A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis

Integrated Data Analysis of Six Clinical Studies Points Toward Model-Informed Precision Dosing of Tamoxifen

Introduction

At tamoxifen standard dosing, ∼20% of breast cancer patients do not reach proposed target endoxifen concentrations >5.97 ng/mL. Thus, better understanding the large interindividual variability in tamoxifen pharmacokinetics (PK) is crucial. By applying non-linear mixed-effects (NLME) modeling to a pooled ‘real-world’ clinical PK database, we aimed to (i) dissect several levels of variability and identify factors predictive for endoxifen exposure and (ii) assess different tamoxifen dosing strategies for their potential to increase the number of patients reaching target endoxifen concentrations.

Methods

Tamoxifen and endoxifen concentrations with genetic and demographic data of 468 breast cancer patients from six reported studies were used to develop a NLME parent-metabolite PK model. Different levels of variability on model parameters or measurements were investigated and the impact of covariates thereupon explored. The model was subsequently applied in a simulation-based comparison of three dosing strategies with increasing degree of dose individualization for a large virtual breast cancer population. Interindividual variability of endoxifen concentrations and the fraction of patients at risk for not reaching target concentrations were assessed for each dosing strategy.

Results and Conclusions

The integrated NLME model enabled to differentiate and quantify four levels of variability (interstudy, interindividual, interoccasion, and intraindividual). Strong influential factors, i.e., CYP2D6 activity score, drug–drug interactions with CYP3A and CYP2D6 inducers/inhibitors and age, were reliably identified, reducing interoccasion variability to <20% CV. Yet, unexplained interindividual variability in endoxifen formation remained large (47.2% CV). Hence, therapeutic drug monitoring seems promising for achieving endoxifen target concentrations. Three tamoxifen dosing strategies [standard dosing (20 mg QD), CYP2D6-guided dosing (20, 40, and 60 mg QD) and individual model-informed precision dosing (MIPD)] using three therapeutic drug monitoring samples (5–120 mg QD) were compared, leveraging the model. The proportion of patients at risk for not reaching target concentrations was 22.2% in standard dosing, 16.0% in CYP2D6-guided dosing and 7.19% in MIPD. While in CYP2D6-guided- and standard dosing interindividual variability in endoxifen concentrations was high (64.0% CV and 68.1% CV, respectively), it was considerably reduced in MIPD (24.0% CV). Hence, MIPD demonstrated to be the most promising strategy for achieving target endoxifen concentrations.

Different ODE models of tumor growth can deliver similar results

BACKGROUND

Simeoni and colleagues introduced a compartmental model for tumor growth that has proved quite successful in modeling experimental therapeutic regimens in oncology. The model is based on a system of ordinary differential equations (ODEs), and accommodates a lag in therapeutic action through delay compartments. There is some ambiguity in the appropriate number of delay compartments, which we examine in this note.

METHODS

We devised an explicit delay differential equation model that reflects the main features of the Simeoni ODE model. We evaluated the original Simeoni model and this adaptation with a sample data set of mammary tumor growth in the FVB/N-Tg(MMTVneu)202Mul/J mouse model.

RESULTS

The experimental data evinced tumor growth heterogeneity and inter-individual diversity in response, which could be accommodated statistically through mixed models. We found little difference in goodness of fit between the original Simeoni model and the delay differential equation model relative to the sample data set.

CONCLUSIONS

One should exercise caution if asserting a particular mathematical model uniquely characterizes tumor growth curve data. The Simeoni ODE model of tumor growth is not unique in that alternative models can provide equivalent representations of tumor growth.

Machine Learning Analysis of Individual Tumor Lesions in Four Metastatic Colorectal Cancer Clinical Studies: Linking Tumor Heterogeneity to Overall Survival

Total tumor size (TS) metrics used in TS models in oncology do not consider tumor heterogeneity, which could help to better predict drug efficacy. We analyzed individual target lesions (iTLs) of patients with metastatic colorectal carcinoma (mCRC) to determine differences in TS dynamics by using the ClassIfication Clustering of Individual Lesions (CICIL) methodology. Results from subgroup analyses comparing genetic mutations and TS metrics were assessed and applied to survival analyses. Data from four mCRC clinical studies were analyzed (1781 patients, 6369 iTLs). CICIL was used to assess differences in lesion TS dynamics within a tissue (intra-class) or across different tissues (inter-class). First, lesions were automatically classified based on their location. Cross-correlation coefficients (CCs) determined if each pair of lesions followed similar or opposite dynamics. Finally, CCs were grouped by using the K-means clustering method. Heterogeneity in tumor dynamics was lower in the intra-class analysis than in the inter-class analysis for patients receiving cetuximab. More tumor heterogeneity was found in KRAS mutated patients compared to KRAS wild-type (KRASwt) patients and when using sum of longest diameters versus sum of products of diameters. Tumor heterogeneity quantified as the median patient's CC was found to be a predictor of overall survival (OS) (HR = 1.44, 95% CI 1.08-1.92), especially in KRASwt patients. Intra- and inter-tumor tissue heterogeneities were assessed with CICIL. Derived metrics of heterogeneity were found to be a predictor of OS time. Considering differences between lesions' TS dynamics could improve oncology models in favor of a better prediction of OS.

Modeling Tumor Growth and Treatment Resistance Dynamics Characterizes Different Response to Gefitinib or Chemotherapy in Non-Small Cell Lung Cancer

Differences in the effect of gefitinib and chemotherapy on tumor burden in non-small cell lung cancer remain to be fully understood. Using a Bayesian hierarchical model of tumor size dynamics, we estimated the rates of tumor growth and treatment resistance for patients in the Iressa Pan-Asia Study study (NCT00322452). The following relationships characterize greater efficacy of gefitinib in epidermal growth factor receptor (EGFR) positive tumors: Maximum drug effect is, in decreasing order, gefitinib in EGFR-positive, chemotherapy in EGFR-positive, chemotherapy in EGFR-negative, and gefitinib in EGFR-negative tumors; the rate of resistance emergence is, in increasing order: gefitinib in EGFR positive, chemotherapy in EGFR positive, while each is plausibly similar to the rate in EGFR negative tumors, which are estimated with less certainty. The rate of growth is smaller in EGFR-positive than in EGFR-negative fully resistant tumors, regardless of treatment. The model can be used to compare treatment effects and resistance dynamics among different drugs.

