Tumor Growth Dynamic Modeling in Oncology Drug Development and Regulatory Approval: Past, Present, and Future Opportunities

Bridging the gap between two-stage and joint models: The case of tumor growth inhibition and overall survival models

Many clinical trials generate both longitudinal biomarker and time-to-event data. We might be interested in their relationship, as in the case of tumor size and overall survival in oncology drug development. Many well-established methods exist for analyzing such data either sequentially (two-stage models) or simultaneously (joint models). Two-stage modeling (2stgM) has been challenged (i) for not acknowledging that biomarkers are endogenous covariable to the survival submodel and (ii) for not propagating the uncertainty of the longitudinal biomarker submodel to the survival submodel. On the other hand, joint modeling (JM), which properly circumvents both problems, has been criticized for being time-consuming, and difficult to use in practice. In this paper, we explore a third approach, referred to as a novel two-stage modeling (N2stgM). This strategy reduces the model complexity without compromising the parameter estimate accuracy. The three approaches (2stgM, JM, and N2stgM) are formulated, and a Bayesian framework is considered for their implementation. Both real and simulated data were used to analyze the performance of such approaches. In all scenarios, our proposal estimated the parameters approximately as JM but without being computationally expensive, while 2stgM produced biased results.

Realizing the promise of Project Optimus: Challenges and emerging opportunities for dose optimization in oncology drug development

Project Optimus is a US Food and Drug Administration Oncology Center of Excellence initiative aimed at reforming the dose selection and optimization paradigm in oncology drug development. This project seeks to bring together pharmaceutical companies, international regulatory agencies, academic institutions, patient advocates, and other stakeholders. Although there is much promise in this initiative, there are several challenges that need to be addressed, including multidimensionality of the dose optimization problem in oncology, the heterogeneity of cancer and patients, importance of evaluating long-term tolerability beyond dose-limiting toxicities, and the lack of reliable biomarkers for long-term efficacy. Through the lens of Totality of Evidence and with the mindset of model-informed drug development, we offer insights into dose optimization by building a quantitative knowledge base integrating diverse sources of data and leveraging quantitative modeling tools to build evidence for drug dosage considering exposure, disease biology, efficacy, toxicity, and patient factors. We believe that rational dose optimization can be achieved in oncology drug development, improving patient outcomes by maximizing therapeutic benefit while minimizing toxicity.

Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment

Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.

Early Decision Making in a Randomized Phase II Trial of Atezolizumab in Biliary Tract Cancer Using a Tumor Growth Inhibition-Survival Modeling Framework

We assess the longitudinal tumor growth inhibition (TGI) metrics and overall survival (OS) predictions applied to patients with advanced biliary tract cancer (BTC) enrolled in IMbrave151 a multicenter randomized phase II, double-blind, placebo-controlled trial evaluating the efficacy and safety of atezolizumab with or without bevacizumab in combination with cisplatin plus gemcitabine. Tumor growth rate (KG) was estimated for patients in IMbrave151. A pre-existing TGI-OS model for patients with hepatocellular carcinoma in IMbrave150 was modified to include available IMbrave151 study covariates and KG estimates and used to simulate IMbrave151 study outcomes. At the interim progression-free survival (PFS) analysis (98 patients, 27 weeks follow-up), clear separation in tumor dynamic profiles with a faster shrinkage rate and slower KG (0.0103 vs. 0.0117 week-1 ; tumor doubling time 67 vs. 59 weeks; KG geometric mean ratio of 0.84) favoring the bevacizumab containing arm was observed. At the first interim analysis for PFS, the simulated OS hazard ratio (HR) 95% prediction interval (PI) of 0.74 (95% PI: 0.58-0.94) offered an early prediction of treatment benefit later confirmed at the final analysis, observed HR of 0.76 based on 159 treated patients and 34 weeks of follow-up. This is the first prospective application of a TGI-OS modeling framework supporting gating of a phase III trial. The findings demonstrate the utility for longitudinal TGI and KG geometric mean ratio as relevant end points in oncology studies to support go/no-go decision making and facilitate interpretation of the IMbrave151 results to support future development efforts for novel therapeutics for patients with advanced BTC.

A comprehensive regulatory and industry review of modeling and simulation practices in oncology clinical drug development

Exposure-response (E-R) analyses are an integral component in the development of oncology products. Characterizing the relationship between drug exposure metrics and response allows the sponsor to use modeling and simulation to address both internal and external drug development questions (e.g., optimal dose, frequency of administration, dose adjustments for special populations). This white paper is the output of an industry-government collaboration among scientists with broad experience in E-R modeling as part of regulatory submissions. The goal of this white paper is to provide guidance on what the preferred methods for E-R analysis in oncology clinical drug development are and what metrics of exposure should be considered.

