/or anti-PD-L1 [immune checkpoint inhibitor (ICI)] on tumor immune interactions in the MC38 syngeneic tumor model. The model was fitted to datasets that assessed the impact of RT in combination with the DNA protein kinase inhibitor (DNAPKi) AZD7648. The model was further fitted to datasets from studies that were used to assess both RT/ICI combinations as well as RT/ICI combinations followed by concurrent administration of the poly ADP ribose polymerase inhibitor (PARPi) olaparib. Nonlinear mixed-effects modeling was performed followed by internal validation with visual predictive checks (VPC). Simulations of alternative dosage regimens and scheduling were performed to identify optimal candidate dosage regimens of RT/DNAPKi and RT/PARPi/ICI. Model fits and VPCs confirmed a successful internal validation for both datasets and demonstrated very small differences in the median, lower, and upper percentile values of tumor diameters between RT/ICI and RT/PARPi/ICI, which indicated that the triple combination of RT/PARPi/ICI at the given dosage and schedule does not provide additional benefit compared with ICI in combination with RT. Simulation of alternative dosage regimens indicated that lowering the dosage of ICI to between 2 and 4 mg/kg could induce similar benefits to the full dosage regimen, which could be of translational benefit. SIGNIFICANCE STATEMENT: This work provides a mixed-effects model framework to quantify the effects of combination radiotherapy/DNA damage response pathway inhibitors/immune checkpoint inhibitors in preclinical tumor models and identify optimal dosage regimens, which could be of translational benefit.

Preclinical Characterization of AZD5305, A Next-Generation, Highly Selective PARP1 Inhibitor and Trapper.

PURPOSE: We hypothesized that inhibition and trapping of PARP1 alone would be sufficient to achieve antitumor activity. In particular, we aimed to achieve selectivity over PARP2, which has been shown to play a role in the survival of hematopoietic/stem progenitor cells in animal models. We developed AZD5305 with the aim of achieving improved clinical efficacy and wider therapeutic window. This next-generation PARP inhibitor (PARPi) could provide a paradigm shift in clinical outcomes achieved by first-generation PARPi, particularly in combination. EXPERIMENTAL DESIGN: AZD5305 was tested in vitro for PARylation inhibition, PARP-DNA trapping, and antiproliferative abilities. In vivo efficacy was determined in mouse xenograft and PDX models. The potential for hematologic toxicity was evaluated in rat models, as monotherapy and combination. RESULTS: AZD5305 is a highly potent and selective inhibitor of PARP1 with 500-fold selectivity for PARP1 over PARP2. AZD5305 inhibits growth in cells with deficiencies in DNA repair, with minimal/no effects in other cells. Unlike first-generation PARPi, AZD5305 has minimal effects on hematologic parameters in a rat pre-clinical model at predicted clinically efficacious exposures. Animal models treated with AZD5305 at doses ≥0.1 mg/kg once daily achieved greater depth of tumor regression compared to olaparib 100 mg/kg once daily, and longer duration of response. CONCLUSIONS: AZD5305 potently and selectively inhibits PARP1 resulting in excellent antiproliferative activity and unprecedented selectivity for DNA repair deficient versus proficient cells. These data confirm the hypothesis that targeting only PARP1 can retain the therapeutic benefit of nonselective PARPi, while reducing potential for hematotoxicity. AZD5305 is currently in phase I trials (NCT04644068).

Epstein-Barr Virus Reactivation After Paediatric Haematopoietic Stem Cell Transplantation: Risk Factors and Sensitivity Analysis of Mathematical Model.

Epstein-Barr virus (EBV) establishes a lifelong latent infection in healthy humans, kept under immune control by cytotoxic T cells (CTLs). Following paediatric haematopoetic stem cell transplantation (HSCT), a loss of immune surveillance leads to opportunistic outgrowth of EBV-infected cells, resulting in EBV reactivation, which can ultimately progress to post-transplant lymphoproliferative disorder (PTLD). The aims of this study were to identify risk factors for EBV reactivation in children in the first 100 days post-HSCT and to assess the suitability of a previously reported mathematical model to mechanistically model EBV reactivation kinetics in this cohort. Retrospective electronic data were collected from 56 children who underwent HSCT at Great Ormond Street Hospital (GOSH) between 2005 and 2016. Using EBV viral load (VL) measurements from weekly quantitative PCR (qPCR) monitoring post-HSCT, a multivariable Cox proportional hazards (Cox-PH) model was developed to assess time to first EBV reactivation event in the first 100 days post-HSCT. Sensitivity analysis of a previously reported mathematical model was performed to identify key parameters affecting EBV VL. Cox-PH modelling revealed EBV seropositivity of the HSCT recipient and administration of anti-thymocyte globulin (ATG) pre-HSCT to be significantly associated with an increased risk of EBV reactivation in the first 100 days post-HSCT (adjusted hazard ratio (AHR) = 2.32, P = 0.02; AHR = 2.55, P = 0.04). Five parameters were found to affect EBV VL in sensitivity analysis of the previously reported mathematical model. In conclusion, we have assessed the effect of multiple covariates on EBV reactivation in the first 100 days post-HSCT in children and have identified key parameters in a previously reported mechanistic mathematical model that affect EBV VL. Future work will aim to fit this model to patient EBV VLs, develop the model to account for interindividual variability and model the effect of clinically relevant covariates such as rituximab therapy and ATG on EBV VL.