Bayesian Individual Dynamic Predictions with Uncertainty of Longitudinal Biomarkers and Risks of Survival Events in a Joint Modelling Framework: a Comparison Between Stan, Monolix, and NONMEM

Given a joint model and its parameters, Bayesian individual dynamic prediction (IDP) of biomarkers and risk of event can be performed for new patients at different landmark times using observed biomarker values. The aim of the present study was to compare IDP, with uncertainty, using Stan 2.18, Monolix 2018R2 and NONMEM 7.4. Simulations of biomarker and survival were performed using a nonlinear joint model of prostate-specific antigen (PSA) kinetics and survival in metastatic prostate cancer. Several scenarios were evaluated, according to the strength of the association between PSA and survival. For various landmark times, a posteriori distribution of PSA kinetic individual parameters was estimated, given individual observations, with each software. Samples of individual parameters were drawn from the posterior distribution. Bias and imprecision of individual parameters as well as coverage of 95% credibility interval for PSA and risk of death were evaluated. All software performed equally well with small biases on individual parameters. Imprecision on individual parameters was comparable across software and showed marked improvements with increasing landmark time. In terms of coverage, results were also comparable and all software were able to well predict PSA kinetics and survival. As for computing time, Stan was faster than Monolix and NONMEM to obtain individual parameters. Stan 2.18, Monolix 2018R2 and NONMEM 7.4 are able to characterize IDP of biomarkers and risk of event in a nonlinear joint modelling framework with correct uncertainty and hence could be used in the context of individualized medicine.

Mechanistic Pharmacokinetic/Pharmacodynamic Model of Sunitinib and Dopamine in MCF-7/Adr Xenografts: Linking Cellular Heterogeneity to Tumour Burden

The self-renewal and differentiation of cancer stem-like cells (CSCs) leads to cellular heterogeneity, causing one of the greatest challenges in cancer therapy. Growing evidence suggests that CSC-targeting therapy enhances the effect of concomitant antitumour therapy. To gain an in-depth understanding of this enhanced effect, the kinetic profile of estimated CSC frequency (the fraction of CSCs in tumour) was evaluated for in vivo characterization of cellular heterogeneity using sunitinib and dopamine as a paradigm combination therapy. Female MCF-7/Adr xenografted Balb/c nude mice were treated with sunitinib (p.o., 20 mg/kg) and dopamine (i.p., 50 mg/kg), alone or in combination. Estimated CSC frequency and tumour size were measured over time. Mechanistic PK/PD modelling was performed to quantitatively describe the relationship between drug concentration, estimated CSC frequency and tumour size. Sunitinib reduced tumour size by inducing apoptosis of differentiated tumour cells (DTCs) and enriched CSCs by stimulating its proliferation. Dopamine exhibited anti-CSC effects by suppressing the capacity of CSCs and inducing its differentiation. Simulation and animal studies indicated that concurrent administration was superior to sequential administration under current experimental conditions. Alongside tumour size, the current study provides mechanistic insights into the estimation of CSC frequency as an indicator for cellular heterogeneity. This forms the conceptual basis for in vivo characterization of other combination therapies in preclinical cancer studies.

Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors

Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported population-level correlation between the Gompertz parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a reduced Gompertz function consisting of a single individual parameter (and one population parameter). Leveraging the population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.

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

There is a need for new approaches and endpoints in oncology drug development, particularly with the advent of immunotherapies and the multiple drug combinations under investigation. Tumor dynamics modeling, a key component to oncology "model-informed drug development," has shown a growing number of applications and a broader adoption by drug developers and regulatory agencies in the past years to support drug development and approval in a variety of ways. Tumor dynamics modeling is also being investigated in personalized cancer therapy approaches. These models and applications are reviewed and discussed, as well as the limitations and issues open for further investigations. A close collaboration between stakeholders like clinical investigators, statisticians, and pharmacometricians is warranted to advance clinical cancer therapeutics.

Using mathematics in MRI data management for glioma assesment

Our aim is to review the mathematical tools usefulness in MR data management for glioma diagnosis and treatment optimization. MRI does not give access to organs variations in hours or days. However a lot of multiparametric data are generated. Mathematics could help to override this paradox, the aim of this article is to show how. We first make a review on mathematical modelling using equations. Afterwards we present statistical analysis. We provide detailed examples in both sections. We finally conclude, giving some clues on in silico models.

Optimization of Cancer Treatment in the Frequency Domain

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

Linking Tumor Growth Dynamics to Survival in Ipilimumab-Treated Patients With Advanced Melanoma Using Mixture Tumor Growth Dynamic Modeling

Early tumor assessments have been widely used to predict overall survival (OS), with potential application to dose selection and early go/no‐go decisions. Most published tumor dynamic models assume a uniform pattern of tumor growth dynamics (TGDs). We developed a mixture TGD model to characterize different patterns of longitudinal tumor sizes. Data from 688 patients with advanced melanoma who received ipilimumab 3 or 10 mg/kg every 3 weeks in a phase III study (NCT01515189) were used in a TGD‐OS analysis. The mixture model described TGD profiles using three subpopulations (no‐growth, intermediate, and fast). The TGD model showed a positive exposure/dose‐response (i.e., a higher proportion of patients in no/intermediate growth subpopulations and a lower tumor growth rate with ipilimumab 10 mg/kg relative to the 3 mg/kg dose). Finally, the mixture TGD model‐based measures of tumor response provided better predictions of OS compared with the nonmixture model.

A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model‐based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model‐based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

Neoadjuvant therapy for locally advanced gastric cancer patients. A population pharmacodynamic modeling

Background

Perioperative chemotherapy (CT) or neoadjuvant chemoradiotherapy (CRT) in patients with locally advanced gastric (GC) or gastroesophageal junction cancer (GEJC) has been shown to improve survival compared to an exclusive surgical approach. However, most patients retain a poor prognosis due to important relapse rates. Population pharmacokinetic-pharmacodynamic (PK/PD) modeling may allow identifying at risk-patients. We aimed to develop a mechanistic PK/PD model to characterize the relationship between the type of neoadjuvant therapy, histopathologic response and survival times in locally advanced GC and GEJC patients.

Methods

Patients with locally advanced GC and GEJC treated with neoadjuvant CT with or without preoperative CRT were analyzed. Clinical response was assessed by CT-scan and EUS. Pathologic response was defined as a reduction on pTNM stage compared to baseline cTNM. Metastasis development risk and overall survival (OS) were described using the population approach with NONMEM 7.3. Model evaluation was performed through predictive checks.

Results

A low correlation was observed between clinical and pathologic TNM stage for both T (R = 0.32) and N (R = 0.19) categories. A low correlation between clinical and pathologic response was noticed (R = -0.29). The OS model adequately described the observed survival rates. Disease recurrence, cTNM stage ≥3 and linitis plastica absence, were correlated to a higher risk of death.

Conclusion

Our model adequately described clinical response profiles, though pathologic response could not be predicted. Although the risk of disease recurrence and survival were linked, the identification of alternative approaches aimed to tailor therapeutic strategies to the individual patient risk warrants further research.

