Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow-Up

Joint modeling of monocyte HLA-DR expression trajectories predicts 28-day mortality in severe SARS-CoV-2 patients

The recent SarsCov2 pandemic has disrupted healthcare system notably impacting intensive care units (ICU). In severe cases, the immune system is dysregulated, associating signs of hyperinflammation and immunosuppression. In the present work, we investigated, using a joint modeling approach, whether the trajectories of cellular immunological parameters were associated with survival of COVID-19 ICU patients. This study is based on the REA-IMMUNO-COVID cohort including 538 COVID-19 patients admitted to ICU between March 2020 and May 2022. Measurements of monocyte HLA-DR expression (mHLA-DR), counts of neutrophils, of total lymphocytes, and of CD4+ and CD8+ subsets were performed five times during the first month after ICU admission. Univariate joint models combining survival at day 28 (D28), hospital discharge and longitudinal analysis of those biomarkers' kinetics with mixed-effects models were performed prior to the building of a multivariate joint model. We showed that a higher mHLA-DR value was associated with a lower risk of death. Predicted mHLA-DR nadir cutoff value that maximized the Youden index was 5414 Ab/C and led to an AUC = 0.70 confidence interval (95%CI) = [0.65; 0.75] regarding association with D28 mortality while dynamic predictions using mHLA-DR kinetics until D7, D12 and D20 showed AUCs of 0.82 [0.77; 0.87], 0.81 [0.75; 0.87] and 0.84 [0.75; 0.93]. Therefore, the final joint model provided adequate discrimination performances at D28 after collection of biomarker samples until D7, which improved as more samples were collected. After severe COVID-19, decreased mHLA-DR expression is associated with a greater risk of death at D28 independently of usual clinical confounders.

Joint modeling of tumor dynamics and progression-free survival in advanced breast cancer: Leveraging data from amcenestrant early phase I-II trials

A joint modeling framework was developed using data from 75 patients of early amcenestrant phase I-II AMEERA-1-2 dose escalation and expansion cohorts. A semi-mechanistic tumor growth inhibition (TGI) model was developed. It accounts for the dynamics of sensitive and resistant tumor cells, an exposure-driven effect on tumor proliferation of sensitive cells, and a delay in the initiation of treatment effect to describe the time course of target lesion tumor size (TS) data. Individual treatment exposure overtime was introduced in the model using concentrations predicted by a population pharmacokinetic model of amcenestrant. This joint modeling framework integrated complex RECISTv1.1 criteria information, linked TS metrics to progression-free survival (PFS), and was externally evaluated using the randomized phase II trial AMEERA-3. We demonstrated that the instantaneous rate of change in TS (TS slope) was an important predictor of PFS and the developed joint model was able to predict well the PFS of amcenestrant phase II monotherapy trial using only early phase I-II data. This provides a good modeling and simulation tool to inform early development decisions.

Tumor growth and overall survival modeling to support decision making in phase Ib/II trials: A comparison of the joint and two-stage approaches

Model-based tumor growth inhibition (TGI) metrics are increasingly used to predict overall survival (OS) data in Phase III immunotherapy clinical trials. However, there is still a lack of understanding regarding the differences between two-stage or joint modeling methods to leverage Phase I/II trial data and help early decision-making. A recent study showed that TGI metrics such as the tumor growth rate constant KG may have good operating characteristics as early endpoints. This previous study used a two-stage approach that is easy to implement and intuitive but prone to bias as it does not account for the relationship between the longitudinal and time-to-event processes. A relevant alternative is to use a joint modeling approach. In the present article, we evaluated the operating characteristics of TGI metrics using joint modeling, assuming an OS model previously developed using historical data. To that end, we used TGI and OS data from IMpower150-a study investigating atezolizumab in over 750 patients suffering from non-small cell lung cancer-to mimic randomized Phase Ib/II trials varying in terms of number of patients included (40 to 15 patients per arm) and follow-up duration (24 to 6 weeks after the last patient included). In this context, joint modeling did not outperform the two-stage approach and provided similar operating characteristics in all the investigated scenarios. Our results suggest that KG geometric mean ratio could be used to support early decision-making provided that 30 or more patients per arm are included and followed for at least 12 weeks.

