Application of the integrated glucose–insulin model for cross‐study characterization of T2DM patients on metformin background treatment

Abstract

Aim

The integrated glucose–insulin (IGI) model is a semi‐mechanistic physiological model which can describe the glucose–insulin homeostasis system following various glucose challenge settings. The aim of the present work was to apply the model to a large and diverse population of metformin‐only‐treated type 2 diabetes mellitus (T2DM) patients and identify patient‐specific covariates.

Methods

Data from four clinical studies were pooled, including glucose and insulin concentration–time profiles from T2DM patients on stable treatment with metformin alone following mixed‐meal tolerance tests. The data were collected from a wide range of patients with respect to the duration of diabetes and level of glycaemic control.

Results

The IGI model was expanded by four patient‐specific covariates. The level of glycaemic control, represented by baseline glycosylated haemoglobin was identified as a significant covariate for steady‐state glucose, insulin‐dependent glucose clearance and the magnitude of the incretin effect, while baseline body mass index was a significant covariate for steady‐state insulin levels. In addition, glucose dose was found to have an impact on glucose absorption rate. The developed model was used to simulate glucose and insulin profiles in different groups of T2DM patients, across a range of glycaemic control, and it was found accurately to characterize their response to the standard oral glucose challenge.

Conclusions

The IGI model was successfully applied to characterize differences between T2DM patients across a wide range of glycaemic control. The addition of patient‐specific covariates in the IGI model might be valuable for the future development of antidiabetic treatment and for the design and simulation of clinical studies.

What is Already Known about this Subject

• The semi‐mechanistic integrated glucose–insulin (IGI) model can quantitatively describe glucose–insulin homeostasis following various glucose challenge settings.

What this Study Adds

• Four patient‐specific covariates have been indentified and included in the IGI model.

• The expanded IGI model allows characterization of different patient groups across a range of glycaemic control.

• The model can be applied for the design and simulation of future clinical studies and optimization of antidiabetic drug treatments.

Table of Links

LIGANDS
Metformin	Insulin

This Table lists key ligands in this article that are hyperlinked to corresponding entries in http://www.guidetopharmacology.org, the common portal for data from the IUPHAR/BPS Guide to PHARMACOLOGY 1.

Introduction

Type 2 diabetes mellitus (T2DM) is characterized by a gradual decline in glycaemic control. This loss of control is driven by a gradual decrease in insulin sensitivity and relative failure of β‐cell function 2, 3, 4. The level of glycaemic control can be measured both in healthy subjects and diabetic patients during glucose provocation experiments, such as oral or intravenous glucose tolerance tests 5.

Several mathematical models have been developed to describe quantitatively the kinetics of glucose and insulin following glucose provocations 6, 7, 8, 9, 10, including an integrated glucose–insulin (IGI) model 11. The IGI model is a semi‐mechanistic physiological model, which can describe glucose and insulin dynamics simultaneously, while taking into account complex feedback mechanisms which are involved in glucose–insulin homeostasis. It has been validated in various types of glucose challenge experiments, including oral, mixed‐meal and intravenous tolerance tests and also clamp experiments, and in various types of individuals such as healthy volunteers and T2DM patients 11, 12, 13, 14. It has been successfully applied to characterize the effect of several antidiabetic treatments on glucose homeostasis, to elucidate their mechanisms of action 15, 16, 17, 18, 19, and has proven valuable in designing phase II trials 20 and prospectively predicting phase II trial outcomes 21. Recently, the IGI model was extended to include the progression of the disease from a prediabetic state (i.e. impaired glucose tolerance) to overt T2DM 22. This progression, driven by a decrease in insulin sensitivity and relative β‐cell failure, was characterized quantitatively as a gradual, linear decline in insulin‐dependent glucose clearance (the IGI model parameter linked to the insulin resistance), insulin first‐phase secretion and the incretin effect 22.

A number of IGI model parameters were found to be different between healthy volunteers and T2DM patients, including insulin‐dependent and ‐independent glucose clearance and first‐phase insulin secretion 12. However, the IGI model does not yet include any T2DM patient‐specific covariates. It is clear that the glucose–insulin homeostasis system is different between early and advanced T2DM patients and between patients with good and poor glycaemic control, and therefore it is expected that some of the IGI model parameters may differ between different types of patients. The aim of the work presented here was to characterize quantitatively those differences by identifying potential patient‐specific covariates using a large cross‐study dataset with over 300 diverse T2DM patients on a stable dose of metformin. Such a quantitative description of the various T2DM patients is likely to be valuable for the future development of antidiabetic treatments and for the design and simulation of clinical studies.