Resistance models to EGFR inhibition and chemotherapy in non-small cell lung cancer via analysis of tumour size dynamics

Purpose

Imaging time-series data routinely collected in clinical trials are predominantly explored for covariates as covariates for survival analysis to support decision-making in oncology drug development. The key objective of this study was to assess if insights regarding two relapse resistance modes, de-novo (treatment selects out a pre-existing resistant clone) or acquired (resistant clone develops during treatment), could be inferred from such data.

Methods

Individual lesion size time-series data were collected from ten Phase III study arms where patients were treated with either first-generation EGFR inhibitors (erlotinib or gefitinib) or chemotherapy (paclitaxel/carboplatin combination or docetaxel). The data for each arm of each study were analysed via a competing models framework to determine which of the two mathematical models of resistance, de-novo or acquired, best-described the data.

Results

Within the first-line setting (treatment naive patients), we found that the de-novo model best-described the gefitinib data, whereas, for paclitaxel/carboplatin, the acquired model was preferred. In patients pre-treated with paclitaxel/carboplatin, the acquired model was again preferred for docetaxel (chemotherapy), but for patients receiving gefitinib or erlotinib, both the acquired and de-novo models described the tumour size dynamics equally well. Furthermore, in all studies where a single model was preferred, we found a degree of correlation in the dynamics of lesions within a patient, suggesting that there is a degree of homogeneity in pharmacological response.

Conclusions

This analysis highlights that tumour size dynamics differ between different treatments and across lines of treatment. The analysis further suggests that these differences could be a manifestation of differing resistance mechanisms.

Electronic supplementary material

The online version of this article (10.1007/s00280-019-03840-3) contains supplementary material, which is available to authorized users.

Modeling long-term tumor growth and kill after combinations of radiation and radiosensitizing agents

PURPOSE

Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology. We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. The model also describes long-term treatment effects including tumor regrowth and eradication.

METHODS

We challenge the model with data from a xenograft study using a clinically relevant administration schedule and use a mixed-effects approach for model-fitting. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE).

RESULTS

The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. Using TSE, we predict the total radiation dose necessary for tumor eradication to be 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg kg^-1 of a radiosensitizer. TSE is also explored via a heat map of different growth and shrinkage rates. Finally, we discuss the translational potential of the model and TSE concept to humans.

CONCLUSIONS

The new model is capable of describing different tumor dynamics including tumor eradication and tumor regrowth with different rates, and can be calibrated using data from standard xenograft experiments. TSE and related concepts can be used to predict tumor shrinkage and eradication, and have the potential to guide new experiments and support translations from animals to humans.

A Population Dynamic Energy Budget-Based Tumor Growth Inhibition Model for Etoposide Effects on Wistar Rats

PURPOSE

This work aimed to develop a population PK/PD tumor-in-host model able to describe etoposide effects on both tumor cells and host in Walker-256 tumor-bearing rats.

METHODS

Etoposide was investigated on thirty-eight Wistar rats randomized in five arms: two groups of tumor-free animals receiving either placebo or etoposide (10 mg/kg bolus for 4 days) and three groups of tumor-bearing animals receiving either placebo or etoposide (5 or 10 mg/kg bolus for 8 or 4 days, respectively). To analyze experimental data, a tumor-in-host growth inhibition (TGI) model, based on the Dynamic Energy Budget (DEB) theory, was developed. Total plasma and free-interstitial tumor etoposide concentrations were assessed as driver of tumor kinetics.

RESULTS

The model simultaneously describes tumor and host growths, etoposide antitumor effect as well as cachexia phenomena related to both the tumor and the drug treatment. The schedule-dependent inhibitory effect of etoposide is also well captured when the intratumoral drug concentration is considered as the driver of the tumor kinetics.

CONCLUSIONS

The DEB-based TGI model capabilities, up to now assessed only in mice, are fully confirmed in this study involving rats. Results suggest that well designed experiments combined with a mechanistic modeling approach could be extremely useful to understand drug effects and to describe all the dynamics characterizing in vivo tumor growth studies.

Exposure-response analysis and simulation of lenvatinib safety and efficacy in patients with radioiodine-refractory differentiated thyroid cancer

Purpose

Once-daily lenvatinib 24 mg is the approved dose for radioiodine-refractory differentiated thyroid cancer. In a phase 3 trial with lenvatinib, the starting dose of 24 mg was associated with a relatively high incidence of adverse events that required dose reductions. We used an exposure–response model to investigate the risk–benefit of different dosing regimens for lenvatinib.

Methods

A population pharmacokinetics/pharmacodynamics modeling analysis was used to simulate the potential benefit of lower starting doses to retain efficacy with improved safety. The seven lenvatinib regimens tested were: 24 mg; and 20 mg, 18 mg, and 14 mg, all with or without up-titration to 24 mg. Exposure–response models for efficacy and safety were created using a 24-week time course.

Results

The approved dose of lenvatinib at 24 mg, predicted the best efficacy. However, the lenvatinib dosing regimens of 14 mg with up-titration or 18 mg without up-titration potentially provides comparable efficacy (objective response rate at 24 weeks) and a better safety profile.

Conclusions

Treatment with lenvatinib at starting doses lower than the approved once-daily 24 mg dose could provide comparable antitumor efficacy and a similar or better safety profile. Based on the results from this modeling and simulation study, a comparator dose of lenvatinib 18 mg without up-titration was selected for evaluation in a clinical trial.

Electronic supplementary material

The online version of this article (10.1007/s00280-018-3687-4) contains supplementary material, which is available to authorized users.

Pembrolizumab Exposure-Response Assessments Challenged by Association of Cancer Cachexia and Catabolic Clearance

PURPOSE

To investigate the relationship of pembrolizumab pharmacokinetics (PK) and overall survival (OS) in patients with advanced melanoma and non-small cell lung cancer (NSCLC).

PATIENTS AND METHODS

PK dependencies in OS were evaluated across three pembrolizumab studies of either 200 mg or 2 to 10 mg/kg every 3 weeks (Q3W). Kaplan-Meier plots of OS, stratified by dose, exposure, and baseline clearance (CL₀), were assessed per indication and study. A Cox proportional hazards model was implemented to explore imbalances of typical prognostic factors in high/low NSCLC CL₀ subgroups.

