Alternate virtual populations elucidate the type I interferon signature predictive of the response to rituximab in rheumatoid arthritis

An industry perspective on current QSP trends in drug development

2023 marks the 10th anniversary of Natpara's submission to the US FDA, which led to the first recorded regulatory interaction where a decision was supported by Quantitative and Systems Pharmacology (QSP) simulations. It had taken about 5 years for the timid QSP discipline to emerge as an effective Model-Informed Drug Development (MIDD) tool with visible impact in the pharmaceutical industry. Since then, the presence of QSP in the regulatory environment has continued to increase, to the point that the Agency reported 60 QSP submissions in 2020 alone, representing ~ 4% of their annual IND submissions [1]. What sort of industry mindset has enabled QSP to reach this level of success? How does QSP fit within the MIDD paradigm? Does QSP mean the same to Discovery and to Clinical Development projects? How do 'platforms' compare to 'fit-for-purpose' QSP models in an industrial setting? Can QSP and empirical Pharmacokinetic-Pharmacodynamic (PKPD) modelling be complementary? What level of validation is required to inform drug development decisions? This article reflects on all these questions, in particular addressing those audiences with limited line-of-sight into the drug industry decision-making machinery.

Quantitative Systems Pharmacology for Rare Disease Drug Development

Though hundreds of drugs have been approved by the US Food and Drug Administration (FDA) for treating various rare diseases, most rare diseases still lack FDA-approved therapeutics. To identify the opportunities for developing therapies for these diseases, the challenges of demonstrating the efficacy and safety of a drug for treating a rare disease are highlighted herein. Quantitative systems pharmacology (QSP) has increasingly been used to inform drug development; our analysis of QSP submissions received by FDA showed that there were 121 submissions as of 2022, for informing rare disease drug development across development phases and therapeutic areas. Examples of published models for inborn errors of metabolism, non-malignant hematological disorders, and hematological malignancies were briefly reviewed to shed light on use of QSP in drug discovery and development for rare diseases. Advances in biomedical research and computational technologies can potentially enable QSP simulation of the natural history of a rare disease in the context of its clinical presentation and genetic heterogeneity. With this function, QSP may be used to conduct in-silico trials to overcome some of the challenges in rare disease drug development. QSP may play an increasingly important role in facilitating development of safe and effective drugs for treating rare diseases with unmet medical needs.

Assessing the performance of QSP models: biology as the driver for validation

Validation of a quantitative model is a critical step in establishing confidence in the model's suitability for whatever analysis it was designed. While processes for validation are well-established in the statistical sciences, the field of quantitative systems pharmacology (QSP) has taken a more piecemeal approach to defining and demonstrating validation. Although classical statistical methods can be used in a QSP context, proper validation of a mechanistic systems model requires a more nuanced approach to what precisely is being validated, and what role said validation plays in the larger context of the analysis. In this review, we summarize current thoughts of QSP validation in the scientific community, contrast the aims of statistical validation from several contexts (including inference, pharmacometrics analysis, and machine learning) with the challenges faced in QSP analysis, and use examples from published QSP models to define different stages or levels of validation, any of which may be sufficient depending on the context at hand.

In silico cancer immunotherapy trials uncover the consequences of therapy-specific response patterns for clinical trial design and outcome

Late-stage cancer immunotherapy trials often lead to unusual survival curve shapes, like delayed curve separation or a plateauing curve in the treatment arm. It is critical for trial success to anticipate such effects in advance and adjust the design accordingly. Here, we use in silico cancer immunotherapy trials - simulated trials based on three different mathematical models - to assemble virtual patient cohorts undergoing late-stage immunotherapy, chemotherapy, or combination therapies. We find that all three simulation models predict the distinctive survival curve shapes commonly associated with immunotherapies. Considering four aspects of clinical trial design - sample size, endpoint, randomization rate, and interim analyses - we demonstrate how, by simulating various possible scenarios, the robustness of trial design choices can be scrutinized, and possible pitfalls can be identified in advance. We provide readily usable, web-based implementations of our three trial simulation models to facilitate their use by biomedical researchers, doctors, and trialists.

Modeling Clinical Phenotype Variability: Consideration of Genomic Variations, Computational Methods, and Quantitative Proteomics

Advances in biomedical and computer technologies have presented the modeling community the opportunity for mechanistically modeling and simulating the variability in a disease phenotype or in a drug response. The capability to quantify response variability can inform a drug development program. Quantitative systems pharmacology scientists have published various computational approaches for creating virtual patient populations (VPops) to model and simulate drug response variability. Genomic variations can impact disease characteristics and drug exposure and response. Quantitative proteomics technologies are increasingly used to facilitate drug discovery and development and inform patient care. Incorporating variations in genomics and quantitative proteomics may potentially inform creation of VPops to model and simulate virtual patient trials, and may help account for, in a predictive manner, phenotypic variations observed clinically.

