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.

Quantitative Systems Pharmacology and Machine Learning: A Match Made in Heaven or Hell?

As pharmaceutical development moves from early-stage in vitro experimentation to later in vivo and subsequent clinical trials, data and knowledge are acquired across multiple time and length scales, from the subcellular to whole patient cohort scale. Realizing the potential of this data for informing decision making in pharmaceutical development requires the individual and combined application of machine learning (ML) and mechanistic multiscale mathematical modeling approaches. Here we outline how these two approaches, both individually and in tandem, can be applied at different stages of the drug discovery and development pipeline to inform decision making compound development. The importance of discerning between knowledge and data are highlighted in informing the initial use of ML or mechanistic quantitative systems pharmacology (QSP) models. We discuss the application of sensitivity and structural identifiability analyses of QSP models in informing future experimental studies to which ML may be applied, as well as how ML approaches can be used to inform mechanistic model development. Relevant literature studies are highlighted and we close by discussing caveats regarding the application of each approach in an age of constant data acquisition. SIGNIFICANCE STATEMENT: We consider when best to apply machine learning (ML) and mechanistic quantitative systems pharmacology (QSP) approaches in the context of the drug discovery and development pipeline. We discuss the importance of prior knowledge and data available for the system of interest and how this informs the individual and combined application of ML and QSP approaches at each stage of the pipeline.

The ingredients for an antimicrobial mathematical modelling broth.

Mathematical modelling has made significant contributions to the optimization of the use of antimicrobial treatments. This article discusses the key processes that such mathematical modelling should attempt to capture. In particular, this article highlights that the response of the host immune system requires quantification, and this is illustrated with a novel model structure.

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.

Free Drug Theory - No Longer Just a Hypothesis?

The Free Drug Hypothesis is a well-established concept within the scientific lexicon pervading many areas of Drug Discovery and Development, and yet it is poorly defined by virtue of many variations appearing in the literature. Clearly, unbound drug is in dynamic equilibrium with respect to absorption, distribution, metabolism, elimination, and indeed, interaction with the desired pharmacological target. Binding interactions be they specific (e.g. high affinity) or nonspecific (e.g. lower affinity/higher capacity) are governed by the same fundamental physicochemical tenets including Hill-Langmuir Isotherms, the Law of Mass Action and Drug Receptor Theory. With this in mind, it is time to recognise a more coherent version and consider it the Free Drug Theory and a hypothesis no longer. Today, we have the experimental and modelling capabilities, pharmacological knowledge, and an improved understanding of unbound drug distribution (e.g. Kpuu) to raise the bar on our understanding and analysis of experimental data. The burden of proof should be to rule out mechanistic possibilities and/or experimental error before jumping to the conclusion that any observations contradict these fundamentals.

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.

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.

Importance of Stability Analysis When Using Nonlinear Semimechanistic Models to Describe Drug-Induced Hematotoxicity.

Stability analysis, often overlooked in pharmacometrics, is essential to explore dynamical systems. The model developed by Friberg et al.1 to describe drug-induced hematotoxicity is widely used to support decisions across drug development, and parameter values are often identified from observed blood counts. We use stability analysis to study the parametric dependence of stable and unstable solutions of several Friberg-type models and highlight the risks associated with system instability in the context of nonlinear mixed effects modeling. We emphasize the consequences of unstable solutions on prediction performance by demonstrating nonbiological system behaviors in a real case study of drug-induced thrombocytopenia. Ultimately, we provide simple criteria for identifying parameters associated with stable solutions of Friberg-type models. For instance, in the original Friberg model, we find that stability depends only on the parameter that governs the feedback from peripheral cells to progenitors and provide the exact range of values that results in stable solutions.

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.

Best Practices to Maximize the Use and Reuse of Quantitative and Systems Pharmacology Models: Recommendations From the United Kingdom Quantitative and Systems Pharmacology Network.

The lack of standardization in the way that quantitative and systems pharmacology (QSP) models are developed, tested, and documented hinders their reproducibility, reusability, and expansion or reduction to alternative contexts. This in turn undermines the potential impact of QSP in academic, industrial, and regulatory frameworks. This article presents a minimum set of recommendations from the UK Quantitative and Systems Pharmacology Network (UK QSP Network) to guide QSP practitioners seeking to maximize their impact, and stakeholders considering the use of QSP models in their environment.

Discovery and Characterization of AZD6738, a Potent Inhibitor of Ataxia Telangiectasia Mutated and Rad3 Related (ATR) Kinase with Application as an Anticancer Agent.

The kinase ataxia telangiectasia mutated and rad3 related (ATR) is a key regulator of the DNA-damage response and the apical kinase which orchestrates the cellular processes that repair stalled replication forks (replication stress) and associated DNA double-strand breaks. Inhibition of repair pathways mediated by ATR in a context where alternative pathways are less active is expected to aid clinical response by increasing replication stress. Here we describe the development of the clinical candidate 2 (AZD6738), a potent and selective sulfoximine morpholinopyrimidine ATR inhibitor with excellent preclinical physicochemical and pharmacokinetic (PK) characteristics. Compound 2 was developed improving aqueous solubility and eliminating CYP3A4 time-dependent inhibition starting from the earlier described inhibitor 1 (AZ20). The clinical candidate 2 has favorable human PK suitable for once or twice daily dosing and achieves biologically effective exposure at moderate doses. Compound 2 is currently being tested in multiple phase I/II trials as an anticancer agent.