RESULTS

A total of 1,453 subjects were included: 340 with pembrolizumab-treated melanoma, 804 with pembrolizumab-treated NSCLC, and 309 with docetaxel-treated NSCLC. OS was dose independent from 2 to 10 mg/kg for pembrolizumab-treated melanoma [HR = 0.98; 95% confidence interval (CI), 0.94-1.02] and NSCLC (HR = 0.98; 95% CI, 0.95-1.01); however, a strong CL₀-OS association was identified for both cancer types (unadjusted melanoma HR = 2.56; 95% CI, 1.72-3.80 and NSCLC HR = 2.64; 95% CI, 1.94-3.57). Decreased OS in subjects with higher pembrolizumab CL₀ paralleled disease severity markers associated with end-stage cancer anorexia-cachexia syndrome. Correction for baseline prognostic factors did not fully attenuate the CL₀-OS association (multivariate-adjusted CL₀ HR = 1.64; 95% CI, 1.06-2.52 for melanoma and HR = 1.88; 95% CI, 1.22-2.89 for NSCLC).

CONCLUSIONS

These data support the lack of dose or exposure dependency in pembrolizumab OS for melanoma and NSCLC between 2 and 10 mg/kg. An association of pembrolizumab CL₀ with OS potentially reflects catabolic activity as a marker of disease severity versus a direct PK-related impact of pembrolizumab on efficacy. Similar data from other trials suggest such patterns of exposure-response confounding may be a broader phenomenon generalizable to antineoplastic mAbs.See related commentary by Coss et al., p. 5787.

Population exposure-response analysis of cabozantinib efficacy and safety endpoints in patients with renal cell carcinoma

BACKGROUND

In the phase III METEOR trial, tyrosine kinase inhibitor cabozantinib significantly improved progression-free survival (PFS), objective response rate (ORR), and overall survival compared to everolimus in patients with advanced renal cell carcinoma (RCC) who had received prior VEGFR inhibitor therapy. In METEOR, RCC patients started at a daily 60-mg cabozantinib tablet (Cabometyx™) dose but could reduce to 40- or 20-mg to achieve a tolerated exposure.

OBJECTIVES AND METHODS

Exposure-response (ER) models were developed to characterize the relationship between cabozantinib at clinically relevant exposures in RCC patients enrolled in METEOR and efficacy (PFS and tumor response) and safety endpoints.

RESULTS

Compared to the average steady-state cabozantinib concentration for a 60-mg dose, exposures at simulated 40- and 20-mg starting doses were predicted to result in higher risk of disease progression or death [hazard ratios (HRs) of 1.10 and 1.39, respectively], lower maximal median reduction in tumor size (- 11.9 vs - 9.1 and - 4.5%, respectively), and lower ORR (19.1 vs 15.6 and 8.7%, respectively). The 60-mg exposure was also associated with higher risk for selected adverse events (AEs) palmar-plantar erythrodysesthesia syndrome (grade ≥ 1), fatigue/asthenia (grade ≥ 3), diarrhea (grade ≥ 3), and hypertension (predicted HRs of 2.21, 2.01, 1.78, and 1.85, respectively) relative to the predicted average steady-state cabozantinib concentration for a 20-mg starting dose.

CONCLUSION

ER modeling predicted that cabozantinib exposures in RCC patients at the 60-mg starting dose would provide greater anti-tumor activity relative to exposures at simulated 40- and 20-mg starting doses that were associated with decreased rates of clinically relevant AEs.

Translational PK-PD modeling analysis of MCLA-128, a HER2/HER3 bispecific monoclonal antibody, to predict clinical efficacious exposure and dose

Introduction MCLA-128 is a bispecific monoclonal antibody targeting the HER2 and HER3 receptors. Pharmacokinetics (PK) and pharmacodynamics (PD) of MCLA-128 have been evaluated in preclinical studies in cynomolgus monkeys and mice. The aim of this study was to characterize the PK and PD of MCLA-128 and to predict a safe starting dose and efficacious clinical dose for the First-In-Human study. Methods A PK-PD model was developed based on PK data from cynomolgus monkeys and tumor growth data from a mouse JIMT-1 xenograft model. Allometric scaling was used to scale PK parameters between species. Simulations were performed to predict the safe and efficacious clinical dose, based on AUCs, receptor occupancies and PK-PD model simulations. Results MCLA-128 PK in cynomolgus monkeys was described by a two-compartment model with parallel linear and nonlinear clearance. The xenograft tumor growth model consisted of a tumor compartment with a zero-order growth rate and a first-order dying rate, both affected by MCLA-128. Human doses of 10 to 480 mg q3wk were predicted to show a safety margin of >10-fold compared to the cynomolgus monkey AUC at the no-observed-adverse-effect-level (NOAEL). Doses of ≥360 mg resulted in predicted receptor occupancies above 99% (C_max and C_ave). These doses showed anti-tumor efficacy in the PK-PD model. Conclusions This analysis predicts that a flat dose of 10 to 480 mg q3wk is suitable as starting dose for a First-in-Human study with MCLA-128. Flat doses ≥360 mg q3wk are expected to be efficacious in human, based on receptor occupancies and PK-PD model simulations.

Emerging roles for clinical pharmacometrics in cancer precision medicine

Purpose of review

Although significant progress has been made in cancer research, there exist unmet needs in patient care as reflected by the 'Cancer Moonshot' goals. This review appreciates the potential utility of quantitative pharmacology in cancer precision medicine.

Recent findings

Precision oncology has received federal funding largely due to 'The Precision Medicine Initiative'. Precision medicine takes into account the inter-individual variability, and allows for tailoring the right medication or the right dose of drug to the best subpopulation of patients who will likely respond to the intervention, thus enhancing therapeutic success and reducing "financial toxicity" to patients, families and caregivers. The National Cancer Institute (NCI) committed US$ 70 million from its fiscal year 2016 budget to advance precision oncology research. Through the 'Critical Path Initiative', pharmacometrics has gained an important role in drug development; however, it is yet to find widespread clinical applicability.

Summary

Stakeholders including clinicians and pharmacometricians need to work in concert to ensure that benefits of model-based approaches are harnessed to personalize cancer care to the individual needs of the patient via better dosing strategies, companion diagnostics, and predictive biomarkers. In medical oncology, where immediate patient care is the clinician's primary concern, pharmacometric approaches can be tailored to build models that rely on patient data already digitally available in the Electronic Health Record (EHR) to facilitate quick collaboration and avoid additional funding needs. Taken together, we offer a roadmap for the future of precision oncology which is fraught with both challenges and opportunities for pharmacometricians and clinicians alike.

