From waterfall plots to spaghetti plots in early oncology clinical development.

Waterfall plots are used to describe changes in tumor size observed in clinical studies. They are frequently used to illustrate the overall drug response in oncology clinical trials because of its simple representation of results. Unfortunately, this visual display suffers a number of limitations including (1) potential misguidance by masking the time dynamics of tumor size, (2) ambiguous labelling of the y-axis, and (3) low data-to-ink ratio. We offer some alternatives to address these shortcomings and recommend moving away from waterfall plots to the benefit of plots showing the individual time profiles of sum of lesion diameters (according to RECIST). The spider plot presents the individual changes in tumor measurements over time relative to baseline tumor burden. Baseline tumor size is a well-known confounding factor of drug effect which has to be accounted for when analyzing data in early clinical trials. While spider plots are conveniently correct for baseline tumor size, they cannot be presented in isolation. Indeed, percentage change from baseline has suboptimal statistical properties (including skewed distribution) and can be overly optimistic in favor of drug efficacy. We argued that plots of raw data (referred to as spaghetti plots) should always accompany spider plots to provide an equipoised illustration of the drug effect on lesion diameters.

Enhanced Method for Diagnosing Pharmacometric Models: Random Sampling from Conditional Distributions.

PURPOSE: For nonlinear mixed-effects pharmacometric models, diagnostic approaches often rely on individual parameters, also called empirical Bayes estimates (EBEs), estimated through maximizing conditional distributions. When individual data are sparse, the distribution of EBEs can "shrink" towards the same population value, and as a direct consequence, resulting diagnostics can be misleading. METHODS: Instead of maximizing each individual conditional distribution of individual parameters, we propose to randomly sample them in order to obtain values better spread out over the marginal distribution of individual parameters. RESULTS: We evaluated, through diagnostic plots and statistical tests, hypothesis related to the distribution of the individual parameters and show that the proposed method leads to more reliable results than using the EBEs. In particular, diagnostic plots are more meaningful, the rate of type I error is correctly controlled and its power increases when the degree of misspecification increases. An application to the warfarin pharmacokinetic data confirms the interest of the approach for practical applications. CONCLUSIONS: The proposed method should be implemented to complement EBEs-based approach for increasing the performance of model diagnosis.

Modeling of Parkinson's Disease Progression and Implications for Detection of Disease Modification in Treatment Trials.

Background: Objectively measuring Parkinson's disease (PD) signs and symptoms over time is critical for the successful development of treatments aimed at halting the disease progression of people with PD. Objective: To create a clinical trial simulation tool that characterizes the natural history of PD progression and enables a data-driven design of randomized controlled studies testing potential disease-modifying treatments (DMT) in early-stage PD. Methods: Data from the Parkinson's Progression Markers Initiative (PPMI) were analyzed with nonlinear mixed-effect modeling techniques to characterize the progression of MDS-UPDRS part I (non-motor aspects of experiences of daily living), part II (motor aspects of experiences of daily living), and part III (motor signs). A clinical trial simulation tool was built from these disease models and used to predict probability of success as a function of trial design. Results: MDS-UPDRS part III progresses approximately 3 times faster than MDS-UPDRS part II and I, with an increase of 3 versus 1 points/year. Higher amounts of symptomatic therapy is associated with slower progression of MDS-UPDRS part II and III. The modeling framework predicts that a DMT effect on MDS-UPDRS part III could precede effect on part II by approximately 2 to 3 years. Conclusions: Our clinical trial simulation tool predicted that in a two-year randomized controlled trial, MDS-UPDRS part III could be used to evaluate a potential novel DMT, while part II would require longer trials of a minimum duration of 3 to 5 years underscoring the need for innovative trial design approaches including novel patient-centric measures.

To develop effective medicines that can slow down or stop the progression of Parkinson's disease (PD), it is important to accurately understand how the disease worsens over time. We used data from an observational study, led by the Michael J. Fox Foundation, called the Parkinson's Progression Markers Initiative (PPMI) to understand the natural progression of  PD. We simulated clinical trials on a computer using different scales to measure the progression of PD. We specifically looked at a physician-reported measure MDS-UPDRS part III, and at a patient-reported measure MDS-UPDRS part II of how PD symptoms worsen over time. To measure the effect of a new medicine slowing down the progression of PD using patient-reported measure MDS-UPDRS part II, we estimate that we may need to conduct a clinical trial of at least 3 to 5 years. On the other hand, to measure an effect using physician-reported measure MDS-UPDRS part III, the duration of the trial could be shorter than 2 years. We were also able to show that worsening recorded by the physician-reported measure MDS-UPDRS part III could be predictive of a later worsening recorded by the patient-reported measure MDS-UPDRS part II. We concluded that MDS-UPDRS part III may be a good endpoint for a clinical trial of a reasonable duration and that MDS-UPDRS part II could be measured in longer studies, for example, open-label extensions.

