A Mechanism-based Disease Progression Model for Comparison of Long-term Effects of Pioglitazone, Metformin and Gliclazide on Disease Processes Underlying Type 2 Diabetes Mellitus

Dynamical modeling the effect of glucagon-like peptide on glucose-insulin regulatory system based on mice experimental observation

As an emerging global epidemic, type 2 diabetes mellitus (T2DM) represents one of the leading causes of morbidity and mortality worldwide. Existing evidences demonstrated that glucagon-like peptide-1 (GLP-1) modulate the glucose regulatory system by enhancing the β-cell function. However, the detailed process of GLP-1 in glycaemic regulator for T2DM remains to be clarified. Thus, in this study, we propose an Institute of Cancer Research (ICR) mice high fat and cholesterol dietary experimental data-driven mathematical model to investigate the secretory effect of GLP-1 on the dynamics of glucose-insulin regulatory system. Specifically, we develop a mathematical model of GLP-1 dynamics as part of the interaction model of β-cell, insulin, and glucose dynamics. The parameter estimation and data fitting are in agreement with the data in mice experiments In addition, uncertainty quantification is performed to explore the possible factors that influence the pathways leading to the pathological state. Model analyses reveal that the high fat or high cholesterol diet stimulated GLP-1 plays an important role in the dynamics of glucose, insulin and β cells in short-term. These results show that enhanced GLP-1 may mitigate the dysregulation of glucose-insulin regulatory system via promoting the β cells function and stimulating secretion of insulin, which offers an in-depth insights into the mechanistic of hyperglycemia from dynamical approach and provide the theoretical basis for GLP-1 served as a potential clinical targeted drug for treatment of T2DM.

A data-driven computational model for obesity-driven diabetes onset and remission through weight loss

Obesity is a major risk factor for the development of type 2 diabetes (T2D), where a sustained weight loss may result in T2D remission in individuals with obesity. To design effective and feasible intervention strategies to prevent or reverse T2D, it is imperative to study the progression of T2D and remission together. Unfortunately, this is not possible through experimental and observational studies. To address this issue, we introduce a data-driven computational model and use human data to investigate the progression of T2D with obesity and remission through weight loss on the same timeline. We identify thresholds for the emergence of T2D and necessary conditions for remission. We explain why remission is only possible within a window of opportunity and the way that window depends on the progression history of T2D, individual's metabolic state, and calorie restrictions. These findings can help to optimize therapeutic intervention strategies for T2D prevention or treatment.

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

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

Modeling the progression of Type 2 diabetes with underlying obesity

Environmentally induced or epigenetic-related beta-cell dysfunction and insulin resistance play a critical role in the progression to diabetes. We developed a mathematical modeling framework capable of studying the progression to diabetes incorporating various diabetogenic factors. Considering the heightened risk of beta-cell defects induced by obesity, we focused on the obesity-diabetes model to further investigate the influence of obesity on beta-cell function and glucose regulation. The model characterizes individualized glucose and insulin dynamics over the span of a lifetime. We then fit the model to the longitudinal data of the Pima Indian population, which captures both the fluctuations and long-term trends of glucose levels. As predicted, controlling or eradicating the obesity-related factor can alleviate, postpone, or even reverse diabetes. Furthermore, our results reveal that distinct abnormalities of beta-cell function and levels of insulin resistance among individuals contribute to different risks of diabetes. This study may encourage precise interventions to prevent diabetes and facilitate individualized patient treatment.

Clinical-GAN: Trajectory forecasting of clinical events using transformer and Generative Adversarial Networks

Predicting the trajectory of a disease at an early stage can aid physicians in offering effective treatment, prompt care to patients, and also avoid misdiagnosis. However, forecasting patient trajectories is challenging due to long-range dependencies, irregular intervals between consecutive admissions, and non-stationarity data. To address these challenges, we propose a novel method called Clinical-GAN, a Transformer-based Generative Adversarial Networks (GAN) to forecast the patients' medical codes for subsequent visits. First, we represent the patients' medical codes as a time-ordered sequence of tokens akin to language models. Then, a Transformer mechanism is used as a Generator to learn from existing patients' medical history and is trained adversarially against a Transformer-based Discriminator. We address the above mentioned challenges based on our data modeling and Transformer-based GAN architecture. Additionally, we enable the local interpretation of the model's prediction using a multi-head attention mechanism. We evaluated our method using a publicly available dataset, Medical Information Mart for Intensive Care IV v1.0 (MIMIC-IV), with more than 500,000 visits completed by around 196,000 adult patients over an 11-year period from 2008-2019. Clinical-GAN significantly outperforms baseline methods and existing works, as demonstrated through various experiments. Source code is at https://github.com/vigi30/Clinical-GAN.

Pharmacometrics: The Already-Present Future of Precision Pharmacology

The use of mathematical modeling to represent, analyze, make predictions or providing information on data obtained in drug research and development has made pharmacometrics an area of great prominence and importance. The main purpose of pharmacometrics is to provide information relevant to the search for efficacy and safety improvements in pharmacotherapy. Regulatory agencies have adopted pharmacometrics analysis to justify their regulatory decisions, making those decisions more efficient. Demand for specialists trained in the field is therefore growing. In this review, we describe the meaning, history, and development of pharmacometrics, analyzing the challenges faced in the training of professionals. Examples of applications in current use, perspectives for the future, and the importance of pharmacometrics for the development and growth of precision pharmacology are also presented.

Role of Disease Progression Models in Drug Development

The use of Disease progression models (DPMs) in Drug Development has been widely adopted across therapeutic areas as a method for integrating previously obtained disease knowledge to elucidate the impact of novel therapeutics or vaccines on disease course, thus quantifying the potential clinical benefit at different stages of drug development programs. This paper provides a brief overview of DPMs and the evolution in data types, analytic methods, and applications that have occurred in their use by Quantitive Clinical Pharmacologists. It also provides examples of how these models have informed decisions and clinical trial design across several therapeutic areas and at various stages of development. It briefly describes potential new applications of DPMs utilizing emerging data sources, and utilizing new analytic techniques, and discuss new challenges faced such as requiring description of multiple endpoints, rapid model development, application of machine learning-based analytics, and use of high dimensional and real-world data. Considerations for the continued evolution future of DPMs to serve as community-maintained expert systems are also provided.

Solving the Evidence Interpretability Crisis in Health Technology Assessment: A Role for Mechanistic Models?