Assessing Similarity Among Individual Tumor Size Lesion Dynamics: The CICIL Methodology

Mathematical models of tumor dynamics generally omit information on individual target lesions (iTLs), and consider the most important variable to be the sum of tumor sizes (TS). However, differences in lesion dynamics might be predictive of tumor progression. To exploit this information, we have developed a novel and flexible approach for the non‐parametric analysis of iTLs, which integrates knowledge from signal processing and machine learning. We called this new methodology ClassIfication Clustering of Individual Lesions (CICIL). We used CICIL to assess similarities among the TS dynamics of 3,223 iTLs measured in 1,056 patients with metastatic colorectal cancer treated with cetuximab combined with irinotecan, in two phase II studies. We mainly observed similar dynamics among lesions within the same tumor site classification. In contrast, lesions in anatomic locations with different features showed different dynamics in about 35% of patients. The CICIL methodology has also been implemented in a user‐friendly and efficient Java‐based framework.

Predicting tumour growth and its impact on survival in gemcitabine-treated patients with advanced pancreatic cancer

The aim of this evaluation was to characterize the impact of the tumour size (TS) effects driven by the anticancer drug gemcitabine on overall survival (OS) in patients with advanced pancreatic cancer by building and validating a predictive semi-mechanistic joint TS-OS model. TS and OS data were obtained from one phase II and one phase III study where gemcitabine was administered (1000-1250 mg/kg over 30-60 min i.v infusion) as single agent to patients (n = 285) with advanced pancreatic cancer. Drug exposure, TS and OS were linked using the population approach with NONMEM 7.3. Pancreatic tumour progression was characterized by exponential growth (doubling time = 67 weeks), and tumour response to treatment was described as a function of the weekly area under the gemcitabine triphosphate concentration vs time curve (AUC), including treatment-related resistance development. The typical predicted percentage of tumour growth inhibition with respect to no treatment was 22.3% at the end of 6 chemotherapy cycles. Emerging resistance elicited a 57% decrease in drug effects during the 6th chemotherapy cycle. Predicted TS profile was identified as main prognostic factor of OS, with tumours responders' profiles improving median OS by 30 weeks compared to stable-disease TS profiles. Results of NCT00574275 trial were predicted using this modelling framework, thereby validating the approach as a prediction tool in clinical development. Our analyses show that despite the advanced stage of the disease in this patient population, the modelling framework herein can be used to predict the likelihood of treatment success using early clinical data.

Population Modeling of Tumor Kinetics and Overall Survival to Identify Prognostic and Predictive Biomarkers of Efficacy for Durvalumab in Patients With Urothelial Carcinoma

Durvalumab is an anti‐PD‐L1 monoclonal antibody approved for patients with locally advanced or metastatic urothelial carcinoma (UC) that has progressed after platinum‐containing chemotherapy. A population tumor kinetic model, coupled with dropout and survival models, was developed to describe longitudinal tumor size data and predict overall survival in UC patients treated with durvalumab (NCT01693562) and to identify prognostic and predictive biomarkers of clinical outcomes. Model‐based covariate analysis identified liver metastasis as the most influential factor for tumor growth and immune‐cell PD‐L1 expression and baseline tumor burden as predictive factors for tumor killing. Tumor or immune‐cell PD‐L1 expression, liver metastasis, baseline hemoglobin, and albumin levels were identified as significant covariates for overall survival. These model simulations provided further insights into the impact of PD‐L1 cutoff values on treatment outcomes. The modeling framework can be a useful tool to guide patient selection and enrichment strategies for immunotherapies across various cancer indications.

Current mathematical models for cancer drug discovery

INTRODUCTION

Pharmacometric models represent the most comprehensive approaches for extracting, summarizing and integrating information obtained in the often sparse, limited, and less-than-optimally designed experiments performed in the early phases of oncology drug discovery. Whilst empirical methodologies may be enough for screening and ranking candidate drugs, modeling approaches are needed for optimizing and making economically viable the learn-confirm cycles within an oncology research program and anticipating the dose regimens to be investigated in the subsequent clinical development. Areas covered: Papers appearing in the literature of approximately the last decade reporting modeling approaches applicable to anticancer drug discovery have been listed and commented. Papers were selected based on the interest in the proposed methodology or in its application. Expert opinion: The number of modeling approaches used in the discovery of anticancer drugs is consistently increasing and new models are developed based on the current directions of research of new candidate drugs. These approaches have contributed to a better understanding of new oncological targets and have allowed for the exploitation of the relatively sparse information generated by preclinical experiments. In addition, they are used in translational approaches for guiding and supporting the choice of dosing regimens in early clinical development.

Single-cell study links metabolism with nutrient signaling and reveals sources of variability

BACKGROUND

The yeast AMPK/SNF1 pathway is best known for its role in glucose de/repression. When glucose becomes limited, the Snf1 kinase is activated and phosphorylates the transcriptional repressor Mig1, which is then exported from the nucleus. The exact mechanism how the Snf1-Mig1 pathway is regulated is not entirely elucidated.

RESULTS

Glucose uptake through the low affinity transporter Hxt1 results in nuclear accumulation of Mig1 in response to all glucose concentrations upshift, however with increasing glucose concentration the nuclear localization of Mig1 is more intense. Strains expressing Hxt7 display a constant response to all glucose concentration upshifts. We show that differences in amount of hexose transporter molecules in the cell could cause cell-to-cell variability in the Mig1-Snf1 system. We further apply mathematical modelling to our data, both general deterministic and a nonlinear mixed effect model. Our model suggests a presently unrecognized regulatory step of the Snf1-Mig1 pathway at the level of Mig1 dephosphorylation. Model predictions point to parameters involved in the transport of Mig1 in and out of the nucleus as a majorsource of cell to cell variability.

CONCLUSIONS

With this modelling approach we have been able to suggest steps that contribute to the cell-to-cell variability. Our data indicate a close link between the glucose uptake rate, which determines the glycolytic rate, and the activity of the Snf1/Mig1 system. This study hence establishes a close relation between metabolism and signalling.

A Pharmacometric Framework for Axitinib Exposure, Efficacy, and Safety in Metastatic Renal Cell Carcinoma Patients

The relationships between exposure, biomarkers (vascular endothelial growth factor (VEGF), soluble VEGF receptors (sVEGFR)-1, -2, -3, and soluble stem cell factor receptor (sKIT)), tumor sum of longest diameters (SLD), diastolic blood pressure (dBP), and overall survival (OS) were investigated in a modeling framework. The dataset included 64 metastatic renal cell carcinoma patients (mRCC) treated with oral axitinib. Biomarker timecourses were described by indirect response (IDR) models where axitinib inhibits sVEGFR-1, -2, and -3 production, and VEGF degradation. No effect was identified on sKIT. A tumor model using sVEGFR-3 dynamics as driver predicted SLD data well. An IDR model, with axitinib exposure stimulating the response, characterized dBP increase. In a time-to-event model the SLD timecourse predicted OS better than exposure, biomarker- or dBP-related metrics. This type of framework can be used to relate pharmacokinetics, efficacy, and safety to long-term clinical outcome in mRCC patients treated with VEGFR inhibitors. (ClinicalTrial.gov identifier NCT00569946.).