Virtual clinical trials of anti-PD-1 and anti-CTLA-4 immunotherapy in advanced hepatocellular carcinoma using a quantitative systems pharmacology model

BACKGROUND

Hepatocellular carcinoma (HCC) is the most common form of primary liver cancer and is the third-leading cause of cancer-related death worldwide. Most patients with HCC are diagnosed at an advanced stage, and the median survival for patients with advanced HCC treated with modern systemic therapy is less than 2 years. This leaves the advanced stage patients with limited treatment options. Immune checkpoint inhibitors (ICIs) targeting programmed cell death protein 1 (PD-1) or its ligand, are widely used in the treatment of HCC and are associated with durable responses in a subset of patients. ICIs targeting cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) also have clinical activity in HCC. Combination therapy of nivolumab (anti-PD-1) and ipilimumab (anti-CTLA-4) is the first treatment option for HCC to be approved by Food and Drug Administration that targets more than one immune checkpoints.

METHODS

In this study, we used the framework of quantitative systems pharmacology (QSP) to perform a virtual clinical trial for nivolumab and ipilimumab in HCC patients. Our model incorporates detailed biological mechanisms of interactions of immune cells and cancer cells leading to antitumor response. To conduct virtual clinical trial, we generate virtual patient from a cohort of 5,000 proposed patients by extending recent algorithms from literature. The model was calibrated using the data of the clinical trial CheckMate 040 (ClinicalTrials.gov number, NCT01658878).

RESULTS

Retrospective analyses were performed for different immune checkpoint therapies as performed in CheckMate 040. Using machine learning approach, we predict the importance of potential biomarkers for immune blockade therapies.

CONCLUSIONS

This is the first QSP model for HCC with ICIs and the predictions are consistent with clinically observed outcomes. This study demonstrates that using a mechanistic understanding of the underlying pathophysiology, QSP models can facilitate patient selection and design clinical trials with improved success.

Applications of Quantitative Systems Pharmacology (QSP) in Drug Development for NAFLD and NASH and Its Regulatory Application

Nonalcoholic steatohepatitis (NASH) is a widely prevalent disease, but approved pharmaceutical treatments are not available. As such, there is great activity within the pharmaceutical industry to accelerate drug development in this area and improve the quality of life and reduce mortality for NASH patients. The use of quantitative systems pharmacology (QSP) can help make this overall process more efficient. This mechanism-based mathematical modeling approach describes both the pathophysiology of a disease and how pharmacological interventions can modify pathophysiologic mechanisms. Multiple capabilities are provided by QSP modeling, including the use of model predictions to optimize clinical studies. The use of this approach has grown over the last 20 years, motivating discussions between modelers and regulators to agree upon methodologic standards. These include model transparency, documentation, and inclusion of clinical pharmacodynamic biomarkers. Several QSP models have been developed that describe NASH pathophysiology to varying extents. One specific application of NAFLDsym, a QSP model of NASH, is described in this manuscript. Simulations were performed to help understand if patient behaviors could help explain the relatively high rate of fibrosis stage reductions in placebo cohorts. Simulated food intake and body weight fluctuated periodically over time. The relatively slow turnover of liver collagen allowed persistent reductions in predicted fibrosis stage despite return to baseline for liver fat, plasma ALT, and the NAFLD activity score. Mechanistic insights such as this that have been derived from QSP models can help expedite the development of safe and effective treatments for NASH patients.

Application of different approaches to generate virtual patient populations for the quantitative systems pharmacology model of erythropoiesis

In a standard situation, a quantitative systems pharmacology model describes a "reference patient," and the model parameters are fixed values allowing only the mean values to be described. However, the results of clinical trials include a description of variability in patients' responses to a drug, which is typically expressed in terms of conventional statistical parameters, such as standard deviations (SDs) from mean values. Therefore, in this study, we propose and compare four different approaches: (1) Monte Carlo Markov Chain (MCMC); (2) model fitting to Monte Carlo sample; (3) population of clones; (4) stochastically bounded selection to generate virtual patient populations based on experimentally measured mean data and SDs. We applied these approaches to generate virtual patient populations in the QSP model of erythropoiesis. According to the results of our research, stochastically bounded selection showed slightly better results than the other three methods as it allowed the description of any number of patients from clinical trials and could be applied in the case of complex models with a large number of variable parameters.

Mathematical Modeling of Complement Pathway Dynamics for Target Validation and Selection of Drug Modalities for Complement Therapies

Motivation: The complement pathway plays a critical role in innate immune defense against infections. Dysregulation between activation and regulation of the complement pathway is widely known to contribute to several diseases. Nevertheless, very few drugs that target complement proteins have made it to the final regulatory approval because of factors such as high concentrations and dosing requirements for complement proteins and serious side effects from complement inhibition.

Methods: A quantitative systems pharmacology (QSP) model of the complement pathway has been developed to evaluate potential drug targets to inhibit complement activation in autoimmune diseases. The model describes complement activation via the alternative and terminal pathways as well as the dynamics of several regulatory proteins. The QSP model has been used to evaluate the effect of inhibiting complement targets on reducing pathway activation caused by deficiency in factor H and CD59. The model also informed the feasibility of developing small-molecule or large-molecule antibody drugs by predicting the drug dosing and affinity requirements for potential complement targets.

