Pharmacometrics Approaches and its Applications in Diabetes: An Overview.

Type 2 diabetes mellitus is the most prevalent and progressive in nature. As the time progress, the multifaceted complications and comorbidities associated to diabetes worsen in the form of macrovascular or microvascular or both. Pharmacometrics modeling is a step forward in minimizing the risk or at least understanding the factors associated to its progression with the passage of time. These models investigate diabetes treatments effects and the progression factors with different viewpoints incorporating insulin-glucose dynamics, dose-response and pharmacokinetics, and pharmacodynamics relationships. Pharmacometrics modeling is an innovative approach in a sense that it is taking us away from the conventional analysis by providing all the opportunities in improving the decision-making in health sector. It has been suggested that we can achieve greater statistical power for determining drug effects through model-based evaluation than through traditional evaluations. The main aim of this review was to evaluate pharmacometrics approaches used in modeling diabetes progression through time and also the integrated models describing glucose-insulin dynamics. Copyright:

INTRODUCTION

Pharmacometrics is the science of developing and applying mathematical and statistical methods to (a) characterize, understand, and predict a drugs' pharmacokinetics and pharmacodynamics (PKPD) behavior, (b) quantify uncertainty of information about that behavior, and (c) rationalize data-driven decision making in the drug development process and pharmacotherapy.[12] Later in 2008, Barret et al. come up with a broader definition of pharmacometrics as the branch of science concerned with mathematical models of biology, pharmacology, disease, and physiology used to described and quantify interactions between xenobiotics and patients, including beneficial effects and side effects resultant from such interfaces.[3] Furthermore, the United States Food and Drug Administration defined pharmacometrics as an emerging science that quantifies drug, disease, and trial information to aid efficiently in the development of drug or making regulatory decisions. Along with that, pharmacometrics disease models provide relationship between biomarkers and clinical outcomes, time course of disease, and placebo effects.[2]

Pharmacometrics analysis usually incorporates nonlinear mixed effect models (NLMEMs) which provides simultaneous estimation of parameters' mean and variance availed from the individuals in the study population describing a biological process.[4] These models provide inter-individual variabilities and estimation of the mean value of parameters in the studied populations. Nonetheless, these models can also be incorporated into the analysis of joint modeling, i.e., PKPD data (biological responses). All these NLMEMs analysis contribute to the population approach, and maximum likelihood estimation is the primary method to produce parameters estimates.[56]

Population approach in pharmacometrics refers to multilevel modeling or mixed-effects modeling. The aim of these models is to estimate the values of parameters obtained from a set of observed data along with the known covariates.[7] The data used in PKPD often involves multiple data points from several individuals; hence, variabilities are unavoidable. In order to explain all of these variabilities and to minimize bias in parameter estimates, it is important to incorporate mixed effect modeling. Parameter level variability exists in mixed-effects models and hence allowing parameters to vary between individuals.[8] Random effects comprised of three level of variabilities, i.e., interindividual variability (IIV) which define the difference between the parameter values in different individual, residual variability which represent the differences between individual predictions of parameters values and observations as well as inter-occasion variability which describe the differences in parameter values between different occasions in a same individual.[6]

In the clinical field, a number of studies were performed using pharmacometrics approaches, especially the PKPD modeling of certain drugs. The common focuses were on the drug models which describe the concentration-effect, dose-response, and PKPD relationship. In addition, the application of pharmacometrics is also expanded on the disease progression modeling in various diseases that describe the relationship between biomarkers and clinical outcomes, time course of the disease, and placebo effects. The focus of this review includes disease progression modeling of diabetes and integrated models for understanding glucose-insulin dynamics.