Modeling tumor response after combined administration of different immune-stimulatory agents.

The aims of this work were as follows: 1) to develop a semimechanistic pharmacodynamic model describing tumor shrinkage after administration of a previously developed antitumor vaccine (CyaA-E7) in combination with CpG (a TLR9 ligand) and/or cyclophosphamide (CTX), and 2) to assess the translational capability of the model to describe tumor effects of different immune-based treatments. Population approach with NONMEM version 7.2 was used to analyze the previously published data. These data were generated by injecting 5 × 10(5) tumor cells expressing human papillomavirus (HPV)-E7 proteins into C57BL/6 mice. Large and established tumors were treated with CpG and/or CTX administered alone or in combination with CyaA-E7. Applications of the model were assessed by comparing model-based simulations with preclinical and clinical outcomes obtained from literature. CpG effects were modeled: 1) as an amplification of the immune signal triggered by the vaccine and 2) by shortening the delayed response of the vaccine. CTX effects were included through a direct decrease of the tumor-induced inhibition of vaccine efficacy over time, along with a delayed induction of tumor cell death. A pharmacodynamic model, built based on plausible biologic mechanisms known for the coadjuvants, successfully characterized tumor response in all experimental scenarios. The model developed was satisfactory applied to reproduce clinical outcomes when CpG or CTX was used in combination with different vaccines. The results found after simulation exercise indicated that the contribution of the coadjuvants to the tumor response elicited by vaccines can be predicted for other immune-based treatments.

Digital Therapeutics as a New Therapeutic Modality: A Review from the Perspective of Clinical Pharmacology.

The promise of transforming digital technologies into treatments is what drives the development of digital therapeutics (DTx), generally known as software applications embedded within accessible technologies-such as smartphones-to treat, manage, or prevent a pathological condition. Whereas DTx solutions that successfully demonstrate effectiveness and safety could drastically improve the life of patients in multiple therapeutic areas, there is a general consensus that generating therapeutic evidence for DTx presents challenges and open questions. We believe there are three main areas where the application of clinical pharmacology principles from the drug development field could benefit DTx development: the characterization of the mechanism of action, the optimization of the intervention, and, finally, its dosing. We reviewed DTx studies to explore how the field is approaching these topics and to better characterize the challenges associated with them. This leads us to emphasize the role that the application of clinical pharmacology principles could play in the development of DTx and to advocate for a development approach that merges such principles from development of traditional therapeutics with important considerations from the highly attractive and fast-paced world of digital solutions.

Reinforcement learning as an innovative model-based approach: Examples from precision dosing, digital health and computational psychiatry.

Model-based approaches are instrumental for successful drug development and use. Anchored within pharmacological principles, through mathematical modeling they contribute to the quantification of drug response variability and enables precision dosing. Reinforcement learning (RL)-a set of computational methods addressing optimization problems as a continuous learning process-shows relevance for precision dosing with high flexibility for dosing rule adaptation and for coping with high dimensional efficacy and/or safety markers, constituting a relevant approach to take advantage of data from digital health technologies. RL can also support contributions to the successful development of digital health applications, recognized as key players of the future healthcare systems, in particular for reducing the burden of non-communicable diseases to society. RL is also pivotal in computational psychiatry-a way to characterize mental dysfunctions in terms of aberrant brain computations-and represents an innovative modeling approach forpsychiatric indications such as depression or substance abuse disorders for which digital therapeutics are foreseen as promising modalities.

Model enhanced reinforcement learning to enable precision dosing: A theoretical case study with dosing of propofol.

