Progress and Opportunities to Advance Clinical Cancer Therapeutics Using Tumor Dynamic Models

Dose Optimization in Oncology Drug Development: An International Consortium for Innovation and Quality in Pharmaceutical Development White Paper

The landscape of oncology drug development has witnessed remarkable advancements over the last few decades, significantly improving clinical outcomes and quality of life for patients with cancer. Project Optimus, introduced by the U.S. Food and Drug Administration, stands as a groundbreaking endeavor to reform dose selection of oncology drugs, presenting both opportunities and challenges for the field. To address complex dose optimization challenges, an Oncology Dose Optimization IQ Working Group was created to characterize current practices, provide recommendations for improvement, develop a clinical toolkit, and engage Health Authorities. Historically, dose selection for cytotoxic chemotherapeutics has focused on the maximum tolerated dose, a paradigm that is less relevant for targeted therapies and new treatment modalities. A survey conducted by this group gathered insights from member companies regarding industry practices in oncology dose optimization. Given oncology drug development is a complex effort with multidimensional optimization and high failure rates due to lack of clinically relevant efficacy, this Working Group advocates for a case-by-case approach to inform the timing, specific quantitative targets, and strategies for dose optimization, depending on factors such as disease characteristics, patient population, mechanism of action, including associated resistance mechanisms, and therapeutic index. This white paper highlights the evolving nature of oncology dose optimization, the impact of Project Optimus, and the need for a tailored and evidence-based approach to optimize oncology drug dosing regimens effectively.

Model-informed Evidence for Clinical Non-inferiority of Every-2-Weeks Versus Standard Weekly Dosing Schedule of Cetuximab in Metastatic Colorectal Cancer

Cetuximab was initially developed and approved as a first-line treatment in patients with unresectable metastatic colorectal cancer (mCRC) for weekly administration (250 mg/m2 Q1W with 400 mg/m2 loading dose). An every-2-weeks schedule (500 mg/m2 Q2W) was approved recently by several health authorities. Being synchronized with chemotherapy, Q2W administration should improve patients' convenience and healthcare resource utilization. Herein, we present evidence of non-inferiority of Q2W cetuximab, compared with Q1W dosing using pharmacometrics modeling and clinical trial simulation (CTS). Pooled data from five phase I-III clinical trials in 852 patients with KRAS wild-type mCRC treated with Q1W or Q2W cetuximab were modeled using a population exposure-tumor size (TS) model linked to overall survival (OS); exposure was derived from a previously established population pharmacokinetic model. A semi-mechanistic TS model adapted from the Claret model incorporated killing rate proportional to cetuximab area under the concentration-time curve over 2 weeks (AUC) with Eastern Cooperative Oncology Group (ECOG) status as covariate on baseline TS. The OS was modeled with Weibull hazard using ECOG, baseline TS, primary tumor location, and predicted percent change in TS at 8 weeks as covariates. Model-based simulations revealed indistinguishable early tumor shrinkage and survival between Q2W vs. Q1W cetuximab. CTS evaluated OS non-inferiority (predefined margin of 1.25) in 1,000 trials, each with 2,000 virtual patients receiving Q2W or Q1W cetuximab (1:1), and demonstrated non-inferiority in 94% of cases. Taken together, these analyses provide model-based evidence for clinical non-inferiority of Q2W vs. Q1W cetuximab in mCRC with potential benefits to patients and healthcare providers.

Organ-specific tumor dynamics predict survival of patients with metastatic colorectal cancer

BACKGROUND

We aim to compare the prognostic value of organ-specific dynamics with the sum of the longest diameter (SLD) dynamics in patients with metastatic colorectal cancer (mCRC).

METHODS

All datasets are accessible in Project Data Sphere, an open-access platform. The tumor growth inhibition models developed based on organ-level SLD and SLD were used to estimate the organ-specific tumor growth rates (KGs) and SLD KG. The early tumor shrinkage (ETS) from baseline to the first measurement after treatment was also evaluated. The relationship between organ-specific dynamics, SLD dynamics, and survival outcomes (overall survival, OS; progression-free survival, PFS) was quantified using Kaplan-Meier analysis and Cox regression.

RESULTS

This study included 3687 patients from 6 phase III mCRC trials. The liver emerged as the most frequent metastatic site (2901, 78.7 %), with variable KGs across different organs in individual patients (liver 0.0243 > lung 0.0202 > lymph node 0.0127 > other 0.0118 [week-1]). Notably, the dynamics for different organs did not equally contribute to predicting survival outcomes. In liver metastasis cases, liver KG proved to be a superior prognostic indicator for OS and surpasses the predictive performance of SLD, (C-index, liver KG 0.610 vs SLD KG 0.606). A similar result can be found for PFS. Moreover, liver ETS also outperforms SLD ETS in predicting survival. Cox regression analysis confirmed liver KG is the most significant variable in survival prediction.

CONCLUSIONS

In mCRC patients with liver metastasis, liver dynamics is the primary prognostic indicator for both PFS and OS. In future drug development for mCRC, greater emphasis should be directed towards understanding the dynamics of liver metastasis development.

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.

Predicting overall survival from tumor dynamics metrics using parametric statistical and machine learning models: application to patients with RET-altered solid tumors

In oncology drug development, tumor dynamics modeling is widely applied to predict patients' overall survival (OS) via parametric models. However, the current modeling paradigm, which assumes a disease-specific link between tumor dynamics and survival, has its limitations. This is particularly evident in drug development scenarios where the clinical trial under consideration contains patients with tumor types for which there is little to no prior institutional data. In this work, we propose the use of a pan-indication solid tumor machine learning (ML) approach whereby all three tumor metrics (tumor shrinkage rate, tumor regrowth rate and time to tumor growth) are simultaneously used to predict patients' OS in a tumor type independent manner. We demonstrate the utility of this approach in a clinical trial of cancer patients treated with the tyrosine kinase inhibitor, pralsetinib. We compared the parametric and ML models and the results showed that the proposed ML approach is able to adequately predict patient OS across RET-altered solid tumors, including non-small cell lung cancer, medullary thyroid cancer as well as other solid tumors. While the findings of this study are promising, further research is needed for evaluating the generalizability of the ML model to other solid tumor types.

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.