Results: Inhibition of several complement proteins was predicted to lead to a significant reduction in complement activation and cell lysis. The complement proteins that are present in very high concentrations or have high turnover rates (C3, factor B, factor D, and C6) were predicted to be challenging to engage with feasible doses of large-molecule antibody compounds (≤20 mg/kg). Alternatively, complement fragments that have a short half-life (C3b, C3bB, and C3bBb) were predicted to be challenging or infeasible to engage with small-molecule compounds because of high drug affinity requirements (>1 nM) for the inhibition of downstream processes. The drug affinity requirements for disease severity reduction were predicted to differ more than one to two orders of magnitude than affinities needed for the conventional 90% target engagement (TE) for several proteins. Thus, the QSP model analyses indicate the importance for accounting for TE requirements for achieving reduction in disease severity endpoints during the lead optimization stage.

Virtual Populations for Quantitative Systems Pharmacology Models

Quantitative systems pharmacology (QSP) places an emphasis on dynamic systems modeling, incorporating considerations from systems biology modeling and pharmacodynamics. The goal of QSP is often to quantitatively predict the effects of clinical therapeutics, their combinations, and their doses on clinical biomarkers and endpoints. In order to achieve this goal, strategies for incorporating clinical data into model calibration are critical. Virtual population (VPop) approaches facilitate model calibration while faced with challenges encountered in QSP model application, including modeling a breadth of clinical therapies, biomarkers, endpoints, utilizing data of varying structure and source, capturing observed clinical variability, and simulating with models that may require more substantial computational time and resources than often found in pharmacometrics applications. VPops are frequently developed in a process that may involve parameterization of isolated pathway models, integration into a larger QSP model, incorporation of clinical data, calibration, and quantitative validation that the model with the accompanying, calibrated VPop is suitable to address the intended question or help with the intended decision. Here, we introduce previous strategies for developing VPops in the context of a variety of therapeutic and safety areas: metabolic disorders, drug-induced liver injury, autoimmune diseases, and cancer. We introduce methodological considerations, prior work for sensitivity analysis and VPop algorithm design, and potential areas for future advancement. Finally, we give a more detailed application example of a VPop calibration algorithm that illustrates recent progress and many of the methodological considerations. In conclusion, although methodologies have varied, VPop strategies have been successfully applied to give valid clinical insights and predictions with the assistance of carefully defined and designed calibration and validation strategies. While a uniform VPop approach for all potential QSP applications may be challenging given the heterogeneity in use considerations, we anticipate continued innovation will help to drive VPop application for more challenging cases of greater scale while developing new rigorous methodologies and metrics.

Understanding virtual patients efficiently and rigorously by combining machine learning with dynamical modelling

Individual biological organisms are characterized by daunting heterogeneity, which precludes describing or understanding populations of ‘patients’ with a single mathematical model. Recently, the field of quantitative systems pharmacology (QSP) has adopted the notion of virtual patients (VPs) to cope with this challenge. A typical population of VPs represents the behavior of a heterogeneous patient population with a distribution of parameter values over a mathematical model of fixed structure. Though this notion of VPs is a powerful tool to describe patients’ heterogeneity, the analysis and understanding of these VPs present new challenges to systems pharmacologists. Here, using a model of the hypothalamic–pituitary–adrenal axis, we show that an integrated pipeline that combines machine learning (ML) and bifurcation analysis can be used to effectively and efficiently analyse the behaviors observed in populations of VPs. Compared with local sensitivity analyses, ML allows us to capture and analyse the contributions of simultaneous changes of multiple model parameters. Following up with bifurcation analysis, we are able to provide rigorous mechanistic insight regarding the influences of ML-identified parameters on the dynamical system’s behaviors. In this work, we illustrate the utility of this pipeline and suggest that its wider adoption will facilitate the use of VPs in the practice of systems pharmacology.

Beyond the single average tumor: Understanding IO combinations using a clinical QSP model that incorporates heterogeneity in patient response

A quantitative systems pharmacology model for metastatic melanoma was developed for immuno‐oncology with the goal of predicting efficacy of combination checkpoint therapy with pembrolizumab and ipilimumab. This literature‐based model is developed at multiple scales: (i) tumor and immune cell interactions at a lesion level; (ii) multiple heterogeneous target lesions, nontarget lesion growth, and appearance of new metastatic lesion at a patient level; and (iii) interpatient differences at a population level. The model was calibrated to pembrolizumab and ipilimumab monotherapy in patients with melanoma from Robert et al., specifically, waterfall plot showing target lesion response and overall response rate (Response Evaluation Criteria in Solid Tumors [RECIST] version 1.1), which additionally considers nontarget lesion growth and appearance of new metastatic lesions. We then used the model to predict waterfall and RECIST version 1.1 for combination treatment reported in Long et al. A key insight from this work was that nontarget lesions growth and appearance of new metastatic lesion contributed significantly to disease progression, despite reduction in target lesions. Further, the lesion level simulations of combination therapy show substantial efficacy in warm lesions (intermediary immunogenicity) but limited advantage of combination in both cold and hot lesions (low and high immunogenicity). Because many patients with metastatic disease are expected to have a mixture of these lesions, disease progression in such patients may be driven by a subset of cold lesions that are unresponsive to checkpoint inhibitors. These patients may benefit more from the combinations which include therapies to target cold lesions than double checkpoint inhibitors.