Health technology assessment (HTA) aims to be a systematic, transparent, unbiased synthesis of clinical efficacy, safety, and value of medical products (MPs) to help policymakers, payers, clinicians, and industry to make informed decisions. The evidence available for HTA has gaps—impeding timely prediction of the individual long-term effect in real clinical practice. Also, appraisal of an MP needs cross-stakeholder communication and engagement. Both aspects may benefit from extended use of modeling and simulation. Modeling is used in HTA for data-synthesis and health-economic projections. In parallel, regulatory consideration of model informed drug development (MIDD) has brought attention to mechanistic modeling techniques that could in fact be relevant for HTA. The ability to extrapolate and generate personalized predictions renders the mechanistic MIDD approaches suitable to support translation between clinical trial data into real-world evidence. In this perspective, we therefore discuss concrete examples of how mechanistic models could address HTA-related questions. We shed light on different stakeholder's contributions and needs in the appraisal phase and suggest how mechanistic modeling strategies and reporting can contribute to this effort. There are still barriers dissecting the HTA space and the clinical development space with regard to modeling: lack of an adapted model validation framework for decision-making process, inconsistent and unclear support by stakeholders, limited generalizable use cases, and absence of appropriate incentives. To address this challenge, we suggest to intensify the collaboration between competent authorities, drug developers and modelers with the aim to implement mechanistic models central in the evidence generation, synthesis, and appraisal of HTA so that the totality of mechanistic and clinical evidence can be leveraged by all relevant stakeholders.

Extrapolation as a Default Strategy in Pediatric Drug Development

Pediatric drug development lags adult development by about 8 years (Mulugeta et al. in Pediatr Clin 64(6):1185-1196, 2017). In such context, many incentives, regulations, and innovative techniques have been proposed to address the disparity for pediatric patients. One such strategy is extrapolation of efficacy from a reference population. Extrapolation is currently justified by providing evidence in support of the effective use of drugs in children when the course of the disease and the expected treatment response would be sufficiently similar in the pediatric and reference population. This paper's position is that, despite uncertainties, pediatric drug development programs should initially assume some degree of extrapolation. The degree to which extrapolation can be used lies along a continuum representing the uncertainties to be addressed through generation of new pediatric evidence. In addressing these uncertainties, the extrapolation strategy should reflect the level of tolerable uncertainty concerning the decision to expose a child to the risks of a new drug. This judgment about the level of tolerable uncertainty should vary with the context (e.g., disease severity, existing therapeutic options) and can be embedded into pediatric drug development archetypes to ascertain the extent of studies needed and whether simultaneous development for adults and adolescents be considered.

CKD subpopulations defined by risk-factors: A longitudinal analysis of electronic health records

Chronic kidney disease (CKD) is a progressive disease that evades early detection and is associated with various comorbidities. Although clinical comprehension and control of these comorbidities is crucial for CKD management, complex pathophysiological interactions and feedback loops make this a formidable task. We have developed a hybrid semimechanistic modeling methodology to investigate CKD progression. The model is represented as a system of ordinary differential equations with embedded neural networks and takes into account complex disease progression pathways, feedback loops, and effects of 53 medications to generate time trajectories of eight clinical biomarkers that capture CKD progression due to various risk factors. The model was applied to real world data of US patients with CKD to map the available longitudinal information onto a set of time‐invariant patient‐specific parameters with a clear biological interpretation. These parameters describing individual patients were used to segment the cohort using a clustering approach. Model‐based simulations were conducted to investigate cluster‐specific treatment strategies. The model was able to reliably reproduce the variability in biomarkers across the cohort. The clustering procedure segmented the cohort into five subpopulations – four with enhanced sensitivity to a specific risk factor (hypertension, hyperlipidemia, hyperglycemia, or impaired kidney) and one that is largely insensitive to any of the risk factors. Simulation studies were used to identify patient‐specific strategies to restrain or prevent CKD progression through management of specific risk factors. The semimechanistic model enables identification of disease progression phenotypes using longitudinal data that aid in prioritizing treatment strategies at individual patient level.

The personalized medicine discourse: archaeology and genealogy

Personalized Medicine (PM) is an evolving and often missinterpreted concept and no agreement of personalization exist. We examined the PM discourse towards foucauldian archeological and genealogical analysis to understand the meaning of "personalization" in medicine. In the archaeological analysis, the historical evolution is characterized by the coexistence of two epistemologies: the holistic vision and the omic sciences. The genealogical analysis shows how these epistemologies may affect the meaning of "person" and, consequently, the ontology of patients. Additionally, substitutions/confusions of the term PM are related to continuously evolving medical knowledge and new technologies; different etymological roots of "personalization" and "person"; and cultural differences. In conclusion, if the definition of "personalization" in medicine is not clear, patients might get wrong expectations about what is achievable for their health. Therefore, epistemological trends should not be separated as they drive same goals: providing accurate diagnosis and treatments based on large data to predict disease progression.

Metabolic Modeling Combined With Machine Learning Integrates Longitudinal Data and Identifies the Origin of LXR-Induced Hepatic Steatosis

Temporal multi-omics data can provide information about the dynamics of disease development and therapeutic response. However, statistical analysis of high-dimensional time-series data is challenging. Here we develop a novel approach to model temporal metabolomic and transcriptomic data by combining machine learning with metabolic models. ADAPT (Analysis of Dynamic Adaptations in Parameter Trajectories) performs metabolic trajectory modeling by introducing time-dependent parameters in differential equation models of metabolic systems. ADAPT translates structural uncertainty in the model, such as missing information about regulation, into a parameter estimation problem that is solved by iterative learning. We have now extended ADAPT to include both metabolic and transcriptomic time-series data by introducing a regularization function in the learning algorithm. The ADAPT learning algorithm was (re)formulated as a multi-objective optimization problem in which the estimation of trajectories of metabolic parameters is constrained by the metabolite data and refined by gene expression data. ADAPT was applied to a model of hepatic lipid and plasma lipoprotein metabolism to predict metabolic adaptations that are induced upon pharmacological treatment of mice by a Liver X receptor (LXR) agonist. We investigated the excessive accumulation of triglycerides (TG) in the liver resulting in the development of hepatic steatosis. ADAPT predicted that hepatic TG accumulation after LXR activation originates for 80% from an increased influx of free fatty acids. The model also correctly estimated that TG was stored in the cytosol rather than transferred to nascent very-low density lipoproteins. Through model-based integration of temporal metabolic and gene expression data we discovered that increased free fatty acid influx instead of de novo lipogenesis is the main driver of LXR-induced hepatic steatosis. This study illustrates how ADAPT provides estimates for biomedically important parameters that cannot be measured directly, explaining (side-)effects of pharmacological treatment with LXR agonists.

cLRT-Mod: An efficient methodology for pharmacometric model-based analysis of longitudinal phase II dose finding studies under model uncertainty

Within the challenging context of phase II dose-finding trials, longitudinal analyses may increase drug effect detection power compared to an end-of-treatment analysis. This work proposes cLRT-Mod, a pharmacometric adaptation of the MCP-Mod methodology, which allows the use of nonlinear mixed effect models to first detect a dose-response signal and then identify the doses for the confirmatory phase while accounting for model structure uncertainty. The method was evaluated through extensive clinical trial simulations of a hypothetical phase II dose-finding trial using different scenarios and comparing different methods such as MCP-Mod. The results show an increase in power using cLRT with longitudinal data compared to an EOT multiple contrast tests for scenarios with small sample size and weak drug effect while maintaining pre-specifiability of the models prior to data analysis and the nominal type I error. This work shows how model averaging provides better coverage probability of the drug effect in the prediction step, and avoids under-estimation of the size of the confidence interval. Finally, for illustration purpose cLRT-Mod was applied to the analysis of a real phase II dose-finding trial.