Comparison of classical tumour growth models for patient derived and cell-line derived xenografts using the nonlinear mixed-effects framework.

In this study we compare seven mathematical models of tumour growth using nonlinear mixed-effects which allows for a simultaneous fitting of multiple data and an estimation of both mean behaviour and variability. This is performed for two large datasets, a patient-derived xenograft (PDX) dataset consisting of 220 PDXs spanning six different tumour types and a cell-line derived xenograft (CDX) dataset consisting of 25 cell lines spanning eight tumour types. Comparison of the models is performed by means of visual predictive checks (VPCs) as well as the Akaike Information Criterion (AIC). Additionally, we fit the models to 500 bootstrap samples drawn from the datasets to expand the comparison of the models under dataset perturbations and understand the growth kinetics that are best fitted by each model. Through qualitative and quantitative metrics the best models are identified the effectiveness and practicality of simpler models is highlighted.

A Spatially Resolved Mechanistic Growth Law for Cancer Drug Development Predicting Tumor Growing Fractions.

Mathematical models used in preclinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumor volume; however, they typically have little connection with the underlying physiologic processes. This lack of a mechanistic underpinning restricts their flexibility and potentially inhibits their translation across studies including from animal to human. Here we present a mathematical model describing tumor growth for the evaluation of single-agent cytotoxic compounds that is based on mechanistic principles. The model can predict spatial distributions of cell subpopulations and account for spatial drug distribution effects within tumors. Importantly, we demonstrate that the model can be reduced to a growth law similar in form to the ones currently implemented in pharmaceutical drug development for preclinical trials so that it can integrated into the current workflow. We validate this approach for both cell-derived xenograft and patient-derived xenograft (PDX) data. This shows that our theoretical model fits as well as the best performing and most widely used models. However, in addition, the model is also able to accurately predict the observed growing fraction of tumours. Our work opens up current preclinical modeling studies to also incorporating spatially resolved and multimodal data without significant added complexity and creates the opportunity to improve translation and tumor response predictions. Significance: This theoretical model has the same mathematical structure as that currently used for drug development. However, its mechanistic basis enables prediction of growing fraction and spatial variations in drug distribution.

Step-by-step comparison of ordinary differential equation and agent-based approaches to pharmacokinetic-pharmacodynamic models.

Mathematical models in oncology aid in the design of drugs and understanding of their mechanisms of action by simulation of drug biodistribution, drug effects, and interaction between tumor and healthy cells. The traditional approach in pharmacometrics is to develop and validate ordinary differential equation models to quantify trends at the population level. In this approach, time-course of biological measurements is modeled continuously, assuming a homogenous population. Another approach, agent-based models, focuses on the behavior and fate of biological entities at the individual level, which subsequently could be summarized to reflect the population level. Heterogeneous cell populations and discrete events are simulated, and spatial distribution can be incorporated. In this tutorial, an agent-based model is presented and compared to an ordinary differential equation model for a tumor efficacy model inhibiting the pERK pathway. We highlight strengths, weaknesses, and opportunities of each approach.

How translational modeling in oncology needs to get the mechanism just right.

Translational model-based approaches have played a role in increasing success in the development of novel anticancer treatments. However, despite this, significant translational uncertainty remains from animal models to patients. Optimization of dose and scheduling (regimen) of drugs to maximize the therapeutic utility (maximize efficacy while avoiding limiting toxicities) is still predominately driven by clinical investigations. Here, we argue that utilizing pragmatic mechanism-based translational modeling of nonclinical data can further inform this optimization. Consequently, a prototype model is demonstrated that addresses the required fundamental mechanisms.

Targeting Cellular DNA Damage Responses in Cancer: An In Vitro-Calibrated Agent-Based Model Simulating Monolayer and Spheroid Treatment Responses to ATR-Inhibiting Drugs.

We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia-telangiectasia-mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately 8 days post-tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article, we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development.

A meta-analysis of tumour response and relapse kinetics based on 34,881 patients: A question of cancer type, treatment and line of treatment.