PHARMACOMETRICS MODELING IN TYPE 2 DIABETES MELLITUS

Diabetes disease progression modeling

Type 2 diabetes mellitus (T2DM) is the most prevalent and usually develops as a part of wider health problem known as metabolic syndrome comprising of obesity, dyslipidemia, hypertension and impaired glucose tolerance (IGT). IGT is characterized by hyperinsulinemia which acts as a compensatory response to the increase insulin resistance.[9] Progression of diabetes from healthy to overt stage starts with the increase in insulin secretion due to increase in insulin resistance for maintaining normoglycemia. Beta cells at a certain stage cannot maintain normoglycemia, and glucose level increases causing changes in beta cell function. Afterward, beta cells mass declines, and the glucose level start to elevate from prediabetic range. When the beta-cell mass decrease severely, the patients become ketotic and get dependent on insulin (in T1DM).[10] Progressive weight gain, declining beta-cell function measured by homeostasis model assessment, loss of glycemic control on medication are other clinical characterization contributing to progression. It has been observed in a study that patients with high baseline body mass index and high fasting plasma glucose (FPG) are prone to the progression to overt diabetes.[11]

There are few pharmacometrics models developed which focused on the progression of diabetes Type 2 as the disease progress over time. Before Topp et al. in 2000, the models by Bergman et al., (1985)[12] and Mathews et al., (1985)[13] examined glucose and insulin dynamics in their models. These models were developed in diabetic patients in which multiple parameter changes for multiple physiological defects were used to simulate glucose and insulin dynamics. Topp et al. developed one such model consisting of a system of three nonlinear ordinary differential equations describing glucose and insulin dynamics as fast relative to beta-cell mass dynamics in healthy individuals (βIG Model). This model effectively investigated the effects of a single or combination of defects on the behavior of the whole system. The model suggested that blood glucose level of more than 250 mg/dl leads to β-cell death which exceeds the rate of replication and hence leading the system to pathological steady state. The model behaved in the same way as glucose regulatory system behave in response to alteration in blood glucose level, insulin sensitivity, beta-cell mass, and rates of beta-cell insulin secretion. Along with that, the model also predicted three distinct pathways in diabetes, i.e., regulated hyperglycemia, bifurcation, and dynamical hyperglycemia. The βIG model provided a framework for the development of experimental protocols for testing hypothesis related to β-cell exhaustion and the pathogenesis of Type 2 diabetes. Furthermore, it provided a tool for understanding the behavior of β-cell mass, plasma glucose, and plasma insulin in response to therapeutic interventions.[14]

TREATMENT EFFECT/FACTORS AFFECTING THE MECHANISTIC PROGRESSION OF DIABETES DEVELOPMENT

The semi mechanistic model by Topp et al. was further developed by Ribbing et al. in 2010. The previous model by Topp et al. was derived from the literature and was not applied to clinical data, and it did not incorporate the effects of anti-diabetic treatment as well as has limitation in considering all the physiological effects. Ribbing et al. adopted the model and used it in T2DM patients incorporating the treatment effects and the effects of disease state on beta-cell mass and insulin sensitivity. The model was developed with data from three clinical trials with Tesaglitazar for the treatment of T2DM. In this model, the progression of diabetes was described by decrease in insulin sensitivity and disturbed adaptation of beta-cell mass. Furthermore, it is observed that reduced insulin sensitivity alone does not contribute to diabetes as beta-cell adapt itself in response which eventually bring FPG back to normal set point. It has also been noted that in some instances, the negative feedback is not as functional in diabetes patients as it is in normal nondiabetic population. This impact of the disease state was implemented as an offset in beta-cell adaptation. The study observed that there was deterioration in beta cell mass and insulin sensitivity in all the diabetic patients in comparison to normal subject, and there was typical decrease in insulin sensitivity by 37%–50% in all subjects while FPG increased by 3.1–3.9 mmol/L. The treatment effects of Tesaglitazar show increased in insulin sensitivity, whereas the effects on beta-cell mass (OFFSET) nearly reached its maximum with higher doses. The model identified a strong association between insulin sensitivity and insulin clearance with the use of tesaglitazar.[15]