Comparison of two-stage and joint TGI-OS modeling using data from six atezolizumab clinical studies in patients with metastatic non-small cell lung cancer

Two-stage and joint modeling approaches are the two main approaches to investigate the link between longitudinal tumor size data and overall survival (OS) and anticipate clinical trial outcome. We here used a large database composed of one phase II and five phase III clinical trials evaluating atezolizumab (an immunotherapy) in monotherapy or in combination with chemotherapies in 3699 patients with non-small cell lung cancer to evaluate the differences between both approaches in terms of parameter estimates, magnitude of covariate effects, and ability to predict OS. Although the two-stage approach may underestimate the magnitude of the impact of tumor growth rate (KG ) on OS compared to joint modeling approach (hazard ratios [HRs] of 0.42-2.52 vs. 0.25-2.85, respectively, for individual KG varying from the 5th and 95th percentiles), this difference did not lead into poorer performance of the two-stage approach to describe the OS distribution in the six clinical studies. Overall, two-stage and joint modeling approaches accurately predicted OS HR with a median (range) difference with the observed OS HR of 0.02 (0.01-0.18) and 0.03 (0.00-0.19), in all cases considered, respectively (e.g., for IMpower150: 0.80 [0.66-0.95] vs. 0.82 [0.70-0.95], respectively, whereas the observed OS HR was 0.80). In our setting, the two-stage approach accurately predicted the benefit of atezolizumab on OS. Further work is needed to verify if similar results are achieved using phase Ib or phase II clinical trials where the number of patients and measurements is limited as well as in other cancer indications.

Bridging the Worlds of Pharmacometrics and Machine Learning

Precision medicine requires individualized modeling of disease and drug dynamics, with machine learning-based computational techniques gaining increasing popularity. The complexity of either field, however, makes current pharmacological problems opaque to machine learning practitioners, and state-of-the-art machine learning methods inaccessible to pharmacometricians. To help bridge the two worlds, we provide an introduction to current problems and techniques in pharmacometrics that ranges from pharmacokinetic and pharmacodynamic modeling to pharmacometric simulations, model-informed precision dosing, and systems pharmacology, and review some of the machine learning approaches to address them. We hope this would facilitate collaboration between experts, with complementary strengths of principled pharmacometric modeling and flexibility of machine learning leading to synergistic effects in pharmacological applications.

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.

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.

Joint modeling under competing risks: Application to survival prediction in patients admitted in Intensive Care Unit for sepsis with daily Sequential Organ Failure Assessment score assessments

Joint models of longitudinal process and time-to-event data have recently gained attention, notably to provide individualized dynamic predictions. In the presence of competing risks, models published mostly involve cause-specific hazard functions jointly estimated with a linear or generalized linear model. Here we propose to extend the modeling to full parametric joint estimation of a nonlinear mixed-effects model and a subdistribution hazard model. We apply this approach on 6046 patients admitted in intensive care unit (ICU) for sepsis with daily Sequential Organ Failure Assessment (SOFA) score measurements. The joint model is built on a randomly selected training set of two thirds of patients and links the current predicted SOFA measurement to the instantaneous risks of ICU death and discharge from ICU, both adjusted on the patient age. Stochastic Approximation Expectation Maximization algorithm in Monolix is used for estimation. SOFA evolution is significantly associated with both risks: 0.37, 95% confidence interval (CI) = [0.35, 0.39] for the risk of death and -0.38, 95% CI = [-0.39, -0.36] for the risk of discharge. A simulation study, inspired from the real data, shows the good estimation properties of the parameters. We assess on the validation set the added value of modeling the longitudinal SOFA follow-up for the prediction of death compared with a model that includes only SOFA at baseline. Time-dependent receiver operating characteristic area under the curve and Brier scores show that when enough longitudinal individual information is available, joint modeling provides better predictions. The methodology can easily be applied to other clinical applications because of the general form of the model.

A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics

Clinical trials investigate treatment endpoints that usually include measurements of pharmacodynamic and efficacy biomarkers in early‐phase studies and patient‐reported outcomes as well as event risks or rates in late‐phase studies. In recent years, a systematic trend in clinical trial data analytics and modeling has been observed, where retrospective data are integrated into a quantitative framework to prospectively support analyses of interim data and design of ongoing and future studies of novel therapeutics. Joint modeling is an advanced statistical methodology that allows for the investigation of clinical trial outcomes by quantifying the association between baseline and/or longitudinal biomarkers and event risk. Using an exemplar data set from non‐small cell lung cancer studies, we propose and test a workflow for joint modeling. It allows a modeling scientist to comprehensively explore the data, build survival models, investigate goodness‐of‐fit, and subsequently perform outcome predictions using interim biomarker data from an ongoing study. The workflow illustrates a full process, from data exploration to predictive simulations, for selected multivariate linear and nonlinear mixed‐effects models and software tools in an integrative and exhaustive manner.