A mathematical model of food intake

The metabolic, hormonal and psychological determinants of the feeding behavior in humans are numerous and complex. A plausible model of the initiation, continuation and cessation of meals taking into account the most relevant such determinants would be very useful in simulating food intake over hours to days, thus providing input into existing models of nutrient absorption and metabolism. In the present work, a meal model is proposed, incorporating stomach distension, glycemic variations, ghrelin dynamics, cultural habits and influences on the initiation and continuation of meals, reflecting a combination of hedonic and appetite components. Given a set of parameter values (portraying a single subject), the timing and size of meals are stochastic. The model parameters are calibrated so as to reflect established medical knowledge on data of food intake from the National Health and Nutrition Examination Survey (NHANES) database during years 2015 and 2016.

Type 2 diabetes: one disease, many pathways

Diabetes is a chronic, progressive disease that calls for longitudinal data and analysis. We introduce a longitudinal mathematical model that is capable of representing the metabolic state of an individual at any point in time during their progression from normal glucose tolerance to type 2 diabetes (T2D) over a period of years. As an application of the model, we account for the diversity of pathways typically followed, focusing on two extreme alternatives, one that goes through impaired fasting glucose (IFG) first and one that goes through impaired glucose tolerance (IGT) first. These two pathways are widely recognized to stem from distinct metabolic abnormalities in hepatic glucose production and peripheral glucose uptake, respectively. We confirm this but go beyond to show that IFG and IGT lie on a continuum ranging from high hepatic insulin resistance and low peripheral insulin resistance to low hepatic resistance and high peripheral resistance. We show that IFG generally incurs IGT and IGT generally incurs IFG on the way to T2D, highlighting the difference between innate and acquired defects and the need to assess patients early to determine their underlying primary impairment and appropriately target therapy. We also consider other mechanisms, showing that IFG can result from impaired insulin secretion, that non-insulin-dependent glucose uptake can also mediate or interact with these pathways, and that impaired incretin signaling can accelerate T2D progression. We consider whether hyperinsulinemia can cause insulin resistance in addition to being a response to it and suggest that this is a minor effect.

Mathematical model of blood glucose dynamics by emulating the pathophysiology of glucose metabolism in type 2 diabetes mellitus

Mathematical modelling has established itself as a theoretical tool to understand fundamental aspects of a variety of medical-biological phenomena. The predictive power of mathematical models on some chronic conditions has been helpful in its proper prevention, diagnosis, and treatment. Such is the case of the modelling of glycaemic dynamics in type 2 diabetes mellitus (T2DM), whose physiology-based mathematical models have captured the metabolic abnormalities of this disease. Through a physiology-based pharmacokinetic-pharmacodynamic approach, this work addresses a mathematical model whose structure starts from a model of blood glucose dynamics in healthy humans. This proposal is capable of emulating the pathophysiology of T2DM metabolism, including the effect of gastric emptying and insulin enhancing effect due to incretin hormones. The incorporation of these effects lies in the implemented methodology since the mathematical functions that represent metabolic rates, with a relevant contribution to hyperglycaemia, are adjusting individually to the clinical data of patients with T2DM. Numerically, the resulting model successfully simulates a scheduled graded intravenous glucose test and oral glucose tolerance tests at different doses. The comparison between simulations and clinical data shows an acceptable description of the blood glucose dynamics in T2DM. It opens the possibility of using this model to develop model-based controllers for the regulation of blood glucose in T2DM.

Unraveling Disease Pathophysiology with Mathematical Modeling

Modeling has enabled fundamental advances in our understanding of the mechanisms of health and disease for centuries, since at least the time of William Harvey almost 500 years ago. Recent technological advances in molecular methods, computation, and imaging generate optimism that mathematical modeling will enable the biomedical research community to accelerate its efforts in unraveling the molecular, cellular, tissue-, and organ-level processes that maintain health, predispose to disease, and determine response to treatment. In this review, we discuss some of the roles of mathematical modeling in the study of human physiology and pathophysiology and some challenges and opportunities in general and in two specific areas: in vivo modeling of pulmonary function and in vitro modeling of blood cell populations.

Model-based meta-analysis of individual International Prostate Symptom Score trajectories in patients with benign prostatic hyperplasia with moderate or severe symptoms

Aims

International Prostate Symptom Score (IPSS) is a marker of lower urinary tract symptoms (LUTS) deterioration or improvement in benign prostate hyperplasia (BPH). Whereas changes in IPSS relative to baseline have been used as endpoints in clinical trials, little attention has been given to the time course of symptoms. The current investigation aimed to develop a drug‐disease model to describe individual IPSS trajectories in moderate and severe BPH patients.

Methods

A model‐based meta‐analytical approach was used including data from 10 238 patients enrolled into Phase III and IV studies receiving placebo, tamsulosin, dutasteride or combination therapy over a period of up to 4 years. Model predictive performance was assessed using statistical and graphical criteria. Subsequently, simulations were performed to illustrate the implications of treatment with drugs showing symptomatic and disease‐modifying properties in patients with varying disease progression rates.

Results

Improvement and worsening of IPSS could be characterized by a model including a sigmoid function which disentangles drug effects from placebo and varying disease progression rates on IPSS. Mean estimate (95% confidence intervals) for the disease progression rate was 0.319 (0.271–0.411) month⁻¹. Treatment effect on IPSS (DELTA) was found to be 0.0605, 0.0139 and 0.0310 month⁻¹ for placebo, tamsulosin and combination therapy, respectively. In addition, it appears that individual trajectories can be clustered together into different phenotypes describing the underlying disease progression rate (i.e. slow, moderate and fast progressors).

Conclusions

The availability of a drug‐disease model enables the evaluation of interindividual differences in disease progression rate, deterioration of symptoms and treatment effects on LUTS/BPH.

Mathematical model of diabetes and lipid metabolism linked to diet, leptin sensitivity, insulin sensitivity and VLDLTG clearance predicts paths to health and type II diabetes

An original model of diabetes linked to carbohydrate and lipid intake is presented and applied to predict the effects on biomarkers of various diets. The variables (biomarkers) are concentrations of fasting plasma glucose, insulin, leptin, glucagon, non-esterified fatty acids (NEFA) and very low density lipoprotein triglyceride (VLDLTG), as well as muscle lipids, hepatic lipids, pancreatic lipids, fat mass and mass of β-cells. The model predicts isocaloric high carbohydrate low fat (HCLF) diet and low carbohydrate high fat (LCHF) diet trajectories to health which vary in fat mass by at most a few kilograms at steady state. The LCHF trajectories to health are faster than isocaloric HCLF trajectories with respect to fat mass loss, although these trajectories may be slower initially if parameters are adjusting from HCLF values. On LC diets, leptin sensitivity and VLDLTG clearance are thought to increase. Increasing leptin sensitivity and VLDLTG clearance is predicted to lower lipids including fat mass and VLDLTG. The model predicts that changes in VLDLTG due to a change in diet happen rapidly, approaching steady state values after a few weeks, reflecting leptin sensitivity and VLDLTG clearance which are much harder to measure. The model predicts that if only insulin sensitivity increases on a LC diet, steady state fat mass would increase slightly. If leptin and insulin sensitivities increase concurrently, the combined effect could be a decrease in fat mass, consistent with the fact that increasing insulin sensitivity is often associated with fat mass loss in trials. The model predicts trajectories to fat type II diabetes with hypertriglyceridemia due to high carbohydrate moderate fat diets, on which insulin rises before falling, as ectopic fat deposits increase; made fatter and more diabetic by higher lipid consumption. It predicts trajectories to non-diabetic states with raised fat mass, VLDLTG and muscle, hepatic and pancreatic lipids due to moderate carbohydrate high fat diets. The model predicts paths to lean type II diabetes, on a diet of moderate energy but low β-cell replication rate or high death rate.