Utility and impact of quantitative pharmacology on dose selection and clinical development of immuno-oncology therapy

Immuno-oncology (IO) therapies have changed the cancer treatment landscape. Immune checkpoint inhibitors (ICIs) have improved overall survival in 20-40% of patients with malignancies that were previously refractory. Due to the uniqueness in biology, modalities and patient responses, drug development strategies for IO differed from that traditionally used for cytotoxic and target therapies in oncology, and quantitative pharmacology utilizing modeling approach can be applied in all phases of the development process. In this review, we used case studies to showcase how various modeling methodologies were applied from translational science and dose selection through to label change, using examples that included anti-programmed-death-1 (anti-PD-1), anti-programmed-death ligand-1 (anti-PD-L1), anti-cytotoxic T-lymphocyte-associated protein 4 (anti-CTLA-4), and anti-glucocorticoid-induced tumor necrosis factor receptor-related protein (anti-GITR) antibodies. How these approaches were utilized to support phase I-III dose selection, the design of phase III trials, and regulatory decisions on label change are discussed to illustrate development strategies. Model-based quantitative approaches have positively impacted IO drug development, and a better understanding of the biology and exposure-response relationship may benefit the development and optimization of new IO therapies.

Tumor growth inhibition-overall survival modeling in non-small cell lung cancer: A case study from GEMSTONE-302

Overall survival is vital for approving new anticancer drugs but is often impractical for early-phase studies. The tumor growth inhibition-overall survival (TGI-OS) model could bridge the gap between early- and late-stage development. This study aimed to identify an appropriate TGI-OS model for patients with non-small cell lung cancer from the GEMSTONE-302 study of sugemalimab. We used three TGI models to delineate tumor trajectories and investigated three OS model for linking TGI metric to OS. All three TGI models accurately captured tumor profiles at the individual level. The published atezolizumab-based TGI-OS model predicted survival time satisfactorily through simulation-based evaluation, whereas the other published model built from multi-treatment underestimated OS. Our study-specific TGI-OS model identified time-to-growth as the most significant metric with the number of metastatic sites and neutrophil-to-lymphocyte ratio at baseline as covariates and exhibited robust OS predictability. Our findings demonstrated the effectiveness of the TGI-OS models in predicting phase III outcomes, which underpins their value as a powerful tool for antitumor drug development.

Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses. In this work, we present a compartment model of tumour volume and tumour composition, which, despite relative simplicity, is capable of producing a wide range of patient responses. We then develop novel statistical methodology and leverage a cohort of existing clinical data to produce a predictive model of both tumour volume progression and the associated level of uncertainty that evolves throughout a patient's course of treatment. To capture inter-patient variability, all model parameters are patient specific, with a bootstrap particle filter-like Bayesian approach developed to model a set of training data as prior knowledge. We validate our approach against a subset of unseen data, and demonstrate both the predictive ability of our trained model and its limitations.

Tumor growth inhibition modeling in patients with second line biliary tract cancer and first line non-small cell lung cancer based on bintrafusp alfa trials

This analysis aimed to quantify tumor dynamics in patients receiving either bintrafusp alfa (BA) or pembrolizumab, by population pharmacokinetic (PK)-pharmacodynamic modeling, and investigate clinical and molecular covariates describing the variability in tumor dynamics by pharmacometric and machine-learning (ML) approaches. Data originated from two clinical trials in patients with biliary tract cancer (BTC; NCT03833661) receiving BA and non-small cell lung cancer (NSCLC; NCT03631706) receiving BA or pembrolizumab. Individual drug exposure was estimated from previously developed population PK models. Population tumor dynamics models were developed for each drug-indication combination, and covariate evaluations performed using nonlinear mixed-effects modeling (NLME) and ML (elastic net and random forest models) approaches. The three tumor dynamics' model structures all included linear tumor growth components and exponential tumor shrinkage. The final BTC model included the effect of drug exposure (area under the curve) and several covariates (demographics, disease-related, and genetic mutations). Drug exposure was not significant in either of the NSCLC models, which included two, disease-related, covariates in the BA arm, and none in the pembrolizumab arm. The covariates identified by univariable NLME and ML highly overlapped in BTC but showed less agreement in NSCLC analyses. Hyperprogression could be identified by higher tumor growth and lower tumor kill rates and could not be related to BA exposure. Tumor size over time was quantitatively characterized in two tumor types and under two treatments. Factors potentially related to tumor dynamics were assessed using NLME and ML approaches; however, their net impact on tumor size was considered as not clinically relevant.

Explainable deep learning for tumor dynamic modeling and overall survival prediction using Neural-ODE

While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic Neural-ODE (TDNODE) as a pharmacology-informed neural network to enable model discovery from longitudinal tumor size data. We show that TDNODE overcomes a key limitation of existing models in its ability to make unbiased predictions from truncated data. The encoder-decoder architecture is designed to express an underlying dynamical law that possesses the fundamental property of generalized homogeneity with respect to time. Thus, the modeling formalism enables the encoder output to be interpreted as kinetic rate metrics, with inverse time as the physical unit. We show that the generated metrics can be used to predict patients' overall survival (OS) with high accuracy. The proposed modeling formalism provides a principled way to integrate multimodal dynamical datasets in oncology disease modeling.

Model-informed drug development of autologous CAR-T cell therapy: Strategies to optimize CAR-T cell exposure leveraging cell kinetic/dynamic modeling

Autologous Chimeric antigen receptor (CAR-T) cell therapy has been highly successful in the treatment of aggressive hematological malignancies and is also being evaluated for the treatment of solid tumors as well as other therapeutic areas. A challenge, however, is that up to 60% of patients do not sustain a long-term response. Low CAR-T cell exposure has been suggested as an underlying factor for a poor prognosis. CAR-T cell therapy is a novel therapeutic modality with unique kinetic and dynamic properties. Importantly, "clear" dose-exposure relationships do not seem to exist for any of the currently approved CAR-T cell products. In other words, dose increases have not led to a commensurate increase in the measurable in vivo frequency of transferred CAR-T cells. Therefore, alternative approaches beyond dose titration are needed to optimize CAR-T cell exposure. In this paper, we provide examples of actionable variables - design elements in CAR-T cell discovery, development, and clinical practice, which can be modified to optimize autologous CAR-T cell exposure. Most of these actionable variables can be assessed throughout the various stages of discovery and development as part of a well-informed research and development program. Model-informed drug development approaches can enable such study and program design choices from discovery through to clinical practice and can be an important contributor to cell therapy effectiveness and efficiency.