PURPOSE: Cancer disease burden is commonly assessed radiologically in solid tumours in support of response assessment via the RECIST criteria. These longitudinal data are amenable to mathematical modelling and these models characterise the initial tumour size, initial tumour shrinkage in responding patients and rate of regrowth as patient's disease progresses. Knowing how these parameters vary between patient populations and treatments would inform translational modelling approaches from non-clinical data as well as clinical trial design. EXPERIMENTAL DESIGN: Here a meta-analysis of reported model parameter values is reported. Appropriate literature was identified via a PubMed search and the application of text-based clustering approaches. The resulting parameter estimates are examined graphically and with ANOVA. RESULTS: Parameter values from a total of 80 treatment arms were identified based on 80 trial arms containing a total of 34,881 patients. Parameter estimates are generally consistent. It is found that a significant proportion of the variation in rates of tumour shrinkage and regrowth are explained by differing cancer and treatment: cancer type accounts for 66% of the variation in shrinkage rate and 71% of the variation in reported regrowth rates. Mean average parameter values by cancer and treatment are also reported. CONCLUSIONS: Mathematical modelling of longitudinal data is most often reported on a per clinical trial basis. However, the results reported here suggest that a more integrative approach would benefit the development of new treatments as well as the further optimisation of those currently used.

Preclinical Comparison of the Blood-brain barrier Permeability of Osimertinib with Other EGFR TKIs.

PURPOSE: Osimertinib is a potent and selective EGFR tyrosine kinase inhibitor (EGFR-TKI) of both sensitizing and T790M resistance mutations. To treat metastatic brain disease, blood-brain barrier (BBB) permeability is considered desirable for increasing clinical efficacy. EXPERIMENTAL DESIGN: We examined the level of brain penetration for 16 irreversible and reversible EGFR-TKIs using multiple in vitro and in vivo BBB preclinical models. RESULTS: In vitro osimertinib was the weakest substrate for human BBB efflux transporters (efflux ratio 3.2). In vivo rat free brain to free plasma ratios (Kpuu) show osimertinib has the most BBB penetrance (0.21), compared with the other TKIs (Kpuu ≤ 0.12). PET imaging in Cynomolgus macaques demonstrated osimertinib was the only TKI among those tested to achieve significant brain penetrance (C max %ID 1.5, brain/blood Kp 2.6). Desorption electrospray ionization mass spectroscopy images of brains from mouse PC9 macrometastases models showed osimertinib readily distributes across both healthy brain and tumor tissue. Comparison of osimertinib with the poorly BBB penetrant afatinib in a mouse PC9 model of subclinical brain metastases showed only osimertinib has a significant effect on rate of brain tumor growth. CONCLUSIONS: These preclinical studies indicate that osimertinib can achieve significant exposure in the brain compared with the other EGFR-TKIs tested and supports the ongoing clinical evaluation of osimertinib for the treatment of EGFR-mutant brain metastasis. This work also demonstrates the link between low in vitro transporter efflux ratios and increased brain penetrance in vivo supporting the use of in vitro transporter assays as an early screen in drug discovery.

Clone Wars: Quantitatively Understanding Cancer Drug Resistance.

A key aim of early clinical development for new cancer treatments is to detect the potential for efficacy early and to identify a safe therapeutic dose to take forward to phase II. Because of this need, researchers have sought to build mathematical models linking initial radiologic tumor response, often assessed after 6 to 8 weeks of treatment, with overall survival. However, there has been mixed success of this approach in the literature. We argue that evolutionary selection pressure should be considered to interpret these early efficacy signals and so optimize cancer therapy.

Opportunities for Quantitative Translational Modeling in Oncology.

A 2-day meeting was held by members of the UK Quantitative Systems Pharmacology Network () in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modeling applications in nonclinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations: Evaluate the predictivity and reproducibility of animal cancer models through precompetitive collaboration. Apply mechanism of action (MoA) based mechanistic models derived from nonclinical data to clinical trial data. Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions. Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design.

Identifying and characterising the impact of excitability in a mathematical model of tumour-immune interactions.

We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may induce tumour cell death, and tumour cells may inactivate immune cells. Exploiting a separation of timescales in the model, we use the method of matched asymptotics to derive a new two-dimensional, long-timescale, approximation of the full model, which differs from the quasi-steady-state approximation introduced by Kuznetsov et al. (1994), but is validated against numerical solutions of the full model. Through a phase-plane analysis, we show that our reduced model is excitable, a feature not traditionally associated with tumour-immune dynamics. Through a systematic parameter sensitivity analysis, we demonstrate that excitability generates complex bifurcating dynamics in the model. These are consistent with a variety of clinically observed phenomena, and suggest that excitability may underpin tumour-immune interactions. The model exhibits the three stages of immunoediting - elimination, equilibrium, and escape, via stable steady states with different tumour cell concentrations. Such heterogeneity in tumour cell numbers can stem from variability in initial conditions and/or model parameters that control the properties of the immune system and its response to the tumour. We identify different biophysical parameter targets that could be manipulated with immunotherapy in order to control tumour size, and we find that preferred strategies may differ between patients depending on the strength of their immune systems, as determined by patient-specific values of associated model parameters.