A novel fast-slow model of diabetes progression: Insights into mechanisms of response to the interventions in the Diabetes Prevention Program

Several models for the long-term development of T2DM already exist, focusing on the dynamics of the interaction between glycemia, insulinemia and β-cell mass. Current models consider representative (fasting or daily average) glycemia and insulinemia as characterizing the compensation state of the subject at some instant in slow time. This implies that only these representative levels can be followed through time and that the role of fast glycemic oscillations is neglected. An improved model (DPM15) for the long-term progression of T2DM is proposed, introducing separate peripheral and hepatic (liver and kidney) insulin actions. The DPM15 model no longer uses near-equilibrium approximation to separate fast and slow time scales, but rather describes, at each step in slow time, a complete day in the life of the virtual subject in fast time. The model can thus represent both fasting and postprandial glycemic levels and describe the effect of interventions acting on insulin-enhanced tissue glucose disposal or on insulin-inhibited hepatic glucose output, as well as on insulin secretion and β-cell replicating ability. The model can simulate long-term variations of commonly used clinical indices (HOMA-B, HOMA-IR, insulinogenic index) as well as of Oral Glucose Tolerance or Euglycemic Hyperinsulinemic Clamp test results. The model has been calibrated against observational data from the Diabetes Prevention Program study: it shows good adaptation to observations as a function of very plausible values of the parameters describing the effect of such interventions as Placebo, Intensive LifeStyle and Metformin administration.

Pharmacodynamic Drug-Drug Interactions

Pharmacodynamic drug-drug interactions (DDIs) occur when the pharmacological effect of one drug is altered by that of another drug in a combination regimen. DDIs often are classified as synergistic, additive, or antagonistic in nature, albeit these terms are frequently misused. Within a complex pathophysiological system, the mechanism of interaction may occur at the same target or through alternate pathways. Quantitative evaluation of pharmacodynamic DDIs by employing modeling and simulation approaches is needed to identify and optimize safe and effective combination therapy regimens. This review investigates the opportunities and challenges in pharmacodynamic DDI studies and highlights examples of quantitative methods for evaluating pharmacodynamic DDIs, with a particular emphasis on the use of mechanism-based modeling and simulation in DDI studies. Advancements in both experimental and computational techniques will enable the application of better, model-informed assessments of pharmacodynamic DDIs in drug discovery, development, and therapeutics.

Predicting outcomes of chronic kidney disease from EMR data based on Random Forest Regression

Chronic kidney disease (CKD) is prevalent across the world, and kidney function is well defined by an estimated glomerular filtration rate (eGFR). The progression of kidney disease can be predicted if the future eGFR can be accurately estimated using predictive analytics. In this study, we developed and validated a prediction model of eGFR by data extracted from a regional health system. This dataset includes demographic, clinical and laboratory information from primary care clinics. The model was built using Random Forest regression and evaluated using Goodness-of-fit statistics and discrimination metrics. After data preprocessing, the patient cohort for model development and validation contained 61,740 patients. The final model included eGFR, age, gender, body mass index (BMI), obesity, hypertension, and diabetes, which achieved a mean coefficient of determination of 0.95. The estimated eGFRs were used to classify patients into CKD stages with high macro-averaged and micro-averaged metrics. In conclusion, a model using real-world electronic medical records (EMR) data can accurately predict future kidney functions and provide clinical decision support.

In vivo and in silico dynamics of the development of Metabolic Syndrome

The Metabolic Syndrome (MetS) is a complex, multifactorial disorder that develops slowly over time presenting itself with large differences among MetS patients. We applied a systems biology approach to describe and predict the onset and progressive development of MetS, in a study that combined in vivo and in silico models. A new data-driven, physiological model (MINGLeD: Model INtegrating Glucose and Lipid Dynamics) was developed, describing glucose, lipid and cholesterol metabolism. Since classic kinetic models cannot describe slowly progressing disorders, a simulation method (ADAPT) was used to describe longitudinal dynamics and to predict metabolic concentrations and fluxes. This approach yielded a novel model that can describe long-term MetS development and progression. This model was integrated with longitudinal in vivo data that was obtained from male APOE*3-Leiden.CETP mice fed a high-fat, high-cholesterol diet for three months and that developed MetS as reflected by classical symptoms including obesity and glucose intolerance. Two distinct subgroups were identified: those who developed dyslipidemia, and those who did not. The combination of MINGLeD with ADAPT could correctly predict both phenotypes, without making any prior assumptions about changes in kinetic rates or metabolic regulation. Modeling and flux trajectory analysis revealed that differences in liver fluxes and dietary cholesterol absorption could explain this occurrence of the two different phenotypes. In individual mice with dyslipidemia dietary cholesterol absorption and hepatic turnover of metabolites, including lipid fluxes, were higher compared to those without dyslipidemia. Predicted differences were also observed in gene expression data, and consistent with the emergence of insulin resistance and hepatic steatosis, two well-known MetS co-morbidities. Whereas MINGLeD specifically models the metabolic derangements underlying MetS, the simulation method ADAPT is generic and can be applied to other diseases where dynamic modeling and longitudinal data are available.

Comparison of Power, Prognosis, and Extrapolation Properties of Four Population Pharmacodynamic Models of HbA1c for Type 2 Diabetes

Reusing published models saves time; time to be used for informing decisions in drug development. In antihyperglycemic drug development, several published HbA1c models are available but selecting the appropriate model for a particular purpose is challenging. This study aims at helping selection by investigating four HbA1c models, specifically the ability to identify drug effects (shape, site of action, and power) and simulation properties. All models could identify glucose effect nonlinearities, although for detecting the site of action, a mechanistic glucose model was needed. Power was highest for models using mean plasma glucose to drive HbA1c formation. Insulin contribution to power varied greatly depending on the drug target; it was beneficial only if the drug target was insulin secretion. All investigated models showed good simulation properties. However, extrapolation with the mechanistic model beyond 12 weeks resulted in drug effect overprediction. This investigation aids drug development in decisions regarding model choice if reusing published HbA1c models.

