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

Finding the right hazard function for time-to-event modeling: A tutorial and Shiny application

Parametric time-to-event analysis is an important pharmacometric method to predict the probability of an event up until a certain time as a function of covariates and/or drug exposure. Modeling is performed at the level of the hazard function describing the instantaneous rate of an event occurring at that timepoint. We give an overview of the parametric time-to-event analysis starting with graphical exploration by Kaplan-Meier plotting for the event data including censoring and nonparametric hazard estimators such as the kernel-based visual hazard comparison for the underlying hazard. The most common hazard functions including the exponential, Gompertz, Weibull, log-normal, log-logistic, and circadian functions are described in detail. A Shiny application was developed to graphically guide the modeler which of the most common hazard functions presents a similar shape compared to the data in order to guide which hazard functions to test in the parametric time-to-event analysis. For the chosen hazard function(s), the Shiny application can additionally be used to explore corresponding parameter values to inform on suitable initial estimates for parametric modeling as well as on possible covariate or treatment relationships to certain parameters. Moreover, it can be used for the dissemination of results as well as communication, training, and workshops on time-to-event analysis. By guiding the modeler on which functions and what parameter values to test and compare as well as to assist in dissemination, the Shiny application developed here greatly supports the modeler in complicated parametric time-to-event modeling.

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.

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.

Artificial Intelligence and Mechanistic Modeling for Clinical Decision Making in Oncology

The amount of "big" data generated in clinical oncology, whether from molecular, imaging, pharmacological, or biological origin, brings novel challenges. To mine efficiently this source of information, mathematical models able to produce predictive algorithms and simulations are required, with applications for diagnosis, prognosis, drug development, or prediction of the response to therapy. Such mathematical and computational constructs can be subdivided into two broad classes: biologically agnostic, statistical models using artificial intelligence techniques, and physiologically based, mechanistic models. In this review, recent advances in the applications of such methods in clinical oncology are outlined. These include machine learning applied to big data (omics, imaging, or electronic health records), pharmacometrics and quantitative systems pharmacology, as well as tumor kinetics and metastasis modeling. Focus is set on studies with high potential of clinical translation, and particular attention is given to cancer immunotherapy. Perspectives are given in terms of combinations of the two approaches: "mechanistic learning."

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.

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.

A PK/PD Analysis of Circulating Biomarkers and Their Relationship to Tumor Response in Atezolizumab-Treated non-small Cell Lung Cancer Patients

To assess circulating biomarkers as predictors of antitumor response to atezolizumab (anti-programmed death-ligand 1 (PD-L1), Tecentriq) serum pharmacokinetic (PK) and 95 plasma biomarkers were analyzed in 88 patients with relapsed/refractory non-small cell lung cancer (NSCLC) receiving atezolizumab i.v. q3w (10-20 mg/kg) in the PCD4989g phase I clinical trial. Following exploratory analyses, two plasma biomarkers were chosen for further study and correlation with change in tumor size (the sum of the longest diameter) was assessed in a pharmacokinetic/pharmacodynamic (PK/PD) tumor modeling framework. When longitudinal kinetics of biomarkers and tumor size were modeled, tumor shrinkage was found to significantly correlate with area under the curve (AUC), baseline factors (metastatic sites, liver metastases, and smoking status), and relative change in interleukin (IL)-18 level from baseline at day 21 (RCFB_{IL -18,d21} ). Although AUC was a major predictor of tumor shrinkage, the effect was estimated to dissipate with an average half-life of 80 days, whereas RCFB_{IL -18,d21} seemed relevant to the duration of the response.

Comparison of tumor size assessments in tumor growth inhibition-overall survival models with second-line colorectal cancer data from the VELOUR study

PURPOSE

To compare lesion-level and volumetric measures of tumor burden with sum of the longest dimensions (SLD) of target lesions on overall survival (OS) predictions using time-to-growth (TTG) as predictor.

METHODS

Tumor burden and OS data from a phase 3 randomized study of second-line FOLFIRI ± aflibercept in metastatic colorectal cancer were available for 918 patients out of 1216 treated (75%). A TGI model that estimates TTG was fit to the longitudinal tumor size data (nonlinear mixed effect modeling) to estimate TTG with: SLD, sum of the measured lesion volumes (SV), individual lesion diameters (ILD), or individual lesion volumes (ILV). A parametric OS model was built with TTG estimates and assessed for prediction of the hazard ratio (HR) for survival.

RESULTS

Individual lesions had consistent dynamics within individuals. Between-lesion variability in rate constants was lower (typically < 27% CV) than inter-patient variability (typically > 50% CV). Estimates of TTG were consistent (around 12 weeks) across tumor size assessments. TTG was highly significant in a log-logistic parametric model of OS (median over 12 months). When individual lesions were considered, TTG of the fastest progressing lesions best predicted OS. TTG obtained from the lesion-level analyses were slightly better predictors of OS than estimates from the sums, with ILV marginally better than ILD. All models predicted VELOUR HR equally well and all predicted study success.

CONCLUSION

This analysis revealed consistent TGI profiles across all tumor size assessments considered. TTG predicted VELOUR HR when based on any of the tumor size measures.

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.

Exposure-Response Analysis of Necitumumab Efficacy in Squamous Non-Small Cell Lung Cancer Patients

We sought to describe the exposure-response relationship of necitumumab efficacy in squamous non-small cell lung cancer patients and evaluate intrinsic and extrinsic patient descriptors that may guide dosing. SQUIRE was a phase III study comparing necitumumab in combination with gemcitabine and cisplatin vs. gemcitabine and cisplatin alone in 1,014 patients. An integrated model for tumor size dynamics and overall survival was developed, where reduction in tumor size results in a decrease in survival hazard. The change in tumor size was characterized using linear growth and first-order shrinkage. Overall survival was described using a combination of a Weibull function and Gompertz function for the hazard, with dynamic tumor size being a predictor for the hazard. Although body weight resulted in higher clearance and lower exposure, simulations showed that an 800 mg flat dose provided optimal response regardless of body weight.