An integrated PK/PD model investigating the impact of tumor size and systemic safety on animal survival in SW1990 pancreatic cancer xenograft

Survival is one of the most important endpoints in cancer therapy, and parametric survival analysis could comprehensively reveal the overall result of disease progression, drug efficacy, toxicity as well as their interactions. In this study we investigated the efficacy and toxicity of dexamethasone (DEX) combined with gemcitabine (GEM) in pancreatic cancer xenograft. Nude mice bearing SW1990 pancreatic cancer cells derived tumor were treated with DEX (4 mg/kg, i.g.) and GEM (15 mg/kg, i.v.) alone or in combination repeatedly (QD, Q3D, Q7D) until the death of animal or the end of study. Tumor volumes and net body weight (NBW) were assessed every other day. Taking NBW as a systemic safety indicator, an integrated pharmacokinetic/pharmacodynamic (PK/PD) model was developed to quantitatively describe the impact of tumor size and systemic safety on animal survival. The PK/PD models with time course data for tumor size and NBW were established, respectively, in a sequential manner; a parametric time-to-event (TTE) model was also developed based on the longitudinal PK/PD models to describe the survival results of the SW1990 tumor-bearing mice. These models were evaluated and externally validated. Only the mice with good tumor growth inhibition and relatively stable NBW had an improved survival result after DEX and GEM combination therapy, and the simulations based on the parametric TTE model showed that NBW played more important role in animals' survival compared with tumor size. The established model in this study demonstrates that tumor size was not always the most important reason for cancer-related death, and parametric survival analysis together with safety issues was also important in the evaluation of oncology therapies in preclinical studies.

Aiding early clinical drug development by elucidation of the relationship between tumor growth inhibition and survival in relapsed/refractory multiple myeloma patients

Early prognosis of clinical efficacy is an urgent need for oncology drug development. Herein, we systemically examined the quantitative approach of tumor growth inhibition (TGI) and survival modeling in the space of relapsed and refractory multiple myeloma (MM), aiming to provide insights into clinical drug development. Longitudinal serum M-protein and progression-free survival (PFS) data from three phase III studies (N = 1367) across six treatment regimens and different patient populations were leveraged. The TGI model successfully described the longitudinal M-protein data in patients with MM. The tumor inhibition and growth parameters were found to vary as per each study, likely due to the patient population and treatment regimen difference. Based on a parametric time-to-event model for PFS, M-protein reduction at week 4 was identified as a significant prognostic factor for PFS across the three studies. Other factors, including Eastern Cooperative Oncology Group performance status, prior anti-myeloma therapeutics, and baseline serum ß2-microglobulin level, were correlated with PFS as well. In conclusion, patient disease characteristics (i.e., baseline tumor burden and treatment lines) were important determinants of tumor inhibition and PFS in MM patients. M-protein change at week 4 was an early prognostic biomarker for PFS.

Impact of pharmacogenetics on variability in exposure to oral vinorelbine among pediatric patients: a model-based population pharmacokinetic analysis

PURPOSE

Better understanding of pharmacokinetics of oral vinorelbine (VNR) in children would help predicting drug exposure and, beyond, clinical outcome. Here, we have characterized the population pharmacokinetics of oral VNR and studied the factors likely to explain the variability observed in VNR exposure among young patients.

DESIGN/METHODS

We collected blood samples from 36 patients (mean age 11.6 years) of the OVIMA multicentric phase II study in children with recurrent/progressive low-grade glioma. Patients received 60 mg/m² of oral VNR on days 1, 8, and 15 during the first 28-day treatment cycle and 80 mg/m², unless contraindicated, from cycle 2-12. Population pharmacokinetic analysis was performed using nonlinear mixed-effects modeling within the Monolix^® software. Fifty SNPs of pharmacokinetic-related genes were genotyped. The influence of demographic, biological, and pharmacogenetic covariates on pharmacokinetic parameters was investigated using a stepwise multivariate procedure.

RESULTS

A three-compartment model, with a delayed double zero-order absorption and a first-order elimination, best described VNR pharmacokinetics in children. Typical population estimates for the apparent central volume of distribution (V_c/F) and elimination rate constant were 803 L and 0.60 h^-1, respectively. Following covariate analysis, BSA, leukocytes count, and drug transport ABCB1-rs2032582 SNP showed a dramatic impact on V_c/F. Conversely, age and sex had no significant effect on VNR pharmacokinetics.