A long-term mechanistic computational model of physiological factors driving the onset of type 2 diabetes in an individual

A computational model of the physiological mechanisms driving an individual's health towards onset of type 2 diabetes (T2D) is described, calibrated and validated using data from the Diabetes Prevention Program (DPP). The objective of this model is to quantify the factors that can be used for prevention of T2D. The model is energy and mass balanced and continuously simulates trajectories of variables including body weight components, fasting plasma glucose, insulin, and glycosylated hemoglobin among others on the time-scale of years. Modeled mechanisms include dynamic representations of intracellular insulin resistance, pancreatic beta-cell insulin production, oxidation of macronutrients, ketogenesis, effects of inflammation and reactive oxygen species, and conversion between stored and activated metabolic species, with body-weight connected to mass and energy balance. The model was calibrated to 331 placebo and 315 lifestyle-intervention DPP subjects, and one year forecasts of all individuals were generated. Predicted population mean errors were less than or of the same magnitude as clinical measurement error; mean forecast errors for weight and HbA1c were ~5%, supporting predictive capabilities of the model. Validation of lifestyle-intervention prediction is demonstrated by synthetically imposing diet and physical activity changes on DPP placebo subjects. Using subject level parameters, comparisons were made between exogenous and endogenous characteristics of subjects who progressed toward T2D (HbA1c > 6.5) over the course of the DPP study to those who did not. The comparison revealed significant differences in diets and pancreatic sensitivity to hyperglycemia but not in propensity to develop insulin resistance. A computational experiment was performed to explore relative contributions of exogenous versus endogenous factors between these groups. Translational uses to applications in public health and personalized healthcare are discussed.

Dynamic population pharmacokinetic-pharmacodynamic modelling and simulation supports similar efficacy in glycosylated haemoglobin response with once or twice-daily dosing of canagliflozin

AIM

Canagliflozin is an SGLT2 inhibitor approved for the treatment of type-2 diabetes. A dynamic population pharmacokinetic-pharmacodynamic (PK/PD) model relating 24-h canagliflozin exposure profiles to effects on glycosylated haemoglobin was developed to compare the efficacy of once-daily and twice-daily dosing.

METHODS

Data from two clinical studies, one with once-daily, and the other with twice-daily dosing of canagliflozin as add-on to metformin were used (n = 1347). An established population PK model was used to predict full 24-h profiles from measured trough concentrations and/or baseline covariates. The dynamic PK/PD model incorporated an E_max relationship between 24-h canagliflozin exposure and HbA1c-lowering with baseline HbA1c affecting the efficacy.

RESULTS

Internal and external model validation demonstrated that the model adequately predicted HbA1c-lowering for canagliflozin once-daily and twice-daily dosing regimens. The differences in HbA1c reduction between the twice-daily and daily mean profiles were minimal (at most 0.023% for 100 mg total daily dose [TDD] and 0.011% for 300 mg TDD, up to week 26, increasing with time and decreasing with TDD) and not considered clinically meaningful.

CONCLUSIONS

Simulations using this model demonstrated the absence of clinically meaningful between-regimen differences in efficacy, supported the regulatory approval of a canagliflozin-metformin immediate release fixed-dose combination tablet and alleviated the need for an additional clinical study.

A Longitudinal HbA1c Model Elucidates Genes Linked to Disease Progression on Metformin

One-third of type-2 diabetic patients respond poorly to metformin. Despite extensive research, the impact of genetic and nongenetic factors on long-term outcome is unknown. In this study we combine nonlinear mixed effect modeling with computational genetic methodologies to identify predictors of long-term response. In all, 1,056 patients contributed their genetic, demographic, and long-term HbA1c data. The top nine variants (of 12,000 variants in 267 candidate genes) accounted for approximately one-third of the variability in the disease progression parameter. Average serum creatinine level, age, and weight were determinants of symptomatic response; however, explaining negligible variability. Two single nucleotide polymorphisms (SNPs) in CSMD1 gene (rs2617102, rs2954625) and one SNP in a pharmacologically relevant SLC22A2 gene (rs316009) influenced disease progression, with minor alleles leading to less and more favorable outcomes, respectively. Overall, our study highlights the influence of genetic factors on long-term HbA1c response and provides a computational model, which when validated, may be used to individualize treatment.

The variability in beta-cell function in placebo-treated subjects with type 2 diabetes: application of the weight-HbA1c-insulin-glucose (WHIG) model

AIM

The weight-glycosylated haemoglobin (HbA1C)-insulin-glucose (WHIG) model describes the effects of changes in weight on insulin sensitivity (IS) in newly diagnosed, obese subjects receiving placebo treatment. This model was applied to a wider population of placebo-treated subjects, to investigate factors influencing the variability in IS and β-cell function.

METHODS

The WHIG model was applied to the WHIG dataset (Study 1) and two other placebo datasets (Studies 2 and 3). Studies 2 and 3 consisted of nonobese subjects and subjects with advanced type 2 diabetes mellitus (T2DM). Body weight, fasting serum insulin (FSI), fasting plasma glucose (FPG) and HbA1c were used for nonlinear mixed-effects modelling (using NONMEM v7.2 software). Sources of interstudy variability (ISV) and potential covariates (age, gender, diabetes duration, ethnicity, compliance) were investigated.

RESULTS

An ISV for baseline parameters (body weight and β-cell function) was required. The baseline β-cell function was significantly lower in subjects with advanced T2DM (median difference: Study 2: 15.6%, P < 0.001; Study 3: 22.7%, P < 0.001) than in subjects with newly diagnosed T2DM (Study 1). A reduction in the estimated insulin secretory response in subjects with advanced T2DM was observed but diabetes duration was not a significant covariate.

CONCLUSION

The WHIG model can be used to describe the changes in weight, IS and β-cell function in the diabetic population. IS remained relatively stable between subjects but a large ISV in β-cell function was observed. There was a trend towards decreasing β-cell responsiveness with diabetes duration, and further studies, incorporating subjects with a longer history of diabetes, are required.

Modeling the Disease Progression from Healthy to Overt Diabetes in ZDSD Rats

Studying the critical transitional phase between healthy to overtly diabetic in type 2 diabetes mellitus (T2DM) is of interest, but acquiring such clinical data is impractical due to ethical concerns and would require a long study duration. A population model using Zucker diabetic Sprague-Dawley (ZDSD) rats was developed to describe this transition through altering insulin sensitivity (IS, %) as a result of accumulating excess body weight and β-cell function (BCF, %) to affect glucose-insulin homeostasis. Body weight, fasting plasma glucose (FPG), and fasting serum insulin (FSI) were collected biweekly over 24 weeks from ZDSD rats (n = 23) starting at age 7 weeks. A semi-mechanistic model previously developed with clinical data was adapted to rat data with BCF and IS estimated relative to humans. Non-linear mixed-effect model estimation was performed using NONMEM. Baseline IS and BCF were 41% compared to healthy humans. BCF was described with a non-linear rise which peaked at 14 weeks before gradually declining to a negligible level. A component for excess growth reflecting obesity was used to affect IS, and a glucose-dependent renal effect exerted a two- to sixfold increase on the elimination of glucose. A glucose-dependent weight loss effect towards the end of experiment was implemented. A semi-mechanistic model to describe the dynamics of glucose and insulin was successfully developed for a rat population, transitioning from healthy to advanced diabetes. It is also shown that weight loss can be modeled to mimic the glucotoxicity phenomenon seen in advanced hyperglycemia.