Disease progression analysis, nonetheless, provide quantitative assessments of the drug effects on the time course of disease progression. Progression modeling incorporates mathematical models to predict and investigate disease status as a function of time.[14] Frey et al. in 2003, developed one such model to see the long-term effects of gliclazide on FPG in T2DM patients. In this study, population PK-PD model was incorporated for evaluating disease progression over time with the use of gliclazide by obtaining repeated FPG determinations. In terms of increasing FPG concentration with gliclazide treatment, a mean rate of disease progression was estimated at 0.84 mmol/L with IIV of 143%. The study evaluated the relationship between gliclazide and its long-term effects and has found that the IIV in response is associated to the patients' disease state. The model although it described the kinetics of hypoglycemic effects of gliclazide and provided better understanding of the IIV, still it was unable to address all the problems associated with diabetes modification with treatment. Furthermore, the model did not include fasting serum insulin (FSI) and glycated hemoglobin (HbA1c) which can provide model predictions of long-term effects.[16]

Taking the work forward of Frey et al., de Winter et al. in 2006 developed a model focusing on newly diagnosed diabetes patients who were naïve to the anti-diabetic treatment, and the study applied mechanism-based population pharmacodynamics progression model. The study approach integrated data on FPG, FSI, and HbA1c into physiologically understandable model structure that provides mechanism-based association between FPG and FSI as well as FPG and HbA1c. The model was developed comparing the effects of pioglitazone with metformin or gliclazide in treatment-naïve diabetes patients, and the data were taken from two parallel 1-year study. Furthermore, it has provided the distinction between the parameters specific to the drugs and those specific to the system (e.g., disease process describing parameters).[14] It has been observed that patients in gliclazide arm experienced somewhat loss in beta-cell function and also insulin sensitivity throughout the study period. While the patients in pioglitazone arm had comparatively reduced rate of loss in insulin sensitivity and had better results in beta cell functions over the 1st year of treatment. For the metformin arm, decrease in FSI was observed with decrease in FPG through homeostatic feedback mechanism which resulted from metformin monotherapy. As metformin is an insulin sensitizer and the results in the model show otherwise, it can be suggested that metformin in addition to its suppressive effects on FPG may have pleiotropic effects on FPG production which resulted in decrease in FSI. In summary, the model adequately described the time course of HbA1c, FPG and to some extent FSI with different class of oral anti-diabetic drugs.[17]

Similarly, taking forward the model by de Winter et al., another semi mechanistic model was developed by Choy et al. introducing weight in understanding the progression of diabetes through a certain period of time. The study was based on placebo arm randomized, double-blind, placebo-controlled, multicenter, parallel-group study which was focused on the effects of topiramate (an anti-convulsant) having weight loss as side effect. The population of the study was obese patients and newly diagnosed with T2DM and naïve to anti-diabetic treatment. This model was based on the previously developed model by the addition of weight factor which can influence insulin sensitivity. The estimated bodyweight of the study population was 104 kg and at the end of the study, an average decrease of 4% was observed. As a result of weight change, there was an estimated increase of insulin sensitivity from 25% to 30.1%. Beta-cell function in the study population was 61% with a 5% natural disease progression reduction of starting beta cell function per year observed. Similarly, FSI decrease of 3.3 μIU/mL was observed in this study. With weight change, FPG decreases for 0.4 mmol/L, and HbA1c decreases for an estimation of 0.3%. Hence, it is noteworthy that the change in weight was successfully implemented in the semi mechanistic model, and the results show the effect of weight change on the disease progression.[18] Both of these models effectively describe the process of progression and the effects of intervention which can help in minimizing the complication associated to the progression of diabetes over a long period of time.[1718] The summary of the diabetes disease progression models developed over time is summarized in Table 1.