A prognostic baseline blood biomarker and tumor growth kinetics integrated model in paclitaxel/platinum treated advanced non-small cell lung cancer patients

Paclitaxel/platinum chemotherapy, the backbone of standard first-line treatment of advanced non-small cell lung cancer (NSCLC), exhibits high interpatient variability in treatment response and high toxicity burden. Baseline blood biomarker concentrations and tumor size (sum of diameters) at week 8 relative to baseline (RS8) are widely investigated prognostic factors. However, joint analysis of data on demographic/clinical characteristics, blood biomarker levels, and chemotherapy exposure-driven early tumor response for improved prediction of overall survival (OS) is clinically not established. We developed a Weibull time-to-event model to predict OS, leveraging data from 365 patients receiving paclitaxel/platinum combination chemotherapy once every three weeks for ≤six cycles. A developed tumor growth inhibition model, combining linear tumor growth and first-order paclitaxel area under the concentration-time curve-induced tumor decay, was used to derive individual RS8. The median model-derived RS8 in all patients was a 20.0% tumor size reduction (range from -78% to +15%). Whereas baseline carcinoembryonic antigen, cytokeratin fragments, and thyroid stimulating hormone levels were not significantly associated with OS in a subset of 221 patients, and lactate dehydrogenase, interleukin-6 and neutrophil-to-lymphocyte ratio levels were significant only in univariate analyses (p value < 0.05); C-reactive protein (CRP) in combination with RS8 most significantly affected OS (p value < 0.01). Compared to the median population OS of 11.3 months, OS was 128% longer at the 5th percentile levels of both covariates and 60% shorter at their 95th percentiles levels. The combined paclitaxel exposure-driven RS8 and baseline blood CRP concentrations enables early individual prognostic predictions for different paclitaxel dosing regimens, forming the basis for treatment decision and optimizing paclitaxel/platinum-based advanced NSCLC chemotherapy.

Clinical Pharmacology Applications of Real-World Data and Real-World Evidence in Drug Development and Approval-An Industry Perspective

Since the 21st Century Cures Act was signed into law in 2016, real-world data (RWD) and real-world evidence (RWE) have attracted great interest from the healthcare ecosystem globally. The potential and capability of RWD/RWE to inform regulatory decisions and clinical drug development have been extensively reviewed and discussed in the literature. However, a comprehensive review of current applications of RWD/RWE in clinical pharmacology, particularly from an industry perspective, is needed to inspire new insights and identify potential future opportunities for clinical pharmacologists to utilize RWD/RWE to address key drug development questions. In this paper, we review the RWD/RWE applications relevant to clinical pharmacology based on recent publications from member companies in the International Consortium for Innovation and Quality in Pharmaceutical Development (IQ) RWD Working Group, and discuss the future direction of RWE utilization from a clinical pharmacology perspective. A comprehensive review of RWD/RWE use cases is provided and discussed in the following categories of application: drug-drug interaction assessments, dose recommendation for patients with organ impairment, pediatric plan development and study design, model-informed drug development (e.g., disease progression modeling), prognostic and predictive biomarkers/factors identification, regulatory decisions support (e.g., label expansion), and synthetic/external control generation for rare diseases. Additionally, we describe and discuss common sources of RWD to help guide appropriate data selection to address questions pertaining to clinical pharmacology in drug development and regulatory decision making.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Support to early clinical decisions in drug development and personalised medicine with checkpoint inhibitors using dynamic biomarker-overall survival models

Longitudinal models of biomarkers such as tumour size dynamics capture treatment efficacy and predict treatment outcome (overall survival) of a variety of anticancer therapies, including chemotherapies, targeted therapies, immunotherapies and their combinations. These pharmacological endpoints like tumour dynamic (tumour growth inhibition) metrics have been proposed as alternative endpoints to complement the classical RECIST endpoints (objective response rate, progression-free survival) to support early decisions both at the study level in drug development as well as at the patients level in personalised therapy with checkpoint inhibitors. This perspective paper presents recent developments and future directions to enable wider and robust use of model-based decision frameworks based on pharmacological endpoints.

COMBI-r: A Prospective, Non-Interventional Study of Dabrafenib Plus Trametinib in Unselected Patients with Unresectable or Metastatic BRAF V600-Mutant Melanoma

Combined BRAF/MEK-inhibition constitutes a relevant treatment option for BRAF-mutated advanced melanoma. The prospective, non-interventional COMBI-r study assessed the effectiveness and tolerability of the BRAF-inhibitor dabrafenib combined with the MEK-inhibitor trametinib in patients with advanced melanoma under routine clinical conditions. Progression-free survival (PFS) was the primary objective, and secondary objectives included overall survival (OS), disease control rate, duration of therapy, and the frequency and severity of adverse events. This study enrolled 472 patients at 55 German sites. The median PFS was 8.3 months (95%CI 7.1-9.3) and the median OS was 18.3 months (14.9-21.3), both tending to be longer in pre-treated patients. In the 147 patients with CNS metastases, PFS was similar in those requiring corticosteroids (probably representing symptomatic patients, 5.6 months (3.9-7.2)) compared with those not requiring corticosteroids (5.9 months (4.8-6.9)); however, OS was shorter in patients with brain metastases who received corticosteroids (7.8 (6.3-11.6)) compared to those who did not (11.9 months (9.6-19.5)). The integrated subjective assessment of tumor growth dynamics proved helpful to predict outcome: investigators' upfront categorization correlated well with time-to-event outcomes. Taken together, COMBI-r mirrored PFS outcomes from other prospective, observational studies and confirmed efficacy and safety findings from the pivotal phase III COMBI-d/-v and COMBI-mb trials.

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.

External validation of a tumor growth inhibition-overall survival model in non-small-cell lung cancer based on atezolizumab studies using alectinib data

BACKGROUND

A modeling framework was previously developed to simulate overall survival (OS) using tumor growth inhibition (TGI) data from six randomized phase 2/3 atezolizumab monotherapy or combination studies in non-small-cell lung cancer (NSCLC). We aimed to externally validate this framework to simulate OS in patients with treatment-naive advanced anaplastic lymphoma kinase (ALK)-positive NSCLC in the alectinib ALEX study.