Materials and methods

Studies

The analysis was performed using integrated data from four clinical studies performed in a diverse population of T2DM patients, who were on stable treatment with metformin alone and did not use any other antidiabetic medications 23, 24, 25, 26. The reason for including patients on metformin monotherapy only was to obtain a more uniform population in terms of background therapy. Details of all studies are provided in Table 1. During the studies, the participants took part in the mixed‐meal tolerance test following an overnight fast, and were given either a liquid meal or a standardized breakfast (see Table 1 for details). The mixed‐meal test was chosen owing to its physiological composition as it provides the information needed to model all aspects of glucose–insulin homeostasis, including the incretin effect. Blood samples were collected for the assessment of glucose and insulin concentrations at the prespecified time points (see Table 1). The studies were conducted in accordance with the ‘Guiding Medical Doctors in Biomedical Research Involving Human Subjects’ contained in the Declaration of Helsinki. All studies were approved by the institutional review board of the ethics committee, and all patients provided written informed consent prior to study participation.

Table 1.

Summary of studies used in the analysis

Study number	Description	Trial duration	n	Glucose challenge	Blood sample collection times (min) a
BCA403 NCT00477581	A phase IV, randomized, double‐blind, crossover study to compare the effects of exenatide and sitagliptin on postprandial glucose in subjects with type 2 diabetes mellitus	28 days	96	Standardized meal (standardized breakfast, details not available; glucose dose: 75 g)	–15, 5, 15, 30, 60, 90, 120, 180, 240
H8OUS‐GWAY NCT00135330	A phase IIIB, multicentre, open‐label, comparator‐controlled, randomized, three‐arm, parallel trial to evaluate the metabolic effects of exenatide, rosiglitazone and exenatide plus rosiglitazone in subjects with type 2 diabetes mellitus treated with metformin	20 weeks	137	Liquid meal (Boost, liquid meal supplement with 240 kcal, 4 g fat, 40 g carbohydrate and 10 g protein per 227 g serving; glucose dose: 40 g)	–15, 0, 15, 30, 60, 90, 120, 150, 180
D6420C00001 NCT02367066	A single centre, double‐blind, randomized, placebo‐controlled, crossover, phase I study to assess the pharmacodynamics of oral AZD1981 after administration of repeated doses for 3 days in subjects with type 2 diabetes mellitus	3 days	20	Liquid meal (Ensure Plus® drink: 472 ml, 100 g carbohydrate; glucose dose: 100 g)	–15, −1, 15, 30, 60, 90, 95, 120, 180, 240
2993–112 NCT00039013	A phase III, randomized, triple‐blind, parallel‐group, long‐term, placebo‐controlled, multicentre study to examine the effect on glucose control (glycosylated haemoglobin) of AC2993 given twice a day in subjects with type 2 diabetes mellitus treated with metformin alone	30 weeks	54	Standardized meal (a composition of 55% carbohydrate, 15% protein and 30% fat; glucose dose: 75 g)	–30, 15, 45, 75, 105, 165

^aBlood samples were collected from every patient at each time point

Data

The data included measurements of glucose and insulin, collected during glucose challenge tests (i.e. mixed‐meal tolerance tests – for details, see Table 1), without the presence of any active treatment apart from stable metformin (i.e. only predose data were included). Measurements from a total of 305 subjects were included in the analysis, with 3030 glucose and 2898 insulin measurements (a total of 5928 measurements).

Model development

The IGI model was used in the analysis 14. The model simultaneously describes the time course of the glucose and insulin concentrations, using mechanism‐based components. A graphical representation of the model can be found in the Supporting Information (Figure S1). Disposition parameters (both population values and variability estimates) from the IGI model were fixed to the same values as in the original model 13 and the following parameters were estimated: insulin‐dependent glucose clearance (CLGI), magnitude of the incretin effect (SINCR), steady‐state glucose concentration (GSS), steady‐state insulin concentration (ISS), glucose absorption rate (KABS) and bioavailability of glucose (BIOG). Different glucose input was used for each study (see Table 1 for details). It should be noted that as subjects in all studies were on a stable dose of metformin, it was not possible to characterize the mechanism of action of metformin (which primarily acts by inhibiting endogenous glucose production rather than simulating insulin secretion). It was assumed that the pharmacokinetic and pharmacodynamic effects of metformin were at steady‐state for all subjects, and therefore it was appropriate to use data from these studies to describe the parameters related to insulin‐mediated effects (e.g. CLGI and SINCR) following the mixed‐meal tolerance test.