The case for AI-driven cancer clinical trials - The efficacy arm in silico

Pharmaceutical agents in oncology currently have high attrition rates from early to late phase clinical trials. Recent advances in computational methods, notably causal artificial intelligence, and availability of rich clinico-genomic databases have made it possible to simulate the efficacy of cancer drug protocols in diverse patient populations, which could inform and improve clinical trial design. Here, we review the current and potential use of in silico trials and causal AI to increase the efficacy and safety of traditional clinical trials. We conclude that in silico trials using causal AI approaches can simulate control and efficacy arms, inform patient recruitment and regimen titrations, and better enable subgroup analyses critical for precision medicine.

FDA-Industry Scientific Exchange on assessing quantitative systems pharmacology models in clinical drug development: a meeting report, summary of challenges/gaps, and future perspective

The pharmaceutical industry is actively applying quantitative systems pharmacology (QSP) to make internal decisions and guide drug development. To facilitate the eventual development of a common framework for assessing the credibility of QSP models for clinical drug development, scientists from US Food and Drug Administration and the pharmaceutical industry organized a full-day virtual Scientific Exchange on July 1, 2020. An assessment form was used to ensure consistency in the evaluation process. Among the cases presented, QSP was applied to various therapeutic areas. Applications mostly focused on phase 2 dose selection. Model transparency, including details on expert knowledge and data used for model development, was identified as a major factor for robust model assessment. The case studies demonstrated some commonalities in the workflow of QSP model development, calibration, and validation but differ in the size, scope, and complexity of QSP models, in the acceptance criteria for model calibration and validation, and in the algorithms/approaches used for creating virtual patient populations. Though efforts are being made to build the credibility of QSP models and the confidence is increasing in applying QSP for internal decisions at the clinical stages of drug development, there are still many challenges facing QSP application to late stage drug development. The QSP community needs a strategic plan that includes the ability and flexibility to Adapt, to establish Common expectations for model Credibility needed to inform drug Labeling and patient care, and to AIM to achieve the goal (ACCLAIM).

History and Future Perspectives on the Discipline of Quantitative Systems Pharmacology Modeling and Its Applications

Mathematical biology and pharmacology models have a long and rich history in the fields of medicine and physiology, impacting our understanding of disease mechanisms and the development of novel therapeutics. With an increased focus on the pharmacology application of system models and the advances in data science spanning mechanistic and empirical approaches, there is a significant opportunity and promise to leverage these advancements to enhance the development and application of the systems pharmacology field. In this paper, we will review milestones in the evolution of mathematical biology and pharmacology models, highlight some of the gaps and challenges in developing and applying systems pharmacology models, and provide a vision for an integrated strategy that leverages advances in adjacent fields to overcome these challenges.

In silico trials predict that combination strategies for enhancing vesicular stomatitis oncolytic virus are determined by tumor aggressivity

Background

Immunotherapies, driven by immune-mediated antitumorigenicity, offer the potential for significant improvements to the treatment of multiple cancer types. Identifying therapeutic strategies that bolster antitumor immunity while limiting immune suppression is critical to selecting treatment combinations and schedules that offer durable therapeutic benefits. Combination oncolytic virus (OV) therapy, wherein complementary OVs are administered in succession, offer such promise, yet their translation from preclinical studies to clinical implementation is a major challenge. Overcoming this obstacle requires answering fundamental questions about how to effectively design and tailor schedules to provide the most benefit to patients.

Methods

We developed a computational biology model of combined oncolytic vaccinia (an enhancer virus) and vesicular stomatitis virus (VSV) calibrated to and validated against multiple data sources. We then optimized protocols in a cohort of heterogeneous virtual individuals by leveraging this model and our previously established in silico clinical trial platform.

Results

Enhancer multiplicity was shown to have little to no impact on the average response to therapy. However, the duration of the VSV injection lag was found to be determinant for survival outcomes. Importantly, through treatment individualization, we found that optimal combination schedules are closely linked to tumor aggressivity. We predicted that patients with aggressively growing tumors required a single enhancer followed by a VSV injection 1 day later, whereas a small subset of patients with the slowest growing tumors needed multiple enhancers followed by a longer VSV delay of 15 days, suggesting that intrinsic tumor growth rates could inform the segregation of patients into clinical trials and ultimately determine patient survival. These results were validated in entirely new cohorts of virtual individuals with aggressive or non-aggressive subtypes.

Conclusions

Based on our results, improved therapeutic schedules for combinations with enhancer OVs can be studied and implemented. Our results further underline the impact of interdisciplinary approaches to preclinical planning and the importance of computational approaches to drug discovery and development.