Pharmacometric Modeling of Liver Metastases' Diameter, Volume, and Density and Their Relation to Clinical Outcome in Imatinib-Treated Patients With Gastrointestinal Stromal Tumors

Three‐dimensional and density‐based tumor metrics have been suggested to better discriminate tumor response to treatment than unidimensional metrics, particularly for tumors exhibiting nonuniform size changes. In the developed pharmacometric modeling framework based on data from 77 imatinib‐treated gastrointestinal patients, the time‐courses of liver metastases' maximum transaxial diameters, software‐calculated actual volumes (V_actual) and calculated ellipsoidal volumes were characterized by logistic growth models, in which imatinib induced a linear dose‐dependent size reduction. An indirect response model best described the reduction in density. Substantial interindividual variability in the drug effect of all response assessments and additional interlesion variability in the drug effect on density were identified. The predictive ability of longitudinal tumor unidimensional and three‐dimensional size and density on overall survival (OS) and progression‐free survival (PFS) were compared using parametric time‐to‐event models. Death hazard increased with increasing V_actual. This framework may guide early clinical interventions based on three‐dimensional tumor responses to enhance benefits for patients with gastrointestinal stromal tumors (GIST).

Thoughtflow: Standards and Tools for Provenance Capture and Workflow Definition to Support Model-Informed Drug Discovery and Development

Pharmacometric analyses are complex and multifactorial. It is essential to check, track, and document the vast amounts of data and metadata that are generated during these analyses (and the relationships between them) in order to comply with regulations, support quality control, auditing, and reporting. It is, however, challenging, tedious, error-prone, and time-consuming, and diverts pharmacometricians from the more useful business of doing science. Automating this process would save time, reduce transcriptional errors, support the retention and transfer of knowledge, encourage good practice, and help ensure that pharmacometric analyses appropriately impact decisions. The ability to document, communicate, and reconstruct a complete pharmacometric analysis using an open standard would have considerable benefits. In this article, the Innovative Medicines Initiative (IMI) Drug Disease Model Resources (DDMoRe) consortium proposes a set of standards to facilitate the capture, storage, and reporting of knowledge (including assumptions and decisions) in the context of model-informed drug discovery and development (MID3), as well as to support reproducibility: "Thoughtflow." A prototype software implementation is provided.

Drug Development of Therapeutic Monoclonal Antibodies

Monoclonal antibodies (MAbs) have become a substantial part of many pharmaceutical company portfolios. However, the development process of MAbs for clinical use is quite different than for small-molecule drugs. MAb development programs require careful interdisciplinary evaluations to ensure the pharmacology of both the MAb and the target antigen are well-understood. Selection of appropriate preclinical species must be carefully considered and the potential development of anti-drug antibodies (ADA) during these early studies can limit the value and complicate the performance and possible duration of preclinical studies. In human studies, many of the typical pharmacology studies such as renal or hepatic impairment evaluations may not be needed but the pharmacokinetics and pharmacodynamics of these agents is complex, often necessitating more comprehensive evaluation of clinical data and more complex bioanalytical assays than might be used for small molecules. This paper outlines concerns and strategies for development of MAbs from the early in vitro assessments needed through preclinical and clinical development. This review focuses on how to develop, submit, and comply with regulatory requirements for MAb therapeutics.

A Review of Modeling Approaches to Predict Drug Response in Clinical Oncology

Model-based approaches have emerged as important tools for quantitatively understanding temporal relationships between drug dose, concentration, and effect over the course of treatment, and have now become central to optimal drug development and tailored drug treatment. In oncology, the therapeutic index of a chemotherapeutic drug is typically narrow and a full dose-response relationship is not available, often because of treatment failure. Noting the benefits of model-based approaches and the low therapeutic index of oncology drugs, in recent years, modeling approaches have been increasingly used to streamline oncologic drug development through early identification and quantification of dose-response relationships. With this background, this report reviews publications that used model-based approaches to evaluate drug treatment outcome variables in oncology therapeutics, ranging from tumor size dynamics to tumor/biomarker time courses and survival response.

Modeling Longitudinal Preclinical Tumor Size Data to Identify Transient Dynamics in Tumor Response to Antiangiogenic Drugs

Experimental evidence suggests that antiangiogenic therapy gives rise to a transient window of vessel normalization, within which the efficacy of radiotherapy and chemotherapy may be enhanced. Preclinical experiments that measure components of vessel normalization are invasive and expensive. We have developed a mathematical model of vascular tumor growth from preclinical time‐course data in a breast cancer xenograft model. We used a mixed‐effects approach for model parameterization, leveraging tumor size data to identify a period of enhanced tumor growth that could potentially correspond to the transient window of vessel normalization. We estimated the characteristics of the window for mice treated with an anti‐VEGF antibody (bevacizumab) or with a bispecific anti‐VEGF/anti‐angiopoietin‐2 antibody (vanucizumab). We show how the mathematical model could theoretically be used to predict how to coordinate antiangiogenic therapy with radiotherapy or chemotherapy to maximize therapeutic effect, reducing the need for preclinical experiments that directly measure vessel normalization parameters.

Translational Pharmacokinetic/Pharmacodynamic Modeling of Tumor Growth Inhibition Supports Dose-Range Selection of the Anti-PD-1 Antibody Pembrolizumab

Pembrolizumab, a humanized monoclonal antibody against programmed death 1 (PD‐1), has a manageable safety profile and robust clinical activity against advanced malignancies. The lowest effective dose for evaluation in further dose‐ranging studies was identified by developing a translational model from preclinical mouse experiments. A compartmental pharmacokinetic model was combined with a published physiologically based tissue compartment, linked to receptor occupancy as the driver of observed tumor growth inhibition. Human simulations were performed using clinical pharmacokinetic data, literature values, and in vitro parameters for drug distribution and binding. Biological and mathematical uncertainties were included in simulations to generate expectations for dose response. The results demonstrated a minimal increase in efficacy for doses higher than 2 mg/kg. The findings of the translational model were successfully applied to select 2 mg/kg as the lowest dose for dose‐ranging evaluations.