In the first step of developing the model, the baseline model, where no differences were assumed between the included patients, was applied to the data. As a next step, potential covariate effects were evaluated using the following covariates: duration of T2DM, baseline glycosylated haemoglobin (HbA1c) and body mass index (BMI). These covariates were selected based on their relevance and the data available. Covariate effects were evaluated on each estimated IGI model parameter and the likelihood ratio test was used, with a difference of at least 10.83 in objective function value for one added parameter considered significant (corresponding to a level of significance of α = 0.001). The impact of covariates was evaluated in NONMEM using the following functional form:

$$T{V}_P=P_1\times {\left({\text{cov}}_i/{\text{cov}}_{\mathit{\text{median}}}\right)}^{\theta 1}$$ (1)

where TV _P is the estimated typical parameter P ₁ (e.g. GSS, CLGI) for the ith subject, P ₁ is the population typical value parameter estimate for subjects with the median value of a particular covariate, cov_i is the measured value of a particular covariate in the ith subject, cov_median is the median value of a particular covariate in the population and θ1 is a fixed‐effect estimate describing the influence of a given covariate on a given parameter. The median values used for baseline HbA1c, disease duration and BMI were 7.9%, 5 years and 32.3 kg m⁻², respectively. In addition, the linear relationship between covariates and IGI model parameters was explored, using the following equation:

$$T{V}_P=P_1\pm {\theta }_1\times {\text{cov}}_i$$ (2)

where P ₁ is the population typical value parameter estimate, θ1 is the slope of the linear relationship and cov_i is the measured value of a particular covariate in the ith subject.

In addition, it was tested whether the glucose dose had an impact on glucose absorption and/or bioavailability. The assessment was done by estimating separate absorption and bioavailability parameter for each glucose dose. A difference of at least 10.83 in the objective function value for one added parameter was considered significant.

Model evaluation

Model evaluation included the assessment of objective function value (OFV), goodness of fit (GOF) plots, relative standard errors (RSEs) and visual predictive checks (VPCs). VPCs were created by simulating 200 replicates of the analysis dataset. The 5th, 50th (median) and 95th percentiles of the simulated data were calculated for each sampling time bin and plotted against time, with the original observed dataset overlaid to assess visually the concordance between the model‐based simulated data and the observed data. In order fully to evaluate the final model, VPCs were stratified using the following criteria: (i) HbA1c baseline, (ii) T2DM duration, (iii) study and (iv) glucose dose. The T2DM duration and HbA1c stratification groups were created by dividing all patients used in the current analysis into four quartiles using their disease duration and baseline HbA1c values, respectively. Four HbA1c quartiles corresponded to: (group 1) HbA1c ≤ 7.3%; (group 2) 7.3% < HbA1c ≤ 7.9%; (group 3) 7.9% < HbA1c ≤ 8.8%; and (group 4) 8.8% < HbA1c. T2DM duration quartiles were as follows: (group 1) duration ≤2 years; (group 2) 2 < duration ≤5 years; (group 3) 5 < duration ≤8 years; and (group 4) 8 years < duration. Details of the T2DM duration and HbA1c quartile groups used in the VPC stratification can be found in the Supporting Information, in Table S1 and Table S2. In addition, a stratification based on HbA1c values used in clinical practice was created, which included the following groups: (i) HbA1c < 7.5%; (ii) 7.5% < HbA1c < 10%; and (iii) HbA1c > 10%. Details of the three additional HbA1c groups can be found in the Supporting Information (Table S3).

Simulations from the final model

Based on the parameter estimates from the final model, glucose and insulin profiles following glucose challenge (standard mixed‐meal test with a glucose input of 75 g) were simulated, grouping patients with T2DM based on their HbA1c baseline values (i.e. the four quartiles described in the previous section).

Software

The software package NONMEM, version 7.3.0 (Globomax, Hanover, MD, USA), was used in the analysis. Xpose (http://xpose.sourceforge.net), PsN, version 4.2.0 (http://psn.sourceforge.net) and R, version 3.0 (R‐project, http://www.r‐project.org) were used for the exploratory analysis and postprocessing of NONMEM output – e.g. to assess GOF.

Results

Patient population

A summary of the demographics and baseline characteristics of the patients included in the analysis can be found in Table 2. The mean T2DM duration, baseline HbA1c and BMI across all patients were: 6.2 years, 8.2% and 32.6 kg m⁻², respectively. Overall, there was a wide spread of T2DM duration, baseline HbA1c and BMI across all patients. Disease duration ranged from 2.5 months to 36 years, and baseline HbA1c between 6.5% and 11.6%, indicating that the patients included in the present analysis ranged between very early, recently diagnosed and advanced diabetics as well as patients with various levels of glycaemic control (from well to poorly controlled).

Table 2.