Table 1

Pharmacometrics disease progression and integrated models for diabetes

Focus	Findings	Reference
Insulin and glucose dynamics in diabetic patients	Glucose and insulin dynamics were simulated by considering multiple parameter changes with multiple physiological defects	Bergman et al. (1985)
Mathews et al. (1985)
Insulin and glucose dynamics in relation to beta-cell mass in healthy individuals	Investigated the effects of single or combined defects on the behavior of the whole system. Blood glucose level of more than 250 mg/dl leads to β-cell death which exceed the rate of replication. The model behavior was same to regulatory system behavior in response to glycemia, insulin sensitivity, and β-cell mass	Topp et al. (2000)
Effects of treatment and disease state on β-cell mass and insulin sensitivity	Tesaglitazar improved insulin sensitivity, and higher doses had maximum effects on β-cell mass. Tesaglitazar was strongly associated with insulin sensitivity and insulin clearance identified by the model	Ribbing et al. (2010)
PK-PD model for diabetes progression over time with the use of gliclazide in diabetic patients	Provide kinetics of hypoglycemic effects of gliclazide with better understanding of interindividual variability. Interindividual variability in response to gliclazide is associated with patients’ disease state	Frey et al. (2003)
Population PD progression model in newly diagnose diabetic patients for comparing the effects of pioglitazone with metformin or gliclazide	Gliclazide was associated with loss in beta-cell function, while pioglitazone show comparatively lesser loss in insulin sensitivity and beta-cell function. Metformin therapy was associated with decrease in fasting serum insulin in response to decrease in fasting plasma glucose.	de Winter et al. (2006)
RCT on the effects of topiramate in newly diagnosed obese T2DM patients	The semi-mechanistic model identified the association of decrease in weight with improved insulin sensitivity, fasting serum insulin, HbA1c, and improved beta-cell function. The model described the process of progression along with the effects of intervention.	Choy et al. (2016)
Integrated models
Glucose and insulin integrated model using IVGTT in mongrel dogs	Insulin sensitivity and glucose effectiveness were modeled. Estimated insulin sensitivity with good precision from simple intravenous glucose injection	Bergman et al. (1979)
Integrated covariates in IVGTT glucose minimal model	Linear mixed-effects modeling showed age, visceral abdominal fat, and basal insulinemia were significant predictors for insulin sensitivity, whereas only age and basal insulinemia were significant for insulin action. Covariate introduction improved the model fit by significantly shrinking the unexplained between subject variability for insulin sensitivity and insulin action	Denti et al. (2010)
Integrated glucose and insulin model in healthy and T2DM patients	Previously presented integrated model was extended to describe glucose and insulin concentrations in healthy volunteers following an oral glucose tolerance test. The characterization of the differences between the healthy and diabetic stages in the integrated glucose-insulin model could potentially be used to extrapolate drug effect from healthy volunteers to T2DM	Silber et al. (2007)

PK: Pharmacokinetics, PD: Pharmacodynamic, T2DM: Type 2 diabetes mellitus, IVGTT: Intravenous glucose tolerance test, RCT: Randomized controlled trail

DIABETES INTEGRATED MODELS

A few pharmacometrics models have been developed to describe the glucose and insulin regulation, which are important components in diabetes. Glucose and insulin are the part of the same system and interact at the same time; hence, it is preferable to analyze the data of both the components simultaneously. In integrated models both insulin and glucose, observations are simultaneously fitted, and a control mechanism is included between both the entities. First in the line was back in 1979 by Bergman et al. known as the minimal model using intravenous glucose tolerance test (IVGTT) in mongrel dogs. In the model, insulin sensitivity and glucose effectiveness were the two main parameters. Sensitivity of glucose clearance to insulin secretion was referred as insulin sensitivity while glucose effectiveness was the insulin-independent glucose secretion. Glucose-insulin interaction is a complex phenomenon and was fixed by having fixed administration of insulin concentration.[19] This model was further adapted to nonlinear mixed effect modeling by Denti et al. in 2010 who implied the minimal model in healthy subjects. The model evaluated insulin-modified IVGTT data including four parameters, i.e., glucose effectiveness, insulin sensitivity, the insulin action parameter, and the apparent volume of distribution of glucose per unity body mass[20] The work by Denti et al. was expanded with the implementation of new software and estimation methods by Largajolli et al. in 2012. Lacking the simultaneous analysis of glucose and insulin dynamics, the model had limited ability for simulation and prediction purposes.[21]