Tumor Static Concentration Curves in Combination Therapy

Combination therapies are widely accepted as a cornerstone for treatment of different cancer types. A tumor growth inhibition (TGI) model is developed for combinations of cetuximab and cisplatin obtained from xenograft mice. Unlike traditional TGI models, both natural cell growth and cell death are considered explicitly. The growth rate was estimated to 0.006 h^-1 and the natural cell death to 0.0039 h^-1 resulting in a tumor doubling time of 14 days. The tumor static concentrations (TSC) are predicted for each individual compound. When the compounds are given as single-agents, the required concentrations were computed to be 506 μg · mL^-1 and 56 ng · mL^-1 for cetuximab and cisplatin, respectively. A TSC curve is constructed for different combinations of the two drugs, which separates concentration combinations into regions of tumor shrinkage and tumor growth. The more concave the TSC curve is, the lower is the total exposure to test compounds necessary to achieve tumor regression. The TSC curve for cetuximab and cisplatin showed weak concavity. TSC values and TSC curves were estimated that predict tumor regression for 95% of the population by taking between-subject variability into account. The TSC concept is further discussed for different concentration-effect relationships and for combinations of three or more compounds.

Population pharmacokinetic/pharmacodynamic modeling of tumor growth kinetics in medullary thyroid cancer patients receiving cabozantinib

Nonlinear mixed effects models were developed to describe the relationship between cabozantinib exposure and target lesion tumor size in a phase III study of patients with progressive metastatic medullary thyroid cancer. These models used cabozantinib exposure estimates from a previously published population pharmacokinetic model for cabozantinib in cancer patients that was updated with data from healthy-volunteer studies. Semi-mechanistic models predict well for tumors with static, increasing, or decreasing growth over time, but they were not considered adequate for predicting tumor sizes in medullary thyroid cancer patients, among whom an early reduction in tumor size was followed by a late stabilization phase in those receiving cabozantinib. A semi-empirical tumor model adequately predicted tumor profiles that were assumed to have a net growth rate constant that was piecewise continuous in the regions of 0-110 and 110-280 days. Emax models relating average concentration to average change in tumor size predicted that an average concentration of 79 and 58 ng/ml, respectively, would yield 50% of the maximum possible tumor reduction during the first 110 days of dosing and during the subsequent 110-280 days of dosing. Simulations of tumor responses showed that daily doses of 60 mg or greater are expected to provide a similar tumor reduction. Both model evaluation of observed data and simulation results suggested that the two protocol-defined cabozantinib dose reductions from 140 to 100 mg/day and from 100 to 60 mg/day are not projected to result in a marked reduction in target lesion regrowth.

Mathematical models of breast and ovarian cancers

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website.

Using the SAEM algorithm for mechanistic joint models characterizing the relationship between nonlinear PSA kinetics and survival in prostate cancer patients

Joint modeling is increasingly popular for investigating the relationship between longitudinal and time-to-event data. However, numerical complexity often restricts this approach to linear models for the longitudinal part. Here, we use a novel development of the Stochastic-Approximation Expectation Maximization algorithm that allows joint models defined by nonlinear mixed-effect models. In the context of chemotherapy in metastatic prostate cancer, we show that a variety of patterns for the Prostate Specific Antigen (PSA) kinetics can be captured by using a mechanistic model defined by nonlinear ordinary differential equations. The use of a mechanistic model predicts that biological quantities that cannot be observed, such as treatment-sensitive and treatment-resistant cells, may have a larger impact than PSA value on survival. This suggests that mechanistic joint models could constitute a relevant approach to evaluate the efficacy of treatment and to improve the prediction of survival in patients.

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

PURPOSE

To describe the natural growth of vestibular schwannoma in patients with neurofibromatosis type 2 and to predict tumor volume evolution in patients treated with bevacizumab and everolimus.

METHODS

Clinical data, including longitudinal tumor volumes in patients treated by bevacizumab (n = 13), everolimus (n = 7) or both (n = 2), were analyzed by means of mathematical modeling techniques. Together with clinical data, data from the literature were also integrated to account for drugs mechanisms of action.

RESULTS

We developed a model of vestibular schwannoma growth that takes into account the effect of vascular endothelial growth factors and mammalian target of rapamycin complex 1 on tumor growth. Behaviors, such as tumor growth rebound following everolimus treatment stops, was correctly described with the model. Preliminary results indicate that the model can be used to predict, based on early tumor volume dynamic, tumor response to variation in treatment dose and regimen.

CONCLUSION

The developed model successfully describes tumor volume growth before and during bevacizumab and/or everolimus treatment. It might constitute a rational tool to predict patients' response to these drugs, thus potentially improving management of this disease.

Systematic evaluation of pembrolizumab dosing in patients with advanced non-small-cell lung cancer

BACKGROUND

In the phase I KEYNOTE-001 study, pembrolizumab demonstrated durable antitumor activity in patients with advanced non-small-cell lung cancer (NSCLC). We sought to characterize the relationship between pembrolizumab dose, exposure, and response to define an effective dose for these patients.

PATIENTS AND METHODS

Patients received pembrolizumab 2 mg/kg every 3 weeks (Q3W) (n = 55), 10 mg/kg Q3W (n = 238), or 10 mg/kg Q2W (n = 156). Response (RECIST v1.1) was assessed every 9 weeks. The relationship between the estimated pembrolizumab area under the concentration-time curve at steady state over 6 weeks (AUCss-6weeks) and the longitudinal change in tumor size (sum of longest diameters) was analyzed by regression and non-linear mixed effects modeling. This model was simultaneously fit to all tumor size data, then used to simulate response rates, normalizing the trial data across dose for prognostic covariates (tumor PD-L1 expression and EGFR mutation status). The exposure-safety relationship was assessed by logistic regression of pembrolizumab AUCss-6weeks versus occurrence of adverse events (AEs) of interest based on their immune etiology.

RESULTS

Overall response rates were 15% [95% confidence interval (CI) 7%-28%] at 2 mg/kg Q3W, 25% (18%-33%) at 10 mg/kg Q3W, and 21% (95% CI 14%-30%) at 10 mg/kg Q2W. Regression analyses of percentage change from baseline in tumor size versus AUCss-6weeks indicated a flat relationship (regression slope P > 0.05). Simulations showed the exposure-response relationship to be similarly flat, thus indicating that the lowest evaluated dose of 2 mg/kg Q3W to likely be at or near the efficacy plateau. Exposure-safety analysis showed the AE incidence to be similar among the clinically tested doses.

CONCLUSIONS

No significant exposure dependency on efficacy or safety was identified for pembrolizumab across doses of 2-10 mg/kg. These results support the use of a 2 mg/kg Q3W dosage in patients with previously treated, advanced NSCLC.

CLINICALTRIALSGOV REGISTRY

NCT01295827.