Patient demographics and baseline characteristics

Parameter	Study number
	ALL (n = 305)	BCA403 (n = 95)	H8OUS‐GWAY (n = 136)	D6420C00001 (n = 20)	2993–112 (n = 54)
T2DM duration (years), mean (range), SD	6.2 (0.2, 36.0) 5.3	7.0 (0.3, 24.0) 5.3	4.7 (0.2, 22.0) 3.7	9.5 (3.0, 18.0) 4.6	7.7 (0.3, 36.0) 7.6
Age (years), mean (range), SD	54.5 (27.0, 75.0) 9.7	54.0 (29.0, 70.0) 9.5	55.2 (27.0, 75.0) 10.1	54.1 (39.0, 69.0) 7.8	54.2 (29.0, 74.0) 9.6
HbA1c (%), mean (range), SD	8.2 (6.5, 11.6) 1.1	8.5 (6.9, 11.0) 1.2	7.8 (6.5, 9.8) 0.8	8.8 (7.1, 10.4) 1.0	8.3 (6.5, 11.6) 1.2
BMI (kg m –2 ), mean (range), SD	32.6 (21.2, 52.9) 5.0	32.4 (24.1, 44.1) 5.3	32.4 (24.3, 43.0) 4.3	31.6 (21.2, 37.9) 4.5	33.6 (23.6, 52.9) 6.3
BW (kg), mean (range), SD	91.7 (51.9, 154.9) 17.3	89.1 (55.2, 144.1) 18.1	92.6 (57.0, 144.0) 15.5	87.8 (51.9, 132.7) 19.4	95.4 (67.0, 154.9) 18.7
HOMA‐IR, mean (range), SD	5.9 (0.3, 33.2) 4.7	6.2 (0.9, 31.3) 5.0	5.7 (0.3, 33.2) 4.4	3.8 (1.3, 9.0) 1.8	6.4 (0.6, 32.7) 5.6
Quicki, mean (range), SD	0.13 (0.11, 0.21) 0.01	0.13 (0.11, 0.17) 0.01	0.13 (0.11, 0.21) 0.02	0.14 (0.12, 0.16) 0.01	0.13 (0.11, 0.18) 0.01
Matsuda index mean (range), SD	1.4 (0.3, 6.6) 0.8	1.2 (0.3, 3.7) 0.7	1.5 (0.3, 6.6) 0.8	1.2 (0.7, 2.2) 0.4	1.4 (0.4, 3.7) 0.8
Gender, n (%)
Male	147 (48.2)	39 (41.1)	69 (50.7)	13 (65.0)	26 (48.1)
Female	158 (51.8)	56 (58.9)	67 (49.3)	7 (35.0)	28 (51.9)
Race, n (%)
Black or African American	35 (11.4)	8 (8.4)	16 (11.8)	2 (10.0)	9 (16.7)
Asian	3 (1.0)	–	2 (1.5)	–	1 (1.9)
Native Hawaiian or other Pacific Islander	1 (0.3)	–	–	1 (5.0)	–
White	148 (48.2)	25 (26.3)	83 (61)	2 (10.0)	38 (70.4)
Hispanic	115 (37.7)	62 (65.3)	32 (23.5)	15 (75.0)	6 (11.1)
Other	3 (1.0)	–	3 (2.2)	–	–
Metformin dose (mg day –1 ), mean (range)	1507 (500, 2550)	1301 (500, 2550)	1505 (500, 2550)	1830 (1000, 2550)	1733 (500, 2550)

The homeostatic model assessment of insulin resistance (HOMA‐IR) index, quantitative insulin sensitivity check index (Quicki) and Matsuda index represent methods to assess insulin resistance and sensitivity, and were calculated as follows: HOMA‐IR: FPG*FPI/22.5 (for glucose measurements in mmol l⁻¹); Quicki: 1/(log FPG + log FPI); Matsuda index: [10 000/square root of (FPG × FPI) × (Mean glucose × Mean insulin)]. BMI, body mass index; BW, body weight; FPG, fasting plasma glucose; FPI, fasting plasma insulin; HbA1c, glycosylated haemoglobin; SD, standard deviation; T2DM, type 2 diabetes mellitus

It can be seen from Table 2 that baseline characteristics differed between the studies. It was noted that patients enrolled in the D6420C00001 study had, on average, a much longer disease duration (9.5 years) and higher HbA1c baseline (8.8%) compared with patients from other studies (see Table 2). By contrast, patients from the H8OUS‐GWAY study had, on average, a much shorter disease duration (average of 4.7 years) and lower baseline HbA1c (average of 7.8%). The exploration of patients' baseline characteristics revealed potential correlations – e.g. a positive relationship between disease duration and baseline HbA1c, as well as trends between baseline HbA1c and the homeostatic model assessment of insulin resistance index, quantitative insulin sensitivity check index and Matsuda index. The correlation plots, as well as the correlation matrix for all parameters, can be found in the Supporting Information (Figures S2 and S3 and Table S4).