Translational approaches to treating dynamical diseases through in silico clinical trials

The primary goal of drug developers is to establish efficient and effective therapeutic protocols. Multifactorial pathologies, including dynamical diseases and complex disorders, can be difficult to treat, given the high degree of inter- and intra-patient variability and nonlinear physiological relationships. Quantitative approaches combining mechanistic disease modeling and computational strategies are increasingly leveraged to rationalize pre-clinical and clinical studies and to establish effective treatment strategies. The development of clinical trials has led to new computational methods that allow for large clinical data sets to be combined with pharmacokinetic and pharmacodynamic models of diseases. Here, we discuss recent progress using in silico clinical trials to explore treatments for a variety of complex diseases, ultimately demonstrating the immense utility of quantitative methods in drug development and medicine.

Predicted Cardiac Hemodynamic Consequences of the Renal Actions of SGLT2i in the DAPA-HF Study Population: A Mathematical Modeling Analysis

The Dapagliflozin and Prevention of Adverse Outcomes in Heart Failure (DAPA-HF) study demonstrated that dapagliflozin, a sodium-glucose cotransporter-2 inhibitor (SGLT2i), reduced heart failure hospitalization and cardiovascular death in patients with heart failure with reduced ejection fraction (HF-rEF), with and without type 2 diabetes mellitus. Multiple potential mechanisms have been proposed to explain this benefit, which may be multifactorial. This study aimed to quantify the contribution of the known natriuretic/diuretic effects of SGLT2is to changes in cardiac hemodynamics, remodeling, and fluid homeostasis in the setting of HF-rEF. An integrated cardiorenal mathematical model was used to simulate inhibition of SGLT2 and its consequences on cardiac hemodynamics in a virtual population of HF-rEF patients generated by varying model parameters over physiologically plausible ranges and matching to baseline characteristics of individual DAPA-HF trial patients. Cardiovascular responses to placebo and SGLT2i over time were then simulated. The baseline characteristics of the HF-rEF virtual population and DAPA-HF were in good agreement. SGLT2i-induced diuresis and natriuresis that reduced blood volume and interstitial fluid volume, relative to placebo within 14 days. This resulted in decreased left ventricular end-diastolic volume and pressure, indicating reduced cardiac preload. Thereafter, blood volume and interstitial fluid volume again began to accumulate, but pressures and volumes remained shifted lower relative to placebo. After 1 year, left ventricle mass was lower and ejection fraction was higher than placebo. These simulations considered only hemodynamic consequences of the natriuretic/diuretic effects of SGLT2i, as other mechanisms may contribute additional benefits besides those predictions.

QSP-IO: A Quantitative Systems Pharmacology Toolbox for Mechanistic Multiscale Modeling for Immuno-Oncology Applications

Immunotherapy has shown great potential in the treatment of cancer; however, only a fraction of patients respond to treatment, and many experience autoimmune‐related side effects. The pharmaceutical industry has relied on mathematical models to study the behavior of candidate drugs and more recently, complex, whole‐body, quantitative systems pharmacology (QSP) models have become increasingly popular for discovery and development. QSP modeling has the potential to discover novel predictive biomarkers as well as test the efficacy of treatment plans and combination therapies through virtual clinical trials. In this work, we present a QSP modeling platform for immuno‐oncology (IO) that incorporates detailed mechanisms for important immune interactions. This modular platform allows for the construction of QSP models of IO with varying degrees of complexity based on the research questions. Finally, we demonstrate the use of the platform through two example applications of immune checkpoint therapy.

Determinants of combination GM-CSF immunotherapy and oncolytic virotherapy success identified through in silico treatment personalization

Oncolytic virotherapies, including the modified herpes simplex virus talimogene laherparepvec (T-VEC), have shown great promise as potent instigators of anti-tumour immune effects. The OPTiM trial, in particular, demonstrated the superior anti-cancer effects of T-VEC as compared to systemic immunotherapy treatment using exogenous administration of granulocyte-macrophage colony-stimulating factor (GM-CSF). Theoretically, a combined approach leveraging exogenous cytokine immunotherapy and oncolytic virotherapy would elicit an even greater immune response and improve patient outcomes. However, regimen scheduling of combination immunostimulation and T-VEC therapy has yet to be established. Here, we calibrate a computational biology model of sensitive and resistant tumour cells and immune interactions for implementation into an in silico clinical trial to test and individualize combination immuno- and virotherapy. By personalizing and optimizing combination oncolytic virotherapy and immunostimulatory therapy, we show improved simulated patient outcomes for individuals with late-stage melanoma. More crucially, through evaluation of individualized regimens, we identified determinants of combination GM-CSF and T-VEC therapy that can be translated into clinically-actionable dosing strategies without further personalization. Our results serve as a proof-of-concept for interdisciplinary approaches to determining combination therapy, and suggest promising avenues of investigation towards tailored combination immunotherapy/oncolytic virotherapy.