METHODS

TGI metrics were estimated from a biexponential model using longitudinal tumor size data from a Phase 3 study evaluating alectinib compared with crizotinib in patients with treatment-naive ALK-positive advanced NSCLC. Baseline prognostic factors and TGI metric estimates were used to predict OS.

RESULTS

286 patients were evaluable (at least baseline and one post-baseline tumor size measurements) out of 303 (94%) followed for up to 5 years (cut-off: 29 November 2019). The tumor growth rate estimate and baseline prognostic factors (inflammatory status, tumor burden, Eastern Cooperative Oncology Group performance status, race, line of therapy, and sex) were used to simulate OS in ALEX study. Observed survival distributions for alectinib and crizotinib were within model 95% prediction intervals (PI) for approximately 2 years. Predicted hazard ratio (HR) between alectinib and crizotinib was in agreement with the observed HR (predicted HR 0.612, 95% PI 0.480-0.770 vs. 0.625 observed HR).

CONCLUSION

The TGI-OS model based on unselected or PD-L1 selected NSCLC patients included in atezolizumab trials is externally validated to predict treatment effect (HR) in a biomarker-selected (ALK-positive) population included in alectinib ALEX trial suggesting that TGI-OS models may be treatment independent.

Semiautomated Pipeline to Quantify Tumor Evolution From Real-World Positron Emission Tomography/Computed Tomography Imaging

PURPOSE

A semiautomated pipeline for the collection and curation of free-text and imaging real-world data (RWD) was developed to quantify cancer treatment outcomes in large-scale retrospective real-world studies. The objectives of this article are to illustrate the challenges of RWD extraction, to demonstrate approaches for quality assurance, and to showcase the potential of RWD for precision oncology.

METHODS

We collected data from patients with advanced melanoma receiving immune checkpoint inhibitors at the Lausanne University Hospital. Cohort selection relied on semantically annotated electronic health records and was validated using process mining. The selected imaging examinations were segmented using an automatic commercial software prototype. A postprocessing algorithm enabled longitudinal lesion identification across imaging time points and consensus malignancy status prediction. Resulting data quality was evaluated against expert-annotated ground-truth and clinical outcomes obtained from radiology reports.

RESULTS

The cohort included 108 patients with melanoma and 465 imaging examinations (median, 3; range, 1-15 per patient). Process mining was used to assess clinical data quality and revealed the diversity of care pathways encountered in a real-world setting. Longitudinal postprocessing greatly improved the consistency of image-derived data compared with single time point segmentation results (classification precision increased from 53% to 86%). Image-derived progression-free survival resulting from postprocessing was comparable with the manually curated clinical reference (median survival of 286 v 336 days, P = .89).

CONCLUSION

We presented a general pipeline for the collection and curation of text- and image-based RWD, together with specific strategies to improve reliability. We showed that the resulting disease progression measures match reference clinical assessments at the cohort level, indicating that this strategy has the potential to unlock large amounts of actionable retrospective real-world evidence from clinical records.

Tumor Dynamic Model-Based Decision Support for Phase Ib/II Combination Studies: A Retrospective Assessment Based on Resampling of the Phase III Study IMpower150

PURPOSE

Model-based tumor growth inhibition (TGI) metrics are increasingly incorporated into go/no-go decisions in early clinical studies. To apply this methodology to new investigational combinations requires independent evaluation of TGI metrics in recently completed Phase III trials of effective immunotherapy.

PATIENTS AND METHODS

Data were extracted from IMpower150, a positive, randomized, Phase III study of first-line therapy in 1,202 patients with non-small cell lung cancer. We resampled baseline characteristics and longitudinal sum of longest diameters of tumor lesions of patients from both arms, atezolizumab+ bevacizumab+chemotherapy (ABCP) versus BCP, to mimic Phase Ib/II studies of 15 to 40 patients/arm with 6 to 24 weeks follow-up. TGI metrics were estimated using a bi-exponential TGI model. Effect sizes were calculated as TGI metrics geometric mean ratio (GMR), objective response rate (ORR) difference (d), and progression-free survival (PFS), hazard ratio (HR) between arms. Correct and incorrect go decisions were evaluated as the probability to achieve desired effect sizes in ABCP versus BCP and BCP versus BCP, respectively, across 500 replicated subsamples for each design.

RESULTS

For 40 patients/24 weeks follow-up, correct go decisions based on probability tumor growth rate (KG) GMR <0.90, dORR >0.10, and PFS HR <0.70 were 83%, 69%, and 58% with incorrect go decision rates of 4%, 12%, and 11%, respectively. For other designs, the ranking did not change with TGI metrics consistently overperforming RECIST endpoints. The predicted overall survival (OS) HR was around 0.80 in most of the scenarios investigated.

CONCLUSIONS

Model-based estimate of KG GMR is an exploratory endpoint that informs early clinical decisions for combination studies.

Comparison of sequential and joint nonlinear mixed effects modeling of tumor kinetics and survival following Durvalumab treatment in patients with metastatic urothelial carcinoma

Standard endpoints such as objective response rate are usually poorly correlated with overall survival (OS) for treatment with immune checkpoint inhibitors. Longitudinal tumor size may serve as a more useful predictor of OS, and establishing a quantitative relationship between tumor kinetics (TK) and OS is a crucial step for successfully predicting OS based on limited tumor size measurements. This study aims to develop a population TK model in combination with a parametric survival model by sequential and joint modeling approaches to characterize durvalumab phase I/II data from patients with metastatic urothelial cancer, and to evaluate and compare the performance of the two modeling approaches in terms of parameter estimates, TK and survival predictions, and covariate identification. The tumor growth rate constant was estimated to be greater for patients with OS ≤ 16 weeks as compared to that for patients with OS > 16 weeks with the joint modeling approach (k_g= 0.130 vs. 0.0551 week^-1, p-value < 0.0001), but similar for both groups (k_g = 0.0624 vs.0.0563 week^-1, p-value = 0.37) with the sequential modeling approach. The predicted TK profiles by joint modeling appeared better aligned with clinical observations. Joint modeling also predicted OS more accurately than the sequential approach according to concordance index and Brier score. The sequential and joint modeling approaches were also compared using additional simulated datasets, and survival was predicted better by joint modeling in the case of a strong association between TK and OS. In conclusion, joint modeling enabled the establishment of a robust association between TK and OS and may represent a better choice for parametric survival analyses over the sequential approach.

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.