Osimertinib for Patients With Leptomeningeal Metastases Associated With EGFR T790M-Positive Advanced NSCLC: The AURA Leptomeningeal Metastases Analysis.

INTRODUCTION: Osimertinib has shown promising activity in patients with leptomeningeal metastases (LMs) of EGFR-positive NSCLC at 160 mg once daily (qd) (BLOOM; NCT02228369). We report LM activity with osimertinib (80 mg qd) in a retrospective analysis of studies across the AURA program (AURA extension, AURA2, AURA17, and AURA3). METHODS: Patients with EGFR T790M-positive advanced NSCLC and progression after previous EGFR-tyrosine kinase inhibitor therapy received osimertinib (80 mg qd). Patients with central nervous system (CNS) metastases (including LMs) were eligible if the lesions were neurologically asymptomatic and stable. Patients with evidence of LMs at the study entry were retrospectively included for the analysis; brain scans were assessed for radiologic LM response by neuroradiologically blinded, independent central review per the modified Response Assessment in Neuro-Oncology LM criteria. LM objective response rate, duration of response, progression-free survival, and overall survival were assessed. A longitudinal analysis was performed to investigate the relationship between changes from the baseline in non-CNS tumor sizes and LM responses at each visit of patients in AURA LM and BLOOM studies. RESULTS: For the 22 patients included in the analysis, LM objective response rate was 55% (95% confidence interval [CI]: 32-76). Median LM duration of response was not reached (95% CI: 2.8-not calculable [NC]). Median LM progression-free survival and overall survival were 11.1 months (95% CI: 4.6-NC) and 18.8 months (95% CI: 6.3-NC), respectively. The longitudinal analysis revealed similar non-CNS and LM responses between the patients in AURA LM and BLOOM programs. CONCLUSIONS: Patients with EGFR T790M-positive NSCLC and radiologically detected LM obtained clinical benefit from osimertinib (80 mg qd).

Quantifying Drug-Induced Bone Marrow Toxicity Using a Novel Haematopoiesis Systems Pharmacology Model.

Haematological toxicity associated with cancer therapeutics is monitored by changes in blood cell count, and their primary effect is on proliferative progenitors in the bone marrow. Using observations in rat bone marrow and blood, we characterize a mathematical model that comprises cell proliferation and differentiation of the full haematopoietic phylogeny, with interacting feedback loops between lineages in homeostasis as well as following carboplatin exposure. We accurately predicted the temporal dynamics of several mature cell types related to carboplatin-induced bone marrow toxicity and identified novel insights into haematopoiesis. Our model confirms a significant degree of plasticity within bone marrow cells, with the number and type of both early progenitors and circulating cells affecting cell balance, via feedback mechanisms, through fate decisions of the multipotent progenitors. We also demonstrated cross-species translation of our predictions to patients, applying the same core model structure and considering differences in drug-dependent and physiology-dependent parameters.

Optimization of Cancer Treatment in the Frequency Domain.

Thorough exploration of alternative dosing frequencies is often not performed in conventional pharmacometrics approaches. Quantitative systems pharmacology (QSP) can provide novel insights into optimal dosing regimen and drug behaviors which could add a new dimension to the design of novel treatments. However, methods for such an approach are currently lacking. Recently, we illustrated the utility of frequency-domain response analysis (FdRA), an analytical method used in control engineering, using several generic pharmacokinetic-pharmacodynamic case studies. While FdRA is not applicable to models harboring ever increasing variables such as those describing tumor growth, studying such models in the frequency domain provides valuable insight into optimal dosing frequencies. Through the analysis of three distinct tumor growth models (cell cycle-specific, metronomic, and acquired resistance), we demonstrate the application of a simulation-based analysis in the frequency domain to optimize cancer treatments. We study the response of tumor growth to dosing frequencies while simultaneously examining treatment safety, and found for all three models that above a certain dosing frequency, tumor size is insensitive to an increase in dosing frequency, e.g., for the cell cycle-specific model, one dose per 3 days, and an hourly dose yield the same reduction of tumor size to 3% of the initial size after 1 year of treatment. Additionally, we explore the effect of drug elimination rate changes on the tumor growth response. In summary, we show that the frequency-domain view of three models of tumor growth dynamics can help in optimizing drug dosing regimen to improve treatment success.