The advent of biological therapies for anti-cancer treatment has had a significant impact on patient outcomes. Targeted xenobiotics, including oncolytic viruses, in combination with existing, more general, immunotherapies like exogenous cytokines show great promise for continuing to improve cancer care. However, determining optimal combination regimens can be difficult, given that testing proposed schedules would require large cohorts of patients enrolled in clinical trials. Fortunately, computational biology can help to address treatment scheduling while simultaneously helping to unravel the mechanisms driving therapeutic responses. In this work, we integrate a mathematical model of GM-CSF and talimogene laherparepvec (T-VEC) oncolytic virotherapy into a virtual clinical trial to optimize their administration in combination. Using this platform, we inferred a clinically-actionable combination schedule for patients with late-stage melanoma that significantly improved virtual patient outcome when compared to GM-CSF and T-VEC monotherapies, and a standard combination strategy. Our results outline a rational approach to therapy optimization with meaningful consequences for how we effectively design and implement clinical trials to maximize their success, and how we treat melanoma with combined immuno- and virotherapy.

Applications of Quantitative Systems Pharmacology in Model-Informed Drug Discovery: Perspective on Impact and Opportunities

Quantitative systems pharmacology (QSP) approaches have been increasingly applied in the pharmaceutical since the landmark white paper published in 2011 by a National Institutes of Health working group brought attention to the discipline. In this perspective, we discuss QSP in the context of other modeling approaches and highlight the impact of QSP across various stages of drug development and therapeutic areas. We discuss challenges to the field as well as future opportunities.

Translational Quantitative Systems Pharmacology in Drug Development: from Current Landscape to Good Practices

Systems pharmacology approaches have the capability of quantitatively linking the key biological molecules relevant to a drug candidate's mechanism of action (drug-induced signaling pathways) to the clinical biomarkers associated with the proposed target disease, thereby quantitatively facilitating its development and life cycle management. In this review, the model attributes of published quantitative systems pharmacology (QSP) modeling for lowering cholesterol, treating salt-sensitive hypertension, and treating rare diseases as well as describing bone homeostasis and related pharmacological effects are critically reviewed with respect to model quality, calibration, validation, and performance. We further reviewed the common practices in optimizing QSP modeling and prediction. Notably, leveraging genetics and genomic studies for model calibration and validation is common. Statistical and quantitative assessment of QSP prediction and handling of model uncertainty are, however, mostly lacking as are the quantitative and statistical criteria for assessing QSP predictions and the covariance matrix of coefficients between the parameters in a validated virtual population. To accelerate advances and application of QSP with consistent quality, a list of key questions is proposed to be addressed when assessing the quality of a QSP model in hopes of stimulating the scientific community to set common expectations. The common expectations as to what constitutes the best QSP modeling practices, which the scientific community supports, will advance QSP modeling in the realm of informed drug development. In the long run, good practices will extend the life cycles of QSP models beyond the life cycles of individual drugs.

Exploration of sexual dimorphism and inter-individual variability in multivariate parameter spaces for a pharmacokinetic compartment model

Pharmacokinetic models are particularly useful to study the underlying and complex physiological mechanisms contributing to clinical differences across patient subgroups or special populations. Unfortunately, the inherent variability of biological systems and knowledge gaps in physiological data limit confidence in model predictions for special populations. Sourcing data to reflect the desired physiologies can be resource intensive, particularly for a larger model. Thus, a critical step in model development for special populations involves an in-depth analysis of model inputs, which can be guided by Monte Carlo simulations. Such an approach enables the generation of parameter values by stochastic sampling that are subsequently restricted to the combinations that describe biologically plausible or target model output. Our approach utilized a published pharmacokinetic compartmental model to demonstrate how sampling in conjunction with global sensitivity analysis can be used to explore sexual dimorphism and inter-individual variability in multivariate parameter spaces for differentiation of model input and behavior across phenotypes. Despite limiting the model output to relatively narrow ranges, male and female phenotypes were associated with wide variability in both individual parameter values and combinations of parameters. Through an integrated approach using a support vector machine, principal component analysis and global sensitivity analysis, our approach revealed that specific combinations of parameters gave rise to a certain phenotype, while individual parameters influenced the shape of plasma concentration profile. Augmenting analysis of the model input with global sensitivity analysis enabled an understanding of both sexual dimorphism and inter-individual variability in pharmacokinetics. While the current study revealed how model input could be separated by sex for a simple compartment model, the approach could be extended to other patient factors, such as age or disease, and to a more complex physiologically-based model that describes absorption, distribution, metabolism, and elimination with more detail.

A Survey of Software Tool Utilization and Capabilities for Quantitative Systems Pharmacology: What We Have and What We Need

Quantitative systems pharmacology (QSP) is a rapidly emerging discipline with application across a spectrum of challenges facing the pharmaceutical industry, including mechanistically informed prioritization of target pathways and combinations in discovery, target population, and dose expansion decisions early in clinical development, and analyses for regulatory authorities late in clinical development. QSP's development has influences from physiologic modeling, systems biology, physiologically‐based pharmacokinetic modeling, and pharmacometrics. Given a varied scientific heritage, a variety of tools to accomplish the demands of model development, application, and model‐based analysis of available data have been developed. We report the outcome from a community survey and resulting analysis of how modelers view the impact and growth of QSP, how they utilize existing tools, and capabilities they need improved to further accelerate their impact on drug development. These results serve as a benchmark and roadmap for advancements to the QSP tool set.