CONCLUSION

Beyond canonical BSA and leukocytes, ABCB1-rs2032582 polymorphism showed a meaningful impact on VNR systemic exposure. Simulations showed that the identified covariates could have an impact on both efficacy and toxicity outcomes. Thus, a personalized dosing strategy, using those covariates, could help to optimize the efficacy/toxicity balance of VNR in children.

Tumor Growth Inhibition-Overall Survival (TGI-OS) Model for Subgroup Analysis Based on Post-Randomization Factors: Application for Anti-drug Antibody (ADA) Subgroup Analysis of Atezolizumab in the IMpower150 Study

Longitudinal changes of tumor size or tumor-associated biomarkers have been receiving growing attention as early markers of treatment benefits. Tumor growth inhibition-overall survival (TGI-OS) models represent mathematical frameworks used to establish a link from tumor size trajectory to survival outcome with the aim of predicting survival benefit with tumor data from a small number of subjects with a short follow-up time. In the present study, we applied the TGI-OS model to assess treatment benefit in the IMpower150 study for patients who exhibited development of anti-drug antibodies (ADA). Direct comparison between subgroups of the active arm [ADA positive (ADA +) and negative (ADA -) groups] to the entire control group is not appropriate, due to potential imbalances of baseline prognostic factors between ADA + and ADA - patients. Thus, the TGI-OS modeling framework was employed to adjust for differences in prognostic factors between the ADA subgroups to more accurately estimate the treatment benefits. After adjustment, the TGI-OS model predicted comparable hazard ratios (HRs) of OS between ADA + and ADA - subgroups, suggesting that the development of ADA does not have a clinically significant impact on the treatment benefit of atezolizumab.

Lenvatinib dose, efficacy, and safety in the treatment of multiple malignancies

INTRODUCTION

Lenvatinib is an oral multitargeted tyrosine kinase inhibitor that has shown efficacy and manageable safety across multiple cancer types. The recommended starting doses for lenvatinib differ across cancer types and indications based on whether it is used as monotherapy or as combination therapy.

AREAS COVERED

This review covers clinical trials that established the dosing paradigm and efficacy of lenvatinib and defined its adverse-event profile as a monotherapy; or in combination with the mTOR inhibitor, everolimus; or the anti-PD-1 antibody, pembrolizumab; and/or chemotherapy.

EXPERT OPINION

Lenvatinib has been established as standard-of-care either as a monotherapy or in combination with other anticancer agents for the treatment of radioiodine-refractory differentiated thyroid carcinoma, hepatocellular carcinoma, renal cell carcinoma, and endometrial carcinoma, and is being investigated further across several other tumor types. The dosing and adverse-event management strategies for lenvatinib have been developed through extensive clinical trial experience. Collectively, the data provide the rationale to start lenvatinib at the recommended doses and then interrupt or dose reduce as necessary to achieve required dose intensity for maximized patient benefit. The adverse-event profile of lenvatinib is consistent with that of other tyrosine kinase inhibitors, and clinicians are encouraged to review and adopt relevant symptom-management strategies.

Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases

The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and the infected cells. Otherwise, it can attack the body’s healthy cells even if there is no invader. Many researchers have developed immunotherapy (or cancer vaccines) and have used chemotherapy for cancer treatment that can kill fast-growing cancer cells or at least slow down tumor growth. However, chemotherapy drugs travel throughout the body and tend to kill both healthy cells and cancer cells. In this study, we consider the fact that chemotherapy can kill tumor cells and that the loss of the immune cells may at the same time stir up cancer growth. We present a dynamic time-delay tumor-immune model with the effects of chemotherapy drugs and autoimmune disease. The modeling results can be used to determine the progression of tumor cells in the human body with the effect of chemotherapy, autoimmune diseases, and time delays based on partial differential equations. It can also be used to predict when the tumor viruses’ free state can be reached as time progresses, as well as the state of the body’s healthy cells as time progresses. We also present a few numerical cases that illustrate that the model can be used to monitor the effects of chemotherapy drug treatment and the growth rate of tumor virus-infected cells and the autoimmune disease.

A Dynamic Model of Multiple Time-Delay Interactions between the Virus-Infected Cells and Body’s Immune System with Autoimmune Diseases

The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.

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.