Modelling the association between biomarkers and clinical outcome: an introduction to nonlinear joint models

Nonlinear joint models are a powerful tool to precisely analyze the association between a nonlinear biomarker and a time-to-event process, such as death. Here, we review the main methodological techniques required to build these models and to make inferences and predictions. We describe the main clinical applications and discuss the future developments of such models.

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.

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

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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.

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

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

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

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.

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.

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.

Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort

The characterization of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral kinetics in hospitalized patients and its association with mortality is unknown. We analyzed death and nasopharyngeal viral kinetics in 655 hospitalized patients from the prospective French COVID cohort. The model predicted a median peak viral load that coincided with symptom onset. Patients with age ≥65 y had a smaller loss rate of infected cells, leading to a delayed median time to viral clearance occurring 16 d after symptom onset as compared to 13 d in younger patients (P < 10-4). In multivariate analysis, the risk factors associated with mortality were age ≥65 y, male gender, and presence of chronic pulmonary disease (hazard ratio [HR] > 2.0). Using a joint model, viral dynamics after hospital admission was an independent predictor of mortality (HR = 1.31, P < 10-3). Finally, we used our model to simulate the effects of effective pharmacological interventions on time to viral clearance and mortality. A treatment able to reduce viral production by 90% upon hospital admission would shorten the time to viral clearance by 2.0 and 2.9 d in patients of age <65 y and ≥65 y, respectively. Assuming that the association between viral dynamics and mortality would remain similar to that observed in our population, this could translate into a reduction of mortality from 19 to 14% in patients of age ≥65 y with risk factors. Our results show that viral dynamics is associated with mortality in hospitalized patients. Strategies aiming to reduce viral load could have an effect on mortality rate in this population.

Early predictions of response and survival from a tumor dynamics model in patients with recurrent, metastatic head and neck squamous cell carcinoma treated with immunotherapy

We developed and evaluated a method for making early predictions of best overall response (BOR) and overall survival at 6 months (OS6) in patients with cancer treated with immunotherapy. This method combines machine learning with modeling of longitudinal tumor size data. We applied our method to data from durvalumab‐exposed patients with recurrent/metastatic head and neck cancer. A fivefold cross‐validation was used for model selection. Independent trial data, with various degrees of data truncation, were used for model validation. Mean classification error rates (90% confidence intervals [CIs]) from cross‐validation were 5.99% (90% CI 2.98%–7.50%) for BOR and 19.8% (90% CI 15.8%–39.3%) for OS6. During model validation, the area under the receiver operating characteristic curves was preserved for BOR (0.97, 0.97, and 0.94) and OS6 (0.85, 0.84, and 0.82) at 24, 18, and 12 weeks, respectively. These results suggest our method predicts trial outcomes accurately from early data and could be used to aid drug development.

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.

Comparison of Various Phase I Combination Therapy Designs in Oncology for Evaluation of Early Tumor Shrinkage Using Simulations

There is still a lack of efficient designs for identifying the dose response in oncology combination therapies in early clinical trials. The concentration response relationship can be identified using the early tumor shrinkage time course, which has been shown to be a good early response marker of clinical efficacy. The performance of various designs using an exposure–tumor growth inhibition model was explored using simulations. Different combination effects of new drug M and cetuximab (reference therapy) were explored first assuming no effect of M on cetuximab (to investigate the type I error (α)), and subsequently assuming additivity or synergy between cetuximab and M. One‐arm, two‐arm, and four‐arm designs were evaluated. In the one‐arm design, 60 patients received cetuximab + M. In the two‐arm design, 30 patients received cetuximab and 30 received cetuximab + M. In the four‐arm design, in addition to cetuximab and cetuximab + M as standard doses, combination arms with lower doses of cetuximab were evaluated (15 patients/arm). Model‐based predictions or “simulated observations” of early tumor shrinkage at week 8 (ETS8) were compared between the different arms. With the same number of individuals, the one‐arm design showed better statistical power than other designs but led to strong inflation of α in case of misestimated reference for ETS8 value. The two‐arm design protected against this misestimation and, with the same total number of subjects, would provide higher statistical power than a four‐arm design. However, a four‐arm design would be helpful for exploring more doses of cetuximab in combination with M to better understand the interaction.

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.

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."