Opportunities and Challenges of Disease Progression Modeling in Drug Development - An IQ Perspective

Disease progression modeling (DPM) represents an important model-informed drug development framework. The scientific communities support the use of DPM to accelerate and increase efficiency in drug development. This article summarizes International Consortium for Innovation & Quality (IQ) in Pharmaceutical Development mediated survey conducted across multiple biopharmaceutical companies on challenges and opportunities for DPM. Additionally, this summary highlights the viewpoints of IQ from the 2021 workshop hosted by the US Food and Drug Administration (FDA). Sixteen pharmaceutical companies participated in the IQ survey with 36 main questions. The types of questions included single/multiple choice, dichotomous, rank questions, and open-ended or free text. The key results show that DPM has different representation, it encompasses natural disease history, placebo response, standard of care as background therapy, and can even be interpreted as pharmacokinetic/pharmacodynamic modeling. The most common reasons for not implementing DPM as frequently seem to be difficulties in internal cross-functional alignment, lack of knowledge of disease/data, and time constraints. If successfully implemented, DPM can have an impact on dose selection, reduction of sample size, trial read-out support, patient selection/stratification, and supportive evidence for regulatory interactions. The key success factors and key challenges of disease progression models were highlighted in the survey and about 24 case studies across different therapeutic areas were submitted from various survey sponsors. Although DPM is still evolving, its current impact is limited but promising. The success of such models in the future will depend on collaboration, advanced analytics, availability of and access to relevant and adequate-quality data, collaborative regulatory guidance, and published examples of impact.

Bayesian forecasting of tumor size metrics and overall survival

The tumor size ratio (TSR), time-to-tumor growth (TTG), and tumor growth rate (kG) are frequently suggested as model-based predictors of overall survival (OS) for different types of tumors. When the tumor metrics are applied in forecasting of the outcome for individual patients at an early stage, the tumor data might be sparse resulting in imprecise prediction. This simulation study aimed to investigate how the tumor follow-up data and estimation approaches influence the accuracy in the tumor size metrics and the predicted hazard of death for individual patients. Longitudinal tumor size and OS data were simulated using tumor growth inhibition and Weibull distribution models, respectively. Based on the model and increasing measurement durations, the accuracy (defined as 80-125% of the simulated "true" value) in individual metrics and hazard was computed. TSR week 6 (TSRw6) accuracy was adequate for 91% of the patients when tumor size was measured up to 12 weeks. For TTG and kG metrics, the highest accuracy observed was lower (43 and 77%, respectively) and occurred later (42 and 60 weeks, respectively). The simultaneous (joint) and sequential estimation approaches resulted in similar accuracies, however, in general, the sequential approach where individual tumor size parameters are fixed, demonstrated inferior estimation properties. The TSRw6 and the model-predicted tumor time course (absolute or relative change) had better forecasting properties than TTG or kG. The population pharmacokinetic (PK) parameters and data approach performed similarly or better than the simultaneous approach and had a better accuracy in estimating individuals' hazard of death than the individual PK parameters method.

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.

Hypothetical generalized framework for a new imaging endpoint of therapeutic activity in early phase clinical trials in brain tumors

Imaging response assessment is a cornerstone of patient care and drug development in oncology. Clinicians/clinical researchers rely on tumor imaging to estimate the impact of new treatments and guide decision making for patients and candidate therapies. This is important in brain cancer, where associations between tumor size/growth and emerging neurological deficits are strong. Accurately measuring the impact of a new therapy on tumor growth early in clinical development, where patient numbers are small, would be valuable for decision making regarding late-stage development activation. Current attempts to measure the impact of a new therapy have limited influence on clinical development, as determination of progression, stability or response does not currently account for individual tumor growth kinetics prior to the initiation of experimental therapies. Therefore, we posit that imaging-based response assessment, often used as a tool for estimating clinical effect, is incomplete as it does not adequately account for growth trajectories or biological characteristics of tumors prior to the introduction of an investigational agent. Here, we propose modifications to the existing framework for evaluating imaging assessment in primary brain tumors that will provide a more reliable understanding of treatment effects. Measuring tumor growth trajectories prior to a given intervention may allow us to more confidently conclude whether there is an anti-tumor effect. This updated approach to imaging-based tumor response assessment is intended to improve our ability to select candidate therapies for later-stage development, including those that may not meet currently sought thresholds for "response" and ultimately lead to identification of effective treatments.

In Silico Investigations of Multi-Drug Adaptive Therapy Protocols

The standard of care for cancer patients aims to eradicate the tumor by killing the maximum number of cancer cells using the maximum tolerated dose (MTD) of a drug. MTD causes significant toxicity and selects for resistant cells, eventually making the tumor refractory to treatment. Adaptive therapy aims to maximize time to progression (TTP), by maintaining sensitive cells to compete with resistant cells. We explored both dose modulation (DM) protocols and fixed dose (FD) interspersed with drug holiday protocols. In contrast to previous single drug protocols, we explored the determinants of success of two-drug adaptive therapy protocols, using an agent-based model. In almost all cases, DM protocols (but not FD protocols) increased TTP relative to MTD. DM protocols worked well when there was more competition, with a higher cost of resistance, greater cell turnover, and when crowded proliferating cells could replace their neighbors. The amount that the drug dose was changed, mattered less. The more sensitive the protocol was to tumor burden changes, the better. In general, protocols that used as little drug as possible, worked best. Preclinical experiments should test these predictions, especially dose modulation protocols, with the goal of generating successful clinical trials for greater cancer control.

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.

Modelling glioma progression, mass effect and intracranial pressure in patient anatomy

Increased intracranial pressure is the source of most critical symptoms in patients with glioma, and often the main cause of death. Clinical interventions could benefit from non-invasive estimates of the pressure distribution in the patient's parenchyma provided by computational models. However, existing glioma models do not simulate the pressure distribution and they rely on a large number of model parameters, which complicates their calibration from available patient data. Here we present a novel model for glioma growth, pressure distribution and corresponding brain deformation. The distinct feature of our approach is that the pressure is directly derived from tumour dynamics and patient-specific anatomy, providing non-invasive insights into the patient's state. The model predictions allow estimation of critical conditions such as intracranial hypertension, brain midline shift or neurological and cognitive impairments. A diffuse-domain formalism is employed to allow for efficient numerical implementation of the model in the patient-specific brain anatomy. The model is tested on synthetic and clinical cases. To facilitate clinical deployment, a high-performance computing implementation of the model has been publicly released.