The Virtual Anemia Trial: An Assessment of Model-Based In Silico Clinical Trials of Anemia Treatment Algorithms in Patients With Hemodialysis

In silico approaches have been proposed as a novel strategy to increase the repertoire of clinical trial designs. Realistic simulations of clinical trials can provide valuable information regarding safety and limitations of treatment protocols and have been shown to assist in the cost‐effective planning of clinical studies. In this report, we present a blueprint for the stepwise integration of internal, external, and ecological validity considerations in virtual clinical trials (VCTs). We exemplify this approach in the context of a model‐based in silico clinical trial aimed at anemia treatment in patients undergoing hemodialysis (HD). Hemoglobin levels and subsequent anemia treatment were simulated on a per patient level over the course of a year and compared to real‐life clinical data of 79,426 patients undergoing HD. The novel strategies presented here, aimed to improve external and ecological validity of a VCT, significantly increased the predictive power of the discussed in silico trial.

Linear-In-Flux-Expressions Methodology: Toward a Robust Mathematical Framework for Quantitative Systems Pharmacology Simulators

Quantitative Systems Pharmacology (QSP) modeling is increasingly used as a quantitative tool for advancing mechanistic hypotheses on the mechanism of action of a drug, and its pharmacological effect in relevant disease phenotypes, to enable linking the right drug to the right patient. Application of QSP models relies on creation of virtual populations for simulating scenarios of interest. Creation of virtual populations requires 2 important steps, namely, identification of a subset of model parameters that can be associated with a phenotype of disease and development of a sampling strategy from identified distributions of these parameters. We improve on existing sampling methodologies by providing a means of representing the structural relationship across model parameters and describing propagation of variability in the model. This gives a robust, systematic method for creating a virtual population. We have developed the Linear-In-Flux-Expressions (LIFE) method to simulate variability in patient pharmacokinetics and pharmacodynamics using relationships between parameters at baseline to create a virtual population. We demonstrate the importance of this methodology on a model of cholesterol metabolism. The LIFE methodology brings us a step closer toward improved QSP simulators through enhanced capture of the observed variability in drug and disease clinical data.

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.

QSP Toolbox: Computational Implementation of Integrated Workflow Components for Deploying Multi-Scale Mechanistic Models

Quantitative systems pharmacology (QSP) modeling has become increasingly important in pharmaceutical research and development, and is a powerful tool to gain mechanistic insights into the complex dynamics of biological systems in response to drug treatment. However, even once a suitable mathematical framework to describe the pathophysiology and mechanisms of interest is established, final model calibration and the exploration of variability can be challenging and time consuming. QSP models are often formulated as multi-scale, multi-compartment nonlinear systems of ordinary differential equations. Commonly accepted modeling strategies, workflows, and tools have promise to greatly improve the efficiency of QSP methods and improve productivity. In this paper, we present the QSP Toolbox, a set of functions, structure array conventions, and class definitions that computationally implement critical elements of QSP workflows including data integration, model calibration, and variability exploration. We present the application of the toolbox to an ordinary differential equations-based model for antibody drug conjugates. As opposed to a single stepwise reference model calibration, the toolbox also facilitates simultaneous parameter optimization and variation across multiple in vitro, in vivo, and clinical assays to more comprehensively generate alternate mechanistic hypotheses that are in quantitative agreement with available data. The toolbox also includes scripts for developing and applying virtual populations to mechanistic exploration of biomarkers and efficacy. We anticipate that the QSP Toolbox will be a useful resource that will facilitate implementation, evaluation, and sharing of new methodologies in a common framework that will greatly benefit the community.

Drug-disease modeling in the pharmaceutical industry - where mechanistic systems pharmacology and statistical pharmacometrics meet

Modeling & simulation (M&S) methodologies are established quantitative tools, which have proven to be useful in supporting the research, development (R&D), regulatory approval, and marketing of novel therapeutics. Applications of M&S help design efficient studies and interpret their results in context of all available data and knowledge to enable effective decision-making during the R&D process. In this mini-review, we focus on two sets of modeling approaches: population-based models, which are well-established within the pharmaceutical industry today, and fall under the discipline of clinical pharmacometrics (PMX); and systems dynamics models, which encompass a range of models of (patho-)physiology amenable to pharmacological intervention, of signaling pathways in biology, and of substance distribution in the body (today known as physiologically-based pharmacokinetic models) - which today may be collectively referred to as quantitative systems pharmacology models (QSP). We next describe the convergence - or rather selected integration - of PMX and QSP approaches into 'middle-out' drug-disease models, which retain selected mechanistic aspects, while remaining parsimonious, fit-for-purpose, and able to address variability and the testing of covariates. We further propose development opportunities for drug-disease systems models, to increase their utility and applicability throughout the preclinical and clinical spectrum of pharmaceutical R&D.

From PK/PD to QSP: Understanding the Dynamic Effect of Cholesterol-Lowering Drugs on Atherosclerosis Progression and Stratified Medicine

Current computational and mathematical tools are demonstrating the high value of using systems modeling approaches (e.g. Quantitative Systems Pharmacology) to understand the effect of a given compound on the biological and physiological mechanisms related to a specific disease. This review provides a short survey of the evolution of the mathematical approaches used to understand the effect of particular cholesterol-lowering drugs, from pharmaco-kinetic (PK) / pharmaco-dynamic (PD) models, through physiologically based pharmacokinetic models (PBPK) to QSP. These mathematical models introduce more mechanistic information related to the effect of these drugs on atherosclerosis progression and demonstrate how QSP could open new ways for stratified medicine in this field.