Extending the potential of precision dosing requires evaluating methodologies offering more flexibility and higher degree of personalization. Reinforcement learning (RL) holds promise in its ability to integrate multidimensional data in an adaptive process built toward efficient decision making centered on sustainable value creation. For general anesthesia in intensive care units, RL is applied and automatically adjusts dosing through monitoring of patient's consciousness. We further explore the problem of optimal control of anesthesia with propofol by combining RL with state-of-the-art tools used to inform dosing in drug development. In particular, we used pharmacokinetic-pharmacodynamic (PK-PD) modeling as a simulation engine to generate experience from dosing scenarios, which cannot be tested experimentally. Through simulations, we show that, when learning from retrospective trial data, more than 100 patients are needed to reach an accuracy within the range of what is achieved with a standard dosing solution. However, embedding a model of drug effect within the RL algorithm improves accuracy by reducing errors to target by 90% through learning to take dosing actions maximizing long-term benefit. Data residual variability impacts accuracy while the algorithm efficiently coped with up to 50% interindividual variability in the PK and 25% in the PD model's parameters. We illustrate how extending the state definition of the RL agent with meaningful variables is key to achieve high accuracy of optimal dosing policy. These results suggest that RL constitutes an attractive approach for precision dosing when rich data are available or when complemented with synthetic data from model-based tools used in model-informed drug development.

Circulating tumor DNA: Opportunities and challenges for pharmacometric approaches.

To support further development of model-informed drug development approaches leveraging circulating tumor DNA (ctDNA), we performed an exploratory analysis of the relationships between treatment-induced changes to ctDNA levels, clinical response and tumor size dynamics in patients with cancer treated with checkpoint inhibitors and targeted therapies. This analysis highlights opportunities for pharmacometrics approaches such as for optimizing sampling design strategies. It also highlights challenges related to the nature of the data and associated variability overall emphasizing the importance of mechanistic modeling studies of the underlying biology of ctDNA processes such as shedding, release and clearance and their relationships with tumor size dynamic and treatment effects.

Model-Informed Artificial Intelligence: Reinforcement Learning for Precision Dosing.

The availability of multidimensional data together with the development of modern techniques for data analysis represent an exceptional opportunity for clinical pharmacology. Data science-defined in this special issue as the novel approaches to the collection, aggregation, and analysis of data-can significantly contribute to characterize drug-response variability at the individual level, thus enabling clinical pharmacology to become a critical contributor to personalized healthcare through precision dosing. We propose a minireview of methodologies for achieving precision dosing with a focus on an artificial intelligence technique called reinforcement learning, which is currently used for individualizing dosing regimen in patients with life-threatening diseases. We highlight the interplay of such techniques with conventional pharmacokinetic/pharmacodynamic approaches and discuss applicability in drug research and early development.

Modelling methodology in physiopathology.

Diseases are complex systems. Modelling them, i.e. systems physiopathology, is a quite demanding, complicated, multidimensional, multiscale process. As such, in order to achieve the goal of the model and further to optimise a rather-time and resource-consuming process, a relevant and easy to practice methodology is required. It includes guidance for validation. Also, the model development should be managed as a complicated process, along a strategy which has been elaborated in the beginning. It should be flexible enough to meet every case. A model is a representation of the available knowledge. All available knowledge does not have the same level of evidence and, further, there is a large variability of the values of all parameters (e.g. affinity constant or ionic current) across the literature. In addition, in a complex biological system there are always values lacking for a few or sometimes many parameters. All these three aspects are sources of uncertainty on the range of validity of the models and raise unsolved problems for designing a relevant model. Tools and techniques for integrating the parameter range of experimental values, level of evidence and missing data are needed.

A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy.

Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical event in cancer development, considerable efforts have been made to identify inhibitors of this process. Cytostatic treatments that target the molecular events of the angiogenesis process have been developed, and have met with some success. However, it is usually difficult to preclinically assess the effectiveness of targeted therapies, and apparently promising compounds sometimes fail in clinical trials. We have developed a multiscale mathematical model of angiogenesis and tumor growth. At the molecular level, the model focuses on molecular competition between pro- and anti-angiogenic substances modeled on the basis of pharmacological laws. At the tissue scale, the model uses partial differential equations to describe the spatio-temporal changes in cancer cells during three stages of the cell cycle, as well as those of the endothelial cells that constitute the blood vessel walls. This model is used to qualitatively assess how efficient endostatin gene therapy is. Endostatin is an anti-angiogenic endogenous substance. The gene therapy entails overexpressing endostatin in the tumor and in the surrounding tissue. Simulations show that there is a critical treatment dose below which increasing the duration of treatment leads to a loss of efficacy. This theoretical model may be useful to evaluate the efficacy of therapies targeting angiogenesis, and could therefore contribute to designing prospective clinical trials.

Models and Machines: How Deep Learning Will Take Clinical Pharmacology to the Next Level.