Assessing the impact of organ-specific lesion dynamics on survival in patients with recurrent urothelial carcinoma treated with atezolizumab or chemotherapy

Background

Tumor dynamics typically rely on the sum of the longest diameters (SLD) of target lesions, and ignore heterogeneity in individual lesion dynamics located in different organs.

Patients and methods

Here we evaluated the benefit of analyzing lesion dynamics in different organs to predict survival in 900 patients with metastatic urothelial carcinoma treated with atezolizumab or chemotherapy (IMvigor211 trial).

Results

Lesion dynamics varied largely across organs, with lymph nodes and lung lesions showing on average a better response to both treatments than those located in the liver and locoregionally. A benefit of atezolizumab was observed on lung and liver lesion dynamics that was attributed to a longer duration of treatment effect as compared to chemotherapy (P value = 0.043 and 0.001, respectively). The impact of lesion dynamics on survival, assessed by a joint model, varied greatly across organs, irrespective of treatment. Liver and locoregional lesion dynamics had a large impact on survival, with an increase of 10 mm of the lesion size increasing the instantaneous risk of death by 12% and 10%, respectively. In comparison, lymph nodes and lung lesions had a lower impact, with a 10-mm increase in the lesion size increasing the instantaneous risk of death by 7% and 5%, respectively. Using our model, we could anticipate the benefit of atezolizumab over chemotherapy as early as 6 months before the end of the study, which is 3 months earlier than a similar model only relying on SLD.

Conclusion

We showed the interest of organ-level tumor follow-up to better understand and anticipate the treatment effect on survival.

•

Nine hundred metastatic urothelial carcinoma patients from the IMvigor211 phase III trial were treated with atezolizumab versus chemotherapy.

•

A total of 4489 organ-specific measurements were made: 1544 measurements in the lymph, 999 in the lung, 691 in the liver, and 559 locoregionally.

•

Longer treatment effect was observed in the lung (P value = 0.043) and liver (P = 0.001) lesions under atezolizumab compared to chemotherapy.

•

Those with a 10-mm growth of liver lesion had their instantaneous risk of death increased by 12%, compared to 5% in the lung.

•

Treatment effect on overall survival could be predicted based on early organ-specific tumor data 6 months after last patient inclusion.

Modeling the Effects of Chemotherapy and Immunotherapy on Tumor Growth

Mathematical modeling has been used to simulate the interaction of chemotherapy and immunotherapy drugs intervention with the dynamics of tumor cells growth. This work studies the interaction of cells in the immune system, such as the natural killer, dendritic, and cytotoxic CD8+ T cells, with chemotherapy. Four different cases were considered in the simulation: no drug intervention, independent interventions (either chemotherapy or immunotherapy), and combined interventions of chemotherapy and immunotherapy. The system of ordinary differential equations was initially solved using the Runge-Kutta method and compared with two additional methods: the Explicit Euler and Heun's methods. Results showed that the combined intervention is more effective compared to the other cases. In addition, when compared with Runge-Kutta, the Heun's method presented a better accuracy than the Explicit Euler technique. The proposed mathematical model can be used as a tool to improve cancer treatments and targeted therapy.

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.

Joint modelling and simulation of M-protein dynamics and progression-free survival for alternative isatuximab dosing with pomalidomide/dexamethasone

AIMS

Addition of isatuximab (Isa) to pomalidomide/dexamethasone (Pd) significantly improved progression-free survival (PFS) in patients with relapsed/refractory multiple myeloma (RRMM). We aimed to characterize the relationship between serum M-protein kinetics and PFS in the phase 3 ICARIA-MM trial (NCT02990338), and to evaluate an alternative dosing regimen of Isa by simulation.

METHODS

Data from the ICARIA-MM trial comparing Isa 10 mg/kg weekly for 4 weeks then every 2 weeks (QW-Q2W) in combination with Pd versus Pd in 256 evaluable RRMM patients were used. A joint model of serum M-protein dynamics and PFS was developed. Trial simulations were then performed to evaluate whether efficacy is maintained after switching to a monthly dosing regimen.

RESULTS

The model identified instantaneous changes (slope) in serum M-protein as the best on-treatment predictor for PFS and baseline patient characteristics impacting serum M-protein kinetics (albumin and β2-microglobulin on baseline levels, non-IgG type on growth rate) and PFS (presence of plasmacytomas). Trial simulations demonstrated that switching to a monthly Isa regimen at 6 months would shorten median PFS by 2.3 weeks and induce 42.3% patients to progress earlier.

CONCLUSIONS

Trial simulations supported selection of the approved Isa 10 mg/kg QW-Q2W regimen and showed that switching to a monthly regimen after 6 months may reduce clinical benefit in the overall population. However, patients with good prognostic characteristics and with a stable, very good partial response may switch to a monthly regimen after 6 months without compromising the risk of disease progression. This hypothesis will be tested in a prospective clinical trial.

Multistate model for pharmacometric analyses of overall survival in HER2-negative breast cancer patients treated with docetaxel

The aim of this study was to develop a multistate model for overall survival (OS) analysis, based on parametric hazard functions and combined with an investigation of predictors derived from a longitudinal tumor size model on the transition hazards. Different states - stable disease, tumor response, progression, second-line treatment, and death following docetaxel treatment initiation (stable state) in patients with HER2-negative breast cancer (n = 183) were used in model building. Past changes in tumor size prospectively predicts the probability of state changes. The hazard of death after progression was lower for subjects who had longer treatment response (i.e., longer time-to-progression). Young age increased the probability of receiving second-line treatment. The developed multistate model adequately described the transitions between different states and jointly the overall event and survival data. The multistate model allows for simultaneous estimation of transition rates along with their tumor model derived metrics. The metrics were evaluated in a prospective manner so not to cause immortal time bias. Investigation of predictors and characterization of the time to develop response, the duration of response, the progression-free survival, and the OS can be performed in a single multistate modeling exercise. This modeling approach can be applied to other cancer types and therapies to provide a better understanding of efficacy of drug and characterizing different states, thereby facilitating early clinical interventions to improve anticancer therapy.

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.

AI-enhanced simultaneous multiparametric 18F-FDG PET/MRI for accurate breast cancer diagnosis

Purpose

To assess whether a radiomics and machine learning (ML) model combining quantitative parameters and radiomics features extracted from simultaneous multiparametric ¹⁸F-FDG PET/MRI can discriminate between benign and malignant breast lesions.