Systems pharmacology - Towards the modeling of network interactions

Mechanism-based pharmacokinetic and pharmacodynamics (PKPD) and disease system (DS) models have been introduced in drug discovery and development research, to predict in a quantitative manner the effect of drug treatment in vivo in health and disease. This requires consideration of several fundamental properties of biological systems behavior including: hysteresis, non-linearity, variability, interdependency, convergence, resilience, and multi-stationarity. Classical physiology-based PKPD models consider linear transduction pathways, connecting processes on the causal path between drug administration and effect, as the basis of drug action. Depending on the drug and its biological target, such models may contain expressions to characterize i) the disposition and the target site distribution kinetics of the drug under investigation, ii) the kinetics of target binding and activation and iii) the kinetics of transduction. When connected to physiology-based DS models, PKPD models can characterize the effect on disease progression in a mechanistic manner. These models have been found useful to characterize hysteresis and non-linearity, yet they fail to explain the effects of the other fundamental properties of biological systems behavior. Recently systems pharmacology has been introduced as novel approach to predict in vivo drug effects, in which biological networks rather than single transduction pathways are considered as the basis of drug action and disease progression. These models contain expressions to characterize the functional interactions within a biological network. Such interactions are relevant when drugs act at multiple targets in the network or when homeostatic feedback mechanisms are operative. As a result systems pharmacology models are particularly useful to describe complex patterns of drug action (i.e. synergy, oscillatory behavior) and disease progression (i.e. episodic disorders). In this contribution it is shown how physiology-based PKPD and disease models can be extended to account for internal systems interactions. It is demonstrated how SP models can be used to predict the effects of multi-target interactions and of homeostatic feedback on the pharmacological response. In addition it is shown how DS models may be used to distinguish symptomatic from disease modifying effects and to predict the long term effects on disease progression, from short term biomarker responses. It is concluded that incorporation of expressions to describe the interactions in biological network analysis opens new avenues to the understanding of the effects of drug treatment on the fundamental aspects of biological systems behavior.

Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology-QSP-models). However, today's multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example-type 2 diabetes-and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them 'personalized' (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.

Weight-HbA1c-insulin-glucose model for describing disease progression of type 2 diabetes

A previous semi‐mechanistic model described changes in fasting serum insulin (FSI), fasting plasma glucose (FPG), and glycated hemoglobin (HbA1c) in patients with type 2 diabetic mellitus (T2DM) by modeling insulin sensitivity and β‐cell function. It was later suggested that change in body weight could affect insulin sensitivity, which this study evaluated in a population model to describe the disease progression of T2DM. Nonlinear mixed effects modeling was performed on data from 181 obese patients with newly diagnosed T2DM managed with diet and exercise for 67 weeks. Baseline β‐cell function and insulin sensitivity were 61% and 25% of normal, respectively. Management with diet and exercise (mean change in body weight = −4.1 kg) was associated with an increase of insulin sensitivity (30.1%) at the end of the study. Changes in insulin sensitivity were associated with a decrease of FPG (range, 7.8–7.3 mmol/L) and HbA1c (6.7–6.4%). Weight change as an effector on insulin sensitivity was successfully evaluated in a semi‐mechanistic population model.

Kinetics of drug action in disease states: towards physiology-based pharmacodynamic (PBPD) models

Gerhard Levy started his investigations on the "Kinetics of Drug Action in Disease States" in the fall of 1980. The objective of his research was to study inter-individual variation in pharmacodynamics. To this end, theoretical concepts and experimental approaches were introduced, which enabled assessment of the changes in pharmacodynamics per se, while excluding or accounting for the cofounding effects of concomitant changes in pharmacokinetics. These concepts were applied in several studies. The results, which were published in 45 papers in the years 1984-1994, showed considerable variation in pharmacodynamics. These initial studies on kinetics of drug action in disease states triggered further experimental research on the relations between pharmacokinetics and pharmacodynamics. Together with the concepts in Levy's earlier publications "Kinetics of Pharmacologic Effects" (Clin Pharmacol Ther 7(3): 362-372, 1966) and "Kinetics of pharmacologic effects in man: the anticoagulant action of warfarin" (Clin Pharmacol Ther 10(1): 22-35, 1969), they form a significant impulse to the development of physiology-based pharmacodynamic (PBPD) modeling as novel discipline in the pharmaceutical sciences. This paper reviews Levy's research on the "Kinetics of Drug Action in Disease States". Next it addresses the significance of his research for the evolution of PBPD modeling as a scientific discipline. PBPD models contain specific expressions to characterize in a strictly quantitative manner processes on the causal path between exposure (in terms of concentration at the target site) and the drug effect (in terms of the change in biological function). Pertinent processes on the causal path are: (1) target site distribution, (2) target binding and activation and (3) transduction and homeostatic feedback.

Evaluation of the long-term durability and glycemic control of fasting plasma glucose and glycosylated hemoglobin for pioglitazone in Japanese patients with type 2 diabetes

BACKGROUND

This study applied a pharmacodynamic model-based approach to evaluate the long-term durability and glycemic control of pioglitazone in comparison with other oral glucose-lowering drugs in Japanese type 2 diabetes mellitus (T2DM) patients.

SUBJECTS AND METHODS

Japanese T2DM patients were enrolled in a prospective, randomized, open-label, blinded-end point study and received pioglitazone with or without other oral glucose-lowering drugs (excluding another thiazolidinedione [TZD]) (n=293) or oral glucose-lowering drugs excluding TZD (n=294). Treatment was adjusted to achieve glycosylated hemoglobin (HbA1c) <6.9%, and samples for fasting plasma glucose (FPG) and HbA1c were collected over 2.5-4 years. A simultaneous cascading indirect response model structure was applied to describe the time course of FPG and HbA1c. HbA1c levels were described using both an FPG-dependent and an FPG-independent function. To account for titration, drug effects for both treatment groups were implemented using a time-dependent Emax model.

RESULTS

Pioglitazone was superior in both time to maximum effect and the magnitude of reduction achieved in FPG and HbA1c. A greater reduction in median FPG (-21 mg/dL vs. -9 mg/dL) was observed with pioglitazone (P<0.05). Maximum drug effect for FPG was predicted to occur earlier (11 months) for pioglitazone than for the control group (14 months). The simulated additional reduction in FPG and HbA1c achieved with pioglitazone was predicted to be maintained beyond the currently observed study duration.

CONCLUSIONS

Pioglitazone was found to result in improved glycemic control and durability compared with control treatment. This model-based approach enabled the quantification of differences in FPG and HbA1c for both treatment groups and simulation to evaluate longer-term durability on FPG and HbA1c.