PK-PD modeling of individual lesion FDG-PET response to predict overall survival in patients with sunitinib-treated gastrointestinal stromal tumor

Pharmacometric models were developed to characterize the relationships between lesion-level tumor metabolic activity, as assessed by the maximum standardized uptake value (SUVmax) obtained on [(18)F]-fluorodeoxyglucose (FDG) positron emission tomography (PET), tumor size, and overall survival (OS) in 66 patients with gastrointestinal stromal tumor (GIST) treated with intermittent sunitinib. An indirect response model in which sunitinib stimulates tumor loss best described the typically rapid decrease in SUVmax during on-treatment periods and the recovery during off-treatment periods. Substantial interindividual and interlesion variability were identified in SUVmax baseline and drug sensitivity. A parametric time-to-event model identified the relative change in SUVmax at one week for the lesion with the most pronounced response as a better predictor of OS than tumor size. Based on the proposed modeling framework, early changes in FDG-PET response may serve as predictor for long-term outcome in sunitinib-treated GIST.

Formation of parametric images using mixed-effects models: a feasibility study

Mixed-effects models have been widely used in the analysis of longitudinal data. By presenting the parameters as a combination of fixed effects and random effects, mixed-effects models incorporating both within- and between-subject variations are capable of improving parameter estimation. In this work, we demonstrate the feasibility of using a non-linear mixed-effects (NLME) approach for generating parametric images from medical imaging data of a single study. By assuming that all voxels in the image are independent, we used simulation and animal data to evaluate whether NLME can improve the voxel-wise parameter estimation. For testing purposes, intravoxel incoherent motion (IVIM) diffusion parameters including perfusion fraction, pseudo-diffusion coefficient and true diffusion coefficient were estimated using diffusion-weighted MR images and NLME through fitting the IVIM model. The conventional method of non-linear least squares (NLLS) was used as the standard approach for comparison of the resulted parametric images. In the simulated data, NLME provides more accurate and precise estimates of diffusion parameters compared with NLLS. Similarly, we found that NLME has the ability to improve the signal-to-noise ratio of parametric images obtained from rat brain data. These data have shown that it is feasible to apply NLME in parametric image generation, and the parametric image quality can be accordingly improved with the use of NLME. With the flexibility to be adapted to other models or modalities, NLME may become a useful tool to improve the parametric image quality in the future. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling of Optimal Targeted Therapies Using Drug-Loaded Magnetic Nanoparticles for Liver Cancer

To enhance locoregional therapies for liver cancer treatment, we propose in this study a mathematical model to optimize the transcatheter arterial delivery of therapeutical agents. To maximize the effect of the treatment and minimize adverse effects on the patient, different mathematical models of the tumor growth are considered in this study to find the optimal number of the therapeutic drug-loaded magnetic nanoparticles to be administered. Three types of therapy models are considered, e.g., angiogenesis inhibition therapy, chemotherapy and radiotherapy. We use state-dependent Riccati equations (SDRE) as an optimal control methodology framework to the Hahnfeldt's tumor growth formulation. Based on this, design optimal rules are derived for each therapy to reduce the growth of a tumor through the administration of appropriate dose of antiangiogenic, radio- and chemo-therapeutic agents. Simulation results demonstrate the validity of the proposed optimal delivery approach, leading to reduced intervention time, low drug administration rates and optimal targeted delivery.

Pharmacodynamic modeling of adverse effects of anti-cancer drug treatment

Purpose

Adverse effects related to anti-cancer drug treatment influence patient’s quality of life, have an impact on the realized dosing regimen, and can hamper response to treatment. Quantitative models that relate drug exposure to the dynamics of adverse effects have been developed and proven to be very instrumental to optimize dosing schedules. The aims of this review were (i) to provide a perspective of how adverse effects of anti-cancer drugs are modeled and (ii) to report several model structures of adverse effect models that describe relationships between drug concentrations and toxicities.

Methods

Various quantitative pharmacodynamic models that model adverse effects of anti-cancer drug treatment were reviewed.

Results

Quantitative models describing relationships between drug exposure and myelosuppression, cardiotoxicity, and graded adverse effects like fatigue, hand-foot syndrome (HFS), rash, and diarrhea have been presented for different anti-cancer agents, including their clinical applicability.

Conclusions

Mathematical modeling of adverse effects proved to be a helpful tool to improve clinical management and support decision-making (especially in establishment of the optimal dosing regimen) in drug development. The reported models can be used as templates for modeling a variety of anti-cancer-induced adverse effects to further optimize therapy.

Comparative Effects of CT Imaging Measurement on RECIST End Points and Tumor Growth Kinetics Modeling

Quantitative assessments of tumor burden and modeling of longitudinal growth could improve phase II oncology trials. To identify obstacles to wider use of quantitative measures we obtained recorded linear tumor measurements from three published lung cancer trials. Model-based parameters of tumor burden change were estimated and compared with similarly sized samples from separate trials. Time-to-tumor growth (TTG) was computed from measurements recorded on case report forms and a second radiologist blinded to the form data. Response Evaluation Criteria in Solid Tumors (RECIST)-based progression-free survival (PFS) measures were perfectly concordant between the original forms data and the blinded radiologist re-evaluation (intraclass correlation coefficient = 1), but these routine interrater differences in the identification and measurement of target lesions were associated with an average 18-week delay (range, -20 to 55 weeks) in TTG (intraclass correlation coefficient = 0.32). To exploit computational metrics for improving statistical power in small clinical trials will require increased precision of tumor burden assessments.

A cancer treatment based on synergy between anti-angiogenic and immune cell therapies

A mathematical model integrating tumor angiogenesis and tumor-targeted cytotoxicity by immune cells was developed to identify the therapeutic window of two distinct modes to treat cancer: (1) an anti-angiogenesis treatment based on the monoclonal antibody bevacizumab that targets tumor vasculature, and (2) immunotherapy involving the injection of unlicensed dendritic cells to boost the anti-tumor adaptive response. The angiogenic cytokine Vascular Endothelial Growth Factor (VEGF) contributes to the immunosuppressive tumor microenvironment, which is responsible for the short-lived therapeutic effect of cancer-targeted immunotherapy. The effect of immunosuppression on the width of the therapeutic window of each treatment was quantified. Experimental evidence has shown that neutralizing immunosuppressive cytokines results in an enhanced immune response against infections and chronic diseases. The model was used to determine treatment protocols involving the combination of anti-VEGF and unlicensed dendritic cell injections that enhance tumor regression. The model simulations predicted that the most effective method to treat tumors involves administering a series of biweekly anti-VEGF injections to disrupt angiogenic processes and limit tumor growth. The simulations also verified the hypothesis that reducing the concentration of the immunosuppressive factor VEGF prior to an injection of unlicensed dendritic cells enhances the cytotoxicity of CD8+ T cells and results in complete tumor elimination. Feasible treatment protocols for tumors that are diagnosed late and have grown to a relatively large size were identified.