Methods

A population of 102 patients with 120 breast lesions (101 malignant and 19 benign) detected on ultrasound and/or mammography was prospectively enrolled. All patients underwent hybrid ¹⁸F-FDG PET/MRI for diagnostic purposes. Quantitative parameters were extracted from DCE (MTT, VD, PF), DW (mean ADC of breast lesions and contralateral breast parenchyma), PET (SUVmax, SUVmean, and SUVminimum of breast lesions, as well as SUVmean of the contralateral breast parenchyma), and T2-weighted images. Radiomics features were extracted from DCE, T2-weighted, ADC, and PET images. Different diagnostic models were developed using a fine Gaussian support vector machine algorithm which explored different combinations of quantitative parameters and radiomics features to obtain the highest accuracy in discriminating between benign and malignant breast lesions using fivefold cross-validation. The performance of the best radiomics and ML model was compared with that of expert reader review using McNemar’s test.

Results

Eight radiomics models were developed. The integrated model combining MTT and ADC with radiomics features extracted from PET and ADC images obtained the highest accuracy for breast cancer diagnosis (AUC 0.983), although its accuracy was not significantly higher than that of expert reader review (AUC 0.868) (p = 0.508).

Conclusion

A radiomics and ML model combining quantitative parameters and radiomics features extracted from simultaneous multiparametric ¹⁸F-FDG PET/MRI images can accurately discriminate between benign and malignant breast lesions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00259-021-05492-z.

Prediction of overall survival in patients across solid tumors following atezolizumab treatments: A tumor growth inhibition-overall survival modeling framework

The objectives of the study were to use tumor size data from 10 phase II/III atezolizumab studies across five solid tumor types to estimate tumor growth inhibition (TGI) metrics and assess the impact of TGI metrics and baseline prognostic factors on overall survival (OS) for each tumor type. TGI metrics were estimated from biexponential models and posttreatment longitudinal data of 6699 patients. TGI‐OS full models were built using parametric survival regression by including all significant baseline covariates from the Cox univariate analysis followed by a backward elimination step. The model performance was evaluated for each trial by 1000 simulations of the OS distributions and hazard ratios (HR) of the atezolizumab‐containing arms versus the respective controls. The tumor growth rate estimate was the most significant predictor of OS across all tumor types. Several baseline prognostic factors, such as inflammatory status (C‐reactive protein, albumin, and/or neutrophil‐to‐lymphocyte ratio), tumor burden (sum of longest diameters, number of metastatic sites, and/or presence of liver metastases), Eastern Cooperative Oncology Group performance status, and lactate dehydrogenase were also highly significant across multiple studies in the final multivariate models. TGI‐OS models adequately described the OS distribution. The model‐predicted HRs indicated good model performance across the 10 studies, with observed HRs within the 95% prediction intervals for all study arms versus controls. Multivariate TGI‐OS models developed for different solid tumor types were able to predict treatment effect with various atezolizumab monotherapy or combination regimens and could be used to support design and analysis of future studies.

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

Tumor growth inhibition modeling of individual lesion dynamics and interorgan variability in HER2-negative breast cancer patients treated with docetaxel

Information on individual lesion dynamics and organ location are often ignored in pharmacometric modeling analyses of tumor response. Typically, the sum of their longest diameters is utilized. Herein, a tumor growth inhibition model was developed for describing the individual lesion time-course data from 183 patients with metastatic HER2-negative breast cancer receiving docetaxel. The interindividual variability (IIV), interlesion variability (ILV), and interorgan variability of parameters describing the lesion time-courses were evaluated. Additionally, a model describing the probability of new lesion appearance and a time-to-event model for overall survival (OS), were developed. Before treatment initiation, the lesions were largest in the soft tissues and smallest in the lungs, and associated with a significant IIV and ILV. The tumor growth rate was 2.6 times higher in the breasts and liver, compared with other metastatic sites. The docetaxel drug effect in the liver, breasts, and soft tissues was greater than or equal to 1.2 times higher compared with other organs. The time-course of the largest lesion, the presence of at least 3 liver lesions, and the time since study enrollment, increased the probability of new lesion appearance. New lesion appearance, along with the time to growth and time-course of the largest lesion at baseline, were identified as the best predictors of OS. This tumor modeling approach, incorporating individual lesion dynamics, provided a more complete understanding of heterogeneity in tumor growth and drug effect in different organs. Thus, there may be potential to tailor treatments based on lesion location, lesion size, and early lesion response to provide better clinical outcomes.

Computing the Hazard Ratios Associated With Explanatory Variables Using Machine Learning Models of Survival Data

PURPOSE

The application of Cox proportional hazards (CoxPH) models to survival data and the derivation of hazard ratio (HR) are well established. Although nonlinear, tree-based machine learning (ML) models have been developed and applied to the survival analysis, no methodology exists for computing HRs associated with explanatory variables from such models. We describe a novel way to compute HRs from tree-based ML models using the SHapley Additive exPlanation values, which is a locally accurate and consistent methodology to quantify explanatory variables' contribution to predictions.

METHODS

We used three sets of publicly available survival data consisting of patients with colon, breast, or pan cancer and compared the performance of CoxPH with the state-of-the-art ML model, XGBoost. To compute the HR for explanatory variables from the XGBoost model, the SHapley Additive exPlanation values were exponentiated and the ratio of the means over the two subgroups was calculated. The CI was computed via bootstrapping the training data and generating the ML model 1,000 times. Across the three data sets, we systematically compared HRs for all explanatory variables. Open-source libraries in Python and R were used in the analyses.

RESULTS

For the colon and breast cancer data sets, the performance of CoxPH and XGBoost was comparable, and we showed good consistency in the computed HRs. In the pan-cancer data set, we showed agreement in most variables but also an opposite finding in two of the explanatory variables between the CoxPH and XGBoost result. Subsequent Kaplan-Meier plots supported the finding of the XGBoost model.

CONCLUSION

Enabling the derivation of HR from ML models can help to improve the identification of risk factors from complex survival data sets and to enhance the prediction of clinical trial outcomes.