Clinical pharmacology = disease progression + drug action

Clinical pharmacology is concerned with understanding how to use medicines to treat disease. Pharmacokinetics and pharmacodynamics have provided powerful methodologies for describing the time course of concentration and effect in individuals and in populations. This population approach may also be applied to describing the progression of disease and the action of drugs to change disease progress. Quantitative models for symptomatic and disease-modifying effects of drugs are valuable not only for describing drugs and diseases but also for identifying criteria to distinguish between types of drug actions, with implications for regulatory decisions and long-term patient care.

Characterization of the ZDSD Rat: A Translational Model for the Study of Metabolic Syndrome and Type 2 Diabetes

Metabolic syndrome and T2D produce significant health and economic issues. Many available animal models have monogenic leptin pathway mutations that are absent in the human population. Development of the ZDSD rat model was undertaken to produce a model that expresses polygenic obesity and diabetes with an intact leptin pathway. A lean ZDF rat with the propensity for beta-cell failure was crossed with a polygenetically obese Crl:CD (SD) rat. Offspring were selectively inbred for obesity and diabetes for >30 generations. In the current study, ZDSD rats were followed for 6 months; routine clinical metabolic endpoints were included throughout the study. In the prediabetic metabolic syndrome phase, ZDSD rats exhibited obesity with increased body fat, hyperglycemia, insulin resistance, dyslipidemia, glucose intolerance, and elevated HbA1c. As disease progressed to overt diabetes, ZDSD rats demonstrated elevated glucose levels, abnormal oral glucose tolerance, increases in HbA1c levels, reductions in body weight, increased insulin resistance with decreasing insulin levels, and dyslipidemia. The ZDSD rat develops prediabetic metabolic syndrome and T2D in a manner that mirrors the development of metabolic syndrome and T2D in humans. ZDSD rats will provide a novel, translational animal model for the study of human metabolic diseases and for the development of new therapies.

Target-mediated pharmacokinetic/pharmacodynamic model based meta-analysis and dosing regimen optimization of a long-acting release formulation of exenatide in patients with type 2 diabetes mellitus

A hybrid pharmacokinetic/pharmacodynamic (PK/PD) model with extended-release (ER) process and target mediated drug disposition (TMDD) was developed for exenatide ER to account for its complex absorption process and glucagon-like peptide 1 receptor (GLP-1R)-mediated non-linear PK behaviors along with its influences to fasting plasma glucose (FPG) and hemoglobin A1c (HbA1c). Using hybrid PK/PD model, simulations were done to explore the potential dosing regimens which could achieve likelihood of more pharmacodynamic exposure with respect to FPG and HbA1c over a much shorter period compared with the currently used treatment protocol. The mean PK/PD data about exenatide ER for type 2 diabetes mellitus (T2DM) were digitized from the publications, and the hybrid PK/PD model was performed using the Monolix 4.3 program. The plasma concentration-time and FPG/HbA1c-time profiles for exenatide ER subcutaneously administrated to patients with T2DM were well described by this hybrid model. Monte Carlo simulation was applied to mimic the PK profiles when higher loading dose 7.5 and 5.0 mg exenatide ER were subcutaneously administrated with different dosing intervals at the first 3 weeks of 30-week treatment. Two potentially optimizing schedules could improve the likelihood of achieving much more FPG and HbA1c exposures than currently used clinical treatment protocol.

Utilization of model-based meta-analysis to delineate the net efficacy of taspoglutide from the response of placebo in clinical trials

The objective of this study was to develop quantitative models to delineate the net efficacy of taspoglutide on fasting plasma glucose (FPG) and glycosylated hemoglobin (HbA1c) from the response of placebo in type 2 diabetes patients, and further find pharmacodynamic potency of taspoglutide and FPG for half of maximum reduction responses of FPG and HbA1c, respectively. Several PD data about taspoglutide treatments for type 2 diabetes patients were digitalized from the published papers related with the clinical development of taspoglutide. The model based meta-analysis (MBMA) studies for FPG and HbA1c were performed with Monolix 4.2 software. The MBMA successfully described the effects of placebo and taspoglutide on pharmacological indexes of FPG and HbA1c through mono and multiple combination therapies in clinical trials. The pharmacodynamic potency (25.3 pmol/l) produced 50% of maximum responses of FPG (−2.39 mmol/l) from the responses of placebo for FPG (−0.371 mmol/l); the response change of FPG (−1.81 mmol/l) affected 50% of maximum response change (−1.74%) for HbA1c from the response of placebo (−0.253%). The leveraging prior knowledge from the longitudinal MBMA will be utilized to guide clinical development of taspoglutide and further support study designs including optimization of dose and duration of therapy.

Osteoarthritis disease progression model using six year follow-up data from the osteoarthritis initiative

The objective was to develop a quantitative model of disease progression of knee osteoarthritis over 6 years using the total WOMAC score from patients enrolled into the Osteoarthritis Initiative (OAI) study. The analysis was performed using data from the Osteoarthritis Initiative database. The time course of the total WOMAC score of patients enrolled into the progression cohort was characterized using non-linear mixed effect modeling in NONMEM. The effect of covariates on the status of the disease and the progression rate was investigated. The final model provided a good description of the experimental data using a linear progression model with a common baseline (19 units of the total WOMAC score). The WOMAC score decreased by 1.77 units/year in 89% of the population or increased by 1.74 units/year in 11% of the population. Multiple covariates were found to affect the baseline and the rate of progression, including BMI, sex, race, the use of pain medications, and the limitation in activity due to symptoms. A mathematical model to describe the disease progression of osteoarthritis in the studied population was developed. The model identified two sub-populations with increasing or decreasing total WOMAC score over time, and the effect of important covariates was quantified.

Modeling energy intake by adding homeostatic feedback and drug intervention

Energy intake (EI) is a pivotal biomarker used in quantification approaches to metabolic disease processes such as obesity, diabetes, and growth disorders. Eating behavior is however under both short-term and long-term control. This control system manifests itself as tolerance and rebound phenomena in EI, when challenged by drug treatment or diet restriction. The paper describes a model with the capability to capture physiological counter-regulatory feedback actions triggered by energy imbalances. This feedback is general as it handles tolerance to both increases and decreases in EI, and works in both acute and chronic settings. A drug mechanism function inhibits (or stimulates) EI. The deviation of EI relative to a reference level (set-point) serves as input to a non-linear appetite control signal which in turn impacts EI in parallel to the drug intervention. Three examples demonstrate the potential usefulness of the model in both acute and chronic dosing situations. The model shifts the predicted concentration-response relationship rightwardly at lower concentrations, in contrast to models that do not handle functional adaptation. A fourth example further shows that the model may qualitatively explain differences in rate and extent of adaptation in observed EI and its concomitants in both rodents and humans.