A Six-Stage Workflow for Robust Application of Systems Pharmacology

Quantitative and systems pharmacology (QSP) is increasingly being applied in pharmaceutical research and development. One factor critical to the ultimate success of QSP is the establishment of commonly accepted language, technical criteria, and workflows. We propose an integrated workflow that bridges conceptual objectives with underlying technical detail to support the execution, communication, and evaluation of QSP projects.

Quantitative Systems Pharmacology: A Framework for Context

Quantitative Systems Pharmacology (QSP) is receiving increased attention. As the momentum builds and the expectations grow it is important to (re)assess and formalize the basic concepts and approaches. In this short review, I argue that QSP, in addition to enabling the rational integration of data and development of complex models, maybe more importantly, provides the foundations for developing an integrated framework for the assessment of drugs and their impact on disease within a broader context expanding the envelope to account in great detail for physiology, environment and prior history. I articulate some of the critical enablers, major obstacles and exciting opportunities manifesting themselves along the way. Charting such overarching themes will enable practitioners to identify major and defining factors as the field progressively moves towards personalized and precision health care delivery.

Efficient Generation and Selection of Virtual Populations in Quantitative Systems Pharmacology Models

Quantitative systems pharmacology models mechanistically describe a biological system and the effect of drug treatment on system behavior. Because these models rarely are identifiable from the available data, the uncertainty in physiological parameters may be sampled to create alternative parameterizations of the model, sometimes termed "virtual patients." In order to reproduce the statistics of a clinical population, virtual patients are often weighted to form a virtual population that reflects the baseline characteristics of the clinical cohort. Here we introduce a novel technique to efficiently generate virtual patients and, from this ensemble, demonstrate how to select a virtual population that matches the observed data without the need for weighting. This approach improves confidence in model predictions by mitigating the risk that spurious virtual patients become overrepresented in virtual populations.

A Mechanistic Systems Pharmacology Model for Prediction of LDL Cholesterol Lowering by PCSK9 Antagonism in Human Dyslipidemic Populations

PCSK9 is a promising target for the treatment of hyperlipidemia and cardiovascular disease. A Quantitative Systems Pharmacology model of the mechanisms of action of statin and anti-PCSK9 therapies was developed to predict low density lipoprotein (LDL) changes in response to anti-PCSK9 mAb for different treatment protocols and patient subpopulations. Mechanistic interactions and cross-regulation of LDL, LDL receptor, and PCSK9 were modeled, and numerous virtual subjects were developed and validated against clinical data. Simulations predict a slightly greater maximum percent reduction in LDL cholesterol (LDLc) when anti-PCSK9 is administered on statin background therapy compared to as a monotherapy. The difference results primarily from higher PCSK9 levels in patients on statin background. However, higher PCSK9 levels are also predicted to increase clearance of anti-PCSK9, resulting in a faster rebound of LDLc. Simulations of subjects with impaired LDL receptor (LDLR) function predict compromised anti-PCSK9 responses in patients such as homozygous familial hypercholesterolemics, whose functional LDLR is below 10% of normal.

Systems biology for simulating patient physiology during the postgenomic era of medicine

Systems pharmacology models capable of accurately recapitulating sophisticated patient phenotypes have enabled the investigation of mechanisms responsible for therapeutic efficacy. Although omics data sets are capable of characterizing the operation of subcellular networks, their utility in mechanistically predicting quantitative, clinically accessible outcome measures has been limited. Developing insights into clinical outcomes from omics data sets will benefit from modeling approaches that can integrate molecular networks mechanistically with simulations of patient pathophysiology across compartments and scales.

Systems toxicology: from basic research to risk assessment

Systems Toxicology is the integration of classical toxicology with quantitative analysis of large networks of molecular and functional changes occurring across multiple levels of biological organization. Society demands increasingly close scrutiny of the potential health risks associated with exposure to chemicals present in our everyday life, leading to an increasing need for more predictive and accurate risk-assessment approaches. Developing such approaches requires a detailed mechanistic understanding of the ways in which xenobiotic substances perturb biological systems and lead to adverse outcomes. Thus, Systems Toxicology approaches offer modern strategies for gaining such mechanistic knowledge by combining advanced analytical and computational tools. Furthermore, Systems Toxicology is a means for the identification and application of biomarkers for improved safety assessments. In Systems Toxicology, quantitative systems-wide molecular changes in the context of an exposure are measured, and a causal chain of molecular events linking exposures with adverse outcomes (i.e., functional and apical end points) is deciphered. Mathematical models are then built to describe these processes in a quantitative manner. The integrated data analysis leads to the identification of how biological networks are perturbed by the exposure and enables the development of predictive mathematical models of toxicological processes. This perspective integrates current knowledge regarding bioanalytical approaches, computational analysis, and the potential for improved risk assessment.