Recent advances in machine learning (ML) have led to enthusiasm about its use throughout the biopharmaceutical industry. The ML methods can be applied to a wide range of problems and have the potential to revolutionize aspects of drug development. The incorporation of ML in modeling and simulation (M&S) has been eagerly anticipated, and in this perspective, we highlight examples in which ML and M&S approaches can be integrated as complementary parts of a clinical pharmacology workflow.

Etoposide pharmacokinetics and survival in patients with small cell lung cancer: a multicentre study.

PURPOSE: To investigate the prognostic value of systemic exposure to etoposide (Area Under the concentration Curve (AUC(VP16))) on overall survival (OS) in patients with small cell lung cancer (SCLC). PATIENTS AND METHODS: Data from 52 patients with limited stage (n=17) or metastatic (n=35) SCLC were analysed. They received at least two courses of etoposide (120mg/(m(2)day) on 3 days) combined with either doxorubicin-ifosfamide (AVI, n=29) or platinum compounds (carboplatin: n=16; cisplatin: n=7). Population pharmacokinetic-pharmacodynamic (PK-PD) study was performed using NON-linear Mixed Effect Model (NONMEM) and Splus software with univariate and multivariate analyses. RESULTS: Etoposide plasma concentration vs. time was described by a two compartment model. Etoposide clearance (CL) was significantly dependant on serum creatinine (Scr). Ifosfamide (IFO) coadministration increased etoposide clearance by 28% (median CL(VP16): 2.42L/h vs. 1.89L/h, p<0.0005) leading to a reduced systemic exposure (median AUC(VP16): 260mgh/L vs. 339mgh/L). No influence of body surface area (BSA) on CL(VP16) was observed. Median percent decrease of absolute neutrophil count (ANC) after the first chemotherapy course was greater when etoposide 24h concentration was above 0.33mg/L (88% vs. 0%, p=0.028). Median OS was significantly longer in patients treated without ifosfamide (11.0 months vs. 7.0 months, p=0.049) and in patients with CL(VP16)<2.22L/h (14 months vs. 7 months, p=0.013) and AUC(VP16)>254.8mgh/L (11 months vs. 7 months, p=0.048). The independent prognostic factors regarding OS were LDH, CL(VP16) and AUC(VP16). CONCLUSION: In this study it was found that CL(VP16) is reduced in patients with elevated serum creatinine, whilst ifosfamide coadministration increases CL(VP16) and reduces AUC(VP16), demonstrating the interaction between VP16 and ifosfamide. CL(VP16) and AUC(VP16) correlate significantly with overall survival of patients with SCLC patients receiving etoposide regimens.

Prediction of the Optimal Dosing Regimen Using a Mathematical Model of Tumor Uptake for Immunocytokine-Based Cancer Immunotherapy.

Purpose: Optimal dosing is critical for immunocytokine-based cancer immunotherapy to maximize efficacy and minimize toxicity. Cergutuzumab amunaleukin (CEA-IL2v) is a novel CEA-targeted immunocytokine. We set out to develop a mathematical model to predict intratumoral CEA-IL2v concentrations following various systemic dosing intensities.Experimental Design: Sequential measurements of CEA-IL2v plasma concentrations in 74 patients with solid tumors were applied in a series of differential equations to devise a model that also incorporates the peripheral concentrations of IL2 receptor-positive cell populations (i.e., CD8+, CD4+, NK, and B cells), which affect tumor bioavailability of CEA-IL2v. Imaging data from a subset of 14 patients were subsequently utilized to additionally predict antibody uptake in tumor tissues.Results: We created a pharmacokinetic/pharmacodynamic mathematical model that incorporates the expansion of IL2R-positive target cells at multiple dose levels and different schedules of CEA-IL2v. Model-based prediction of drug levels correlated with the concentration of IL2R-positive cells in the peripheral blood of patients. The pharmacokinetic model was further refined and extended by adding a model of antibody uptake, which is based on drug dose and the biological properties of the tumor. In silico predictions of our model correlated with imaging data and demonstrated that a dose-dense schedule comprising escalating doses and shortened intervals of drug administration can improve intratumoral drug uptake and overcome consumption of CEA-IL2v by the expanding population of IL2R-positive cells.Conclusions: The model presented here allows simulation of individualized treatment plans for optimal dosing and scheduling of immunocytokines for anticancer immunotherapy. Clin Cancer Res; 24(14); 3325-33. ©2018 AACRSee related commentary by Ruiz-Cerdá et al., p. 3236.

A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies.