Modelling Cell Invasion: A Review of What JD Murray and the Embryo Can Teach Us

Cell invasion and cell plasticity are critical to human development but are also striking features of cancer metastasis. By distributing a multipotent cell type from a place of birth to distal locations, the vertebrate embryo builds organs. In comparison, metastatic tumor cells often acquire a de-differentiated phenotype and migrate away from a primary site to inhabit new microenvironments, disrupting normal organ function. Countless observations of both embryonic cell migration and tumor metastasis have demonstrated complex cell signaling and interactive behaviors that have long confounded scientist and clinician alike. James D. Murray realized the important role of mathematics in biology and developed a unique strategy to address complex biological questions such as these. His work offers a practical template for constructing clear, logical, direct and verifiable models that help to explain complex cell behaviors and direct new experiments. His pioneering work at the interface of development and cancer made significant contributions to glioblastoma cancer and embryonic pattern formation using often simple models with tremendous predictive potential. Here, we provide a brief overview of advances in cell invasion and cell plasticity using the embryonic neural crest and its ancestral relationship to aggressive cancers that put into current context the timeless aspects of his work.

Application of Machine Learning for Tumor Growth Inhibition - Overall Survival Modeling Platform

Machine learning (ML) was used to leverage tumor growth inhibition (TGI) metrics to characterize the relationship with overall survival (OS) as a novel approach and to compare with traditional TGI‐OS modeling methods. Historical dataset from a phase III non‐small cell lung cancer study (OAK, atezolizumab vs. docetaxel, N = 668) was used. ML methods support the validity of TGI metrics in predicting OS. With lasso, the best model with TGI metrics outperforms the best model without TGI metrics. Boosting was the best linear ML method for this dataset with reduced estimation bias and lowest Brier score, suggesting better prediction accuracy. Random forest did not outperform linear ML methods despite hyperparameter optimization. Kernel machine was marginally the best nonlinear ML method for this dataset and uncovered nonlinear and interaction effects. Nonlinear ML may improve prediction by capturing nonlinear effects and covariate interactions, but its predictive performance and value need further evaluation with larger datasets.

Confounding factors in exposure-response analyses and mitigation strategies for monoclonal antibodies in oncology

Dose selection and optimization is an important topic in drug development to maximize treatment benefits for all patients. While exposure-response (E-R) analysis is a useful method to inform dose-selection strategy, in oncology, special considerations for prognostic factors are needed due to their potential to confound the E-R analysis for monoclonal antibodies. The current review focuses on 3 different approaches to mitigate the confounding effects for monoclonal antibodies in oncology: (i) Cox-proportional hazards modelling and case-matching; (ii) tumour growth inhibition-overall survival modelling; and (iii) multiple dose level study design. In the presence of confounding effects, studying multiple dose levels may be required to reveal the true E-R relationship. However, it is impractical for pivotal trials in oncology drug development programmes. Therefore, the strengths and weaknesses of the other 2 approaches are considered, and the favourable utility of tumour growth inhibition-overall survival modelling to address confounding in E-R analyses is described. In the broader scope of oncology drug development, this review discusses the downfall of the current emphasis on E-R analyses using data from single dose level trials and proposes that development programmes be designed to study more dose levels in earlier trials.

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.

Bayesian inference using Hamiltonian Monte-Carlo algorithm for nonlinear joint modeling in the context of cancer immunotherapy

Treatment evaluation in advanced cancer mainly relies on overall survival and tumor size dynamics. Both markers and their association can be simultaneously analyzed by using joint models, and these approaches are supported by many softwares or packages. However, these approaches are essentially limited to linear models for the longitudinal part, which limit their biological interpretation. More biological models of tumor dynamics can be obtained by using nonlinear models, but they are limited by the fact that parameter identifiability require rich dataset. In that context Bayesian approaches are particularly suited to incorporate the biological knowledge and increase the information available, but they are limited by the high computing cost of Monte-Carlo by Markov Chains algorithms. Here, we aimed to assess the performances of the Hamiltonian Monte-Carlo (HMC) algorithm implemented in Stan for inference in a nonlinear joint model. The method was validated on simulated data where HMC provided proper posterior distributions and credibility intervals in a reasonable computational time. Then the association between tumor size dynamics and survival was assessed in patients with advanced or metastatic bladder cancer treated with atezolizumab, an immunotherapy agent. HMC confirmed limited sensitivity to prior distributions. A cross-validation approach was developed and identified the current slope of tumor size dynamics as the most relevant driver of survival. In summary, HMC is an efficient approach to perform nonlinear joint models in a Bayesian framework, and opens the way for the use of nonlinear models to characterize both the rapid dynamics and the intersubject variability observed during cancer immunotherapy treatment.

Enhanced Detection of Treatment Effects on Metastatic Colorectal Cancer with Volumetric CT Measurements for Tumor Burden Growth Rate Evaluation

PURPOSE

Mathematical models combined with new imaging technologies could improve clinical oncology studies. To improve detection of therapeutic effect in patients with cancer, we assessed volumetric measurement of target lesions to estimate the rates of exponential tumor growth and regression as treatment is administered.

EXPERIMENTAL DESIGN

Two completed phase III trials were studied (988 patients) of aflibercept or panitumumab added to standard chemotherapy for advanced colorectal cancer. Retrospectively, radiologists performed semiautomated measurements of all metastatic lesions on CT images. Using exponential growth modeling, tumor regression (d) and growth (g) rates were estimated for each patient's unidimensional and volumetric measurements.

RESULTS

Exponential growth modeling of volumetric measurements detected different empiric mechanisms of effect for each drug: panitumumab marginally augmented the decay rate [tumor half-life; d [IQR]: 36.5 days (56.3, 29.0)] of chemotherapy [d: 44.5 days (67.2, 32.1), two-sided Wilcoxon P = 0.016], whereas aflibercept more significantly slowed the growth rate [doubling time; g = 300.8 days (154.0, 572.3)] compared with chemotherapy alone [g = 155.9 days (82.2, 347.0), P ≤ 0.0001]. An association of g with overall survival (OS) was observed. Simulating clinical trials using volumetric or unidimensional tumor measurements, fewer patients were required to detect a treatment effect using a volumetric measurement-based strategy (32-60 patients) than for unidimensional measurement-based strategies (124-184 patients).

CONCLUSIONS

Combined tumor volume measurement and estimation of tumor regression and growth rate has potential to enhance assessment of treatment effects in clinical studies of colorectal cancer that would not be achieved with conventional, RECIST-based unidimensional measurements.