A semi-mechanistic model for the effects of a novel glucagon receptor antagonist on glucagon and the interaction between glucose, glucagon, and insulin applied to adaptive phase II design

A potent novel compound (MK-3577) was developed for the treatment of type 2 diabetes mellitus (T2DM) through blocking the glucagon receptor. A semi-mechanistic model was developed to describe the drug effect on glucagon and the interaction between glucagon, insulin, and glucose in healthy subjects (N = 36) during a glucagon challenge study in which glucagon, octreotide (Sandostatin), and basal insulin were infused for 2 h starting from 3, 12, or 24 h postdose of a single 0-900 mg MK-3577 administration. The drug effect was modeled by using an inhibitory E max model (I max = 0.96 and IC50 = 13.9 nM) to reduce the ability of glucagon to increase the glucose production rate (GPROD). In addition, an E max model (E max = 0.79 and EC50 = 575 nM) to increase glucagon secretion by the drug was used to account for the increased glucagon concentrations prechallenge (via compensatory feedback). The model adequately captured the observed profiles of glucagon, glucose, and insulin pre- and postchallenge. The model was then adapted for the T2DM patient population. A linear model to correlate fasting plasma glucose (FPG) to weighted mean glucose (WMG) was developed and provided robust predictions to assist with the dose adjustment for the interim analysis of a phase IIa study.

The relationship between fasting plasma glucose and HbA1c during intensive periods of glucose control in antidiabetic therapy

OBJECTIVE

HbA1c measurements are typically less variable than fasting plasma glucose (FPG) for diagnosing diabetes, and for assessment of progress on glucose control therapy. However HbA1c reaches steady-state relative to average plasma glucose over about 120 days. HbA1c thus overestimates average FPG during first three months of starting therapy in newly diagnosed diabetic patients, and care needs to be exercised in interpreting HbA1c measurements during this period. At steady-state excellent regression exists between HbA1c and FPG. We hypothesize that this regression can also be used to obtain reliable estimates of HbA1c relative to FPG at 4 and 8 weeks following the onset of therapy.

MATERIALS AND METHODS

We collected FPG and HbA1c data of type 2 diabetic patients over the first 8 weeks of starting antidiabetic treatment. We fit linear and nonlinear regression models to steady-state data, and estimated how much measured HbA1c deviates at 4 and 8 weeks from these theoretical relations.

RESULTS

If measured HbA1c is decremented by 0.7% (8 mmol/mol) at 4 weeks and 0.3% (3 mmol/mol) at 8 weeks, this corrected HbA1c is a better predictor of the corresponding FPG. Using hyperbolic regression, corrections to HbA1c are 0.5 and 0.1% (5 and 1 mmol/mol), respectively.

CONCLUSION

With the corrections proposed here, HbA1c measurements can be better interpreted in the early weeks of antidiabetic treatment.

Effects of IL-1β-Blocking Therapies in Type 2 Diabetes Mellitus: A Quantitative Systems Pharmacology Modeling Approach to Explore Underlying Mechanisms

Recent clinical studies suggest sustained treatment effects of interleukin-1β (IL-1β)–blocking therapies in type 2 diabetes mellitus. The underlying mechanisms of these effects, however, remain underexplored. Using a quantitative systems pharmacology modeling approach, we combined ex vivo data of IL-1β effects on β-cell function and turnover with a disease progression model of the long-term interactions between insulin, glucose, and β-cell mass in type 2 diabetes mellitus. We then simulated treatment effects of the IL-1 receptor antagonist anakinra. The result was a substantial and partly sustained symptomatic improvement in β-cell function, and hence also in HbA1C, fasting plasma glucose, and proinsulin–insulin ratio, and a small increase in β-cell mass. We propose that improved β-cell function, rather than mass, is likely to explain the main IL-1β–blocking effects seen in current clinical data, but that improved β-cell mass might result in disease-modifying effects not clearly distinguishable until >1 year after treatment.

Preclinical PK/PD modeling and human efficacious dose projection for a glucokinase activator in the treatment of diabetes

Human Hexokinase IV, or glucokinase (GK), is a regulator of glucose concentrations in the body. It plays a key role in pancreatic insulin secretion as well as glucose biotransformation in the liver, making it a potentially viable target for treatment of Type 2 diabetes. Allosteric activators of GK have been shown to decrease blood glucose concentrations in both animals and humans. Here, the development of a mathematical model is presented that describes glucose modulation in an ob/ob mouse model via administration of a potent GK activator, with the goal of projecting a human efficacious dose and plasma exposure. The model accounts for the allosteric interaction between GK, the activator, and glucose using a modified Hill function. Based on model simulations using data from the ob/ob mouse and in vitro studies, human projections of glucose response to the GK activator are presented, along with dose and regimen predictions to maintain clinically significant decreases in blood glucose in a Type 2 diabetic patient. This effort serves as a basis to build a detailed mechanistic understanding of GK and its role as a therapeutic target for Type 2 diabetes, and it highlights the benefits of using such an approach in a drug discovery setting.

Longitudinal Modeling of the Relationship Between Mean Plasma Glucose and HbA1c Following Antidiabetic Treatments

Late-phase clinical trials within diabetes generally have a duration of 12–24 weeks, where 12 weeks may be too short to reach steady-state glycated hemoglobin (HbA1c). The main determinant for HbA1c is blood glucose, which reaches steady state much sooner. In spite of this, few publications have used individual data to assess the time course of both glucose and HbA1c, for predicting HbA1c. In this paper, we present an approach for predicting HbA1c at end-of-trial (24–28 weeks) using glucose and HbA1c measurements up to 12 weeks. The approach was evaluated using data from 4 trials covering 12 treatment arms (oral antidiabetic drug, glucagon-like peptide-1, and insulin treatment) with measurements at 24–28 weeks to evaluate predictions vs. observations. HbA1c percentage was predicted for each arm at end-of-trial with a mean prediction error of 0.14% [0.01;0.24]. Furthermore, end points in terms of HbA1c reductions relative to comparator were accurately predicted. The proposed model provides a good basis to optimize late-stage clinical development within diabetes.

A drug and disease model for lixisenatide, a GLP-1 receptor agonist in type 2 diabetes

Incretin hormone analogs such as glucagon-like peptide-1 (GLP-1) receptor agonists have emerged as promising new options for the treatment of type 2 diabetes mellitus (T2DM), targeting several of its pathophysiological traits, including reduced insulin sensitivity, inadequate insulin secretion, and loss of β-cell mass (BCM). This article describes the semi-mechanistic modeling of lixisenatide dose-response over time using fasting plasma glucose (FPG), fasting serum insulin (FSI) and glycated hemoglobin (HbA1c) data from two Phase II and four Phase III clinical trials, for a total of 2470 T2DM patients. Previously published models for FPG, FSI, and BCM as well as HbA1c were adapted and expanded to describe the available data. The model incorporated aspects describing disease progression, standard-of-care, FPG-dependent and -independent HbA1c synthesis, and covariate effects of body size, race, and sex. The final model described lixisenatide effects on β-cell responsiveness, insulin sensitivity and FPG-independent HbA1c synthesis, was able to describe the observed FPG, FSI, and HbA1c data accurately, and was successful in predicting data from an unseen Phase III clinical study.