BACKGROUND: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. METHODS: In this paper, we propose a multiscale model of cancer growth based on the genetic and molecular features of the evolution of colorectal cancer. The model includes key genes, cellular kinetics, tissue dynamics, macroscopic tumor evolution and radiosensitivity dependence on the cell cycle phase. We investigate the role of gene-dependent cell cycle regulation in the response of tumors to therapeutic irradiation protocols. RESULTS: Simulation results emphasize the importance of tumor tissue features and the need to consider regulating factors such as hypoxia, as well as tumor geometry and tissue dynamics, in predicting and improving radiotherapeutic efficacy. CONCLUSION: This model provides insight into the coupling of complex biological processes, which leads to a better understanding of oncogenesis. This will hopefully lead to improved irradiation therapy.

Mechanism-based modeling of the clinical effects of bevacizumab and everolimus on vestibular schwannomas of patients with neurofibromatosis type 2.

PURPOSE: To describe the natural growth of vestibular schwannoma in patients with neurofibromatosis type 2 and to predict tumor volume evolution in patients treated with bevacizumab and everolimus. METHODS: Clinical data, including longitudinal tumor volumes in patients treated by bevacizumab (n = 13), everolimus (n = 7) or both (n = 2), were analyzed by means of mathematical modeling techniques. Together with clinical data, data from the literature were also integrated to account for drugs mechanisms of action. RESULTS: We developed a model of vestibular schwannoma growth that takes into account the effect of vascular endothelial growth factors and mammalian target of rapamycin complex 1 on tumor growth. Behaviors, such as tumor growth rebound following everolimus treatment stops, was correctly described with the model. Preliminary results indicate that the model can be used to predict, based on early tumor volume dynamic, tumor response to variation in treatment dose and regimen. CONCLUSION: The developed model successfully describes tumor volume growth before and during bevacizumab and/or everolimus treatment. It might constitute a rational tool to predict patients' response to these drugs, thus potentially improving management of this disease.

Early change in tumour size predicts overall survival in patients with first-line metastatic breast cancer.

PURPOSE: Clinical trials using change in tumour size (CTS) as a primary end-point benefit from earlier evaluation of treatment effect and increased study power over progression-free survival, ultimately resulting in more timely regulatory approvals for cancer patients. In this work, a modelling framework was established to further characterise the relationship between CTS and overall survival (OS) in first-line metastatic breast cancer (mBC). METHODS: Data from three randomised phase III trials designed to evaluate the clinical benefit of gemcitabine combination therapy in mBC patients were collated. Two drug-dependent models were developed to describe tumour growth dynamics: the first for paclitaxel/gemcitabine treatment and the second for docetaxel/gemcitabine treatment. A parametric survival model was used to characterise survival as a function of CTS and baseline patient demographics. RESULTS: While the paclitaxel/gemcitabine model incorporated tumour shrinkage by both paclitaxel and gemcitabine with resistance to paclitaxel, the docetaxel/gemcitabine model incorporated shrinkage and resistance to docetaxel alone. Predictors for OS were CTS at week 8, baseline tumour size and ECOG performance status. Model predictions reveal that for an asymptomatic mBC patient with a 6-cm tumour burden, first-line paclitaxel/gemcitabine treatment offers a median OS of 28.6 months, compared to 26.0 months for paclitaxel alone. CONCLUSION: A modelling framework was established, quantitatively describing the tumour growth inhibitory effects of various gemcitabine combotherapies and the effect of the resulting CTS on survival in first-line mBC. This work further supports the use of early CTS as a go/no-go decision point during phase II clinical evaluation of treatments for mBC.

Multi-scale Modeling in Clinical Oncology: Opportunities and Barriers to Success.

Hierarchical processes spanning several orders of magnitude of both space and time underlie nearly all cancers. Multi-scale statistical, mathematical, and computational modeling methods are central to designing, implementing and assessing treatment strategies that account for these hierarchies. The basic science underlying these modeling efforts is maturing into a new discipline that is close to influencing and facilitating clinical successes. The purpose of this review is to capture the state-of-the-art as well as the key barriers to success for multi-scale modeling in clinical oncology. We begin with a summary of the long-envisioned promise of multi-scale modeling in clinical oncology, including the synthesis of disparate data types into models that reveal underlying mechanisms and allow for experimental testing of hypotheses. We then evaluate the mathematical techniques employed most widely and present several examples illustrating their application as well as the current gap between pre-clinical and clinical applications. We conclude with a discussion of what we view to be the key challenges and opportunities for multi-scale modeling in clinical oncology.