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

Model‐informed drug development (MIDD) approaches have rapidly advanced in drug development in recent years. Additionally, the Prescription Drug User Fee Act (PDUFA) VI has specific commitments to further enhance MIDD. Tumor growth dynamic (TGD) modeling, as one of the commonly utilized MIDD approaches in oncology, fulfills the purposes to accelerate the drug development, to support new drug and biologics license applications, and to guide the market access. Increasing knowledge of TGD modeling methodologies, encouraging applications in clinical setting for patients’ survival, and complementing assessment of regulatory review for submissions, together fueled promising potentials for imminent enhancement of TGD in oncology. This review is to comprehensively summarize the history of TGD, and present case examples of the recent advance of TGD modeling (mixture model and joint model), as well as the TGD impact on regulatory decisions, thus illustrating challenges and opportunities. Additionally, this review presents the future perspectives for TGD approach.

Comparing Circulating Tumor Cell Counts with Dynamic Tumor Size Changes as Predictor of Overall Survival: A Quantitative Modeling Framework

PURPOSE

Quantitative relationships between treatment-induced changes in tumor size and circulating tumor cell (CTC) counts, and their links to overall survival (OS), are lacking. We present a population modeling framework identifying and quantifying such relationships, based on longitudinal data collected in patients with metastatic colorectal cancer (mCRC) to evaluate the value of tumor size and CTC counts as predictors of OS.

EXPERIMENTAL DESIGN

A pharmacometric approach (i.e., population pharmacodynamic modeling) was used to characterize the changes in tumor size and CTC count and evaluate them as predictors of OS in 451 patients with mCRC treated with chemotherapy and targeted therapy in a prospectively randomized phase III study (CAIRO2).

RESULTS

A tumor size model of tumor quiescence and drug resistance was used to characterize the tumor size time-course, and was, in addition to the total normalized dose (i.e., of all administered drugs) in a given cycle, related to the CTC counts through a negative binomial model (CTC model). Tumor size changes did not contribute additional predictive value when the mean CTC count was a predictor of OS. Treatment reduced the typical mean count from 1.43 to 0.477 (HR = 3.94). The modeling framework was applied to explore whether dose modifications (increased and reduced) would result in a CTC count below 1/7.5 mL after 1 to 2 weeks of treatment.

CONCLUSIONS

Time-varying CTC counts can be useful for early predicting OS in patients with mCRC, and may therefore have potential for model-based treatment individualization. Although tumor size was connected to CTC, its link to OS was weaker.

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.

Tumor Time-Course Predicts Overall Survival in Non-Small Cell Lung Cancer Patients Treated with Atezolizumab: Dependency on Follow-Up Time

The large heterogeneity in response to immune checkpoint inhibitors is driving the exploration of predictive biomarkers to identify patients who will respond to such treatment. We extended our previously suggested modeling framework of atezolizumab pharmacokinetics, IL18, and tumor size (TS) dynamics, to also include overall survival (OS). Baseline and model‐derived variables were explored as predictors of OS in 88 patients with non‐small cell lung cancer treated with atezolizumab. To investigate the impact of follow‐up length on the inclusion of predictors of OS, four different censoring strategies were applied. The time‐course of TS change was the most significant predictor in all scenarios, whereas IL18 was not significant. Identified predictors of OS were similar regardless of censoring strategy, although OS was underpredicted when patients were censored 5 months after last dose. The study demonstrated that the tumor‐time course‐OS relationship could be identified based on early phase I data.

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.

Setting the Dose of Checkpoint Inhibitors: The Role of Clinical Pharmacology

Cancer immunotherapy is based on checkpoint inhibitors (CPIs) that significantly improve the clinical outcome of several malignant diseases. These inhibitors are monoclonal antibodies (mAbs) directed at cytotoxic T lymphocyte-associated protein 4 (CTLA-4), programmed cell death 1 (PD-1), or programmed death-ligand 1 (PD-L1), sharing most of the clinical pharmacokinetic characteristics of mAb targeted therapies, all of which differ from those of cytotoxics and small molecules. Establishing the labeled dose of mAbs, and particularly of the CPIs, represents a true challenge. This review therefore examines the main criteria used for dose selection, along with their limits. The relationships between CPI pharmacokinetic parameters and treatment outcome (efficacy and/or toxicity) differ somewhat among the various drugs, but general features can be identified. Nevertheless, the interpretation of these relationships remains quite controversial. A first interpretation asserts that inter-individual pharmacokinetic variability in clearance has an impact on outcome and should be taken into consideration for dosing individualization. The second considers that higher clearance values observed in some patients result from characteristics associated with poor predictive factors of efficacy. Finally, the schedule, and particularly its frequency of administration, merits rethinking.