In addition, a one compartment model was proposed by de Gaetano et al. back in 2000, and in that model, glucose and insulin were modeled simultaneously through control mechanism between the two components.[22] Following the proposed model of integration of glucose and insulin, Silber et al. in 2007, develop integrated glucose-insulin (IGI) model in healthy and T2DM patients using IVGTT data. In that study, through nonlinear mixed effect modeling a model was developed for total glucose, hot glucose, and insulin concentration-time, and the data were analyzed simultaneously for healthy controls and diabetes patients.[23] Furthermore, this model has also been developed in oral glucose tolerance test of healthy and T2DM patients.[2425] The IGI model has good mechanistic basis with excellent simulation and estimation abilities. Based on all these characteristics, the integrated model on glucose and insulin has become a precious tool for application in diabetes drug development.[24] The summary of the integrated model developed for insulin-glucose is provided in Table 1.

EMPIRICAL DESCRIPTION OF DIABETES PROGRESSION

Besides describing glucose and insulin regulations, several models were also developed to quantify the relationship between glucose, insulin, and HBA1c that is crucial for the diabetes disease progression modeling. There are few models developed based on the FPG and mean plasma glucose (MPG) in relationship with HBA1c. One such model was developed by Hamren et al. in T2DM patients for describing the glycosylation of HbA1c to HbA1c. It was mechanism-based pharmacodynamic model for finding association between FPG and HbA1c for defining the relationship between FPG and HbA1c a transit compartment model was developed. This model can handle the situations between small and large variations in individual red blood cells life span[26]. As FPG can be more prone to measurement errors, MPG relationship with HbA1c was also investigated by Garcia et al. and Moller et al. in 2013. It has shown better results in predicting changes in HbA1c as MPG is availed through multiple glucose readings and has less sensitivity to measurement errors.[2728] Garcia et al. model can predict the impact of changes in MPG on HbA1c. Furthermore, MPG does not only take the FPG in consideration as postprandial glucose can also contribute to the changes in HbA1c. The MPG data in this model by Moller et al. were obtained from 8 to 11 points in 24 h span, data from 12 weeks for HbA1c were taken from T2DM patients, and a good prediction at 24–28 weeks of trial was obtained.[27] The model with high accuracy can be a useful tool in improving Phase III dose selection based on Phase II data in the development of anti-diabetic agents.

WHAT IS STILL LACKING?

Although a number of models has been developed on diabetes disease progression, drug effects and the integration between glucose and insulin regulation, there is lack of pharmacometrics model describing the relationship between glycemic control (i.e., HbA1c) and the progression of diabetes to macrovascular or microvascular complications over time. These models may be considered as the need of the time for minimizing the burden associated to diabetes complications, for example, diabetic nephropathy which can lead to a more complicated treatment regimen and increase in healthcare cost. As pharmacometrics modeling may improve the process of drug development, it can also help healthcare practitioners in determining individual-based treatment strategies in minimizing the risk of complications, thus further reducing the disease burden.

Study limitations

The present review was more focused on the integrated and disease progression modeling, although there exists a wide application of pharmacometrics approaches in PKPD modeling. Furthermore, the review focused on the application of pharmacometrics in diabetes, which may not represent the immense application of these approaches in other progressive disorders. The present review has included the basic model development strategies implied, which were further used for developing more sophisticated models.

CONCLUSIONS

It has been suggested that we can achieve greater statistical power for determining drug effects through model-based evaluation than through conventional analysis. Disease progression modeling is nonetheless one of the important aspects of pharmacometrics where disease progression can be quantified with the inclusion of drug effects. Furthermore, pharmacometrics approaches in developing PK/PD models will further enhance the insight on the effects of drugs in progressive disease. Time-to-event pharmacometrics modeling will further improve our understanding about the progression of diseases over time and may be a dependable tool in formulating treatment strategies in the near future.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.