Time course of the glucose and the insulin concentrations

The time course of the glucose and insulin concentrations measured during each study can be found in the Supporting Information (Figures S4 and S5). It can be seen that the profiles differ between the studies. For example, patients from the H8OUS‐GWAY study displayed a fast increase in glucose and insulin levels, with a the time for maximum concentration (t_max) of around 1 h, while patients in the D6420C00001 study appeared to have much more prolonged glucose and insulin profiles, with a much later t_max (around 3 h). In these patients, both glucose and insulin levels did not decrease down to baseline levels (i.e. pre‐glucose challenge), even after 4 h.

Baseline IGI model

As a first step in the model development process, the baseline model was fitted to all data. It was explored whether the variability in the model parameters could be explained by the prespecified covariates: baseline HbA1c, disease duration or baseline BMI. In order to assess this, the estimated variability for each of the parameters of interest was plotted against each covariate (Supporting Information, Figures S6‐S8). The potential correlations were then tested for statistical significance during the covariate analysis. Eta shrinkage was evaluated for the estimated IGI parameters, and the results can be found in the Supporting Information (Table S5). In general, eta shrinkage was low or medium (less than 20–30%), apart from the BIOG parameter (high shrinkage of 47%).

Final IGI model

A number of covariates were found significantly to improve model fit to the data, and the details of statistical significance can be found in the Supporting Information (Table S6). The final IGI model consisted of all parameters described in the original model 13 and the additional four parameters that were identified during covariate analysis: (i) impact of HbA1c on baseline glucose concentration; (ii) impact of HbA1c on insulin‐dependent glucose clearance; (iii) impact of HbA1c on slope of incretin effect; and (iv) impact of BMI on baseline insulin concentration. In addition, KABS was estimated separately for each glucose dose (i.e. 40 g, 75 g and 100 g), as it was found that this approach significantly improved the fit to the data. A number of parameters were fixed to the values from the original model – specifically: volume of distribution of central and peripheral glucose compartments (VG and VP), volume of distribution of insulin (VI), intercompartmental clearance of glucose (Q), insulin clearance (CLI), insulin‐independent glucose clearance (CLG), rate constant for the glucose and insulin effect compartments (KEOG and KEOI) and glucose effect on insulin production (IPRG). All other parameters were estimated during the modelling. The final parameter estimates from the IGI model, including all significant covariate effects, can be found in Table 3. The model was found to fit the data well, as judged by GOF plots and VPCs (see Figure 1 and Supporting Information, Figures S9‐S13). Figure 2 shows the impact of significant covariates on the IGI model parameters.

Table 3.

Final parameter estimates

Parameter	Description (unit)	Estimate	RSE (%)	IIV(%)
VG	Volume of distribution of central glucose compartment (l)	9.33	−	30
Q	Intercompartmental clearance of glucose (l h−1)	26.5	−	85
VI	Volume of distribution of insulin (l)	6.09	−	41
CLG	Insulin‐independent glucose clearance (l h−1)	1.72		59
CLGI	Insulin‐dependent glucose clearance [(l h −1 )/mU l −1 ]	0.422	0.2	65
CLI	Insulin clearance (l h−1)	73.2	−	29
VP	Volume of distribution of peripheral glucose compartment (l)	8.56	−	30
KEOG	Rate constant for the glucose effect compartment (h–1)	0.738	−	53
KEOI	Rate constant for the insulin effect compartment (h–1)	0.464	−	45
IPRG	Glucose effect on insulin production	1.42	−	35
BIOG	Bioavailability of glucose	0.805	0.3	13
KABS, 40 g	Glucose absorption rate for 40 g glucose dose (h –1 )	1.74	1.9	27
KABS, 75 g	Glucose absorption rate for 75 g glucose dose (h –1 )	0.911	0.1	27
KABS, 100 g	Glucose absorption rate for 100 g glucose dose (h –1 )	0.583	0.2	27
SINCR	Slope of the incretin effect (mg –1 )	0.00101	0.1	49
GSS	Baseline glucose concentration (mmol l −1 )	8.7	0.1	19
ISS	Baseline insulin concentration (mU)	11.4	0.3	55
HBA1c ~ GSS	impact of HbA1c on baseline glucose concentration	1.1	1.1	−
HBA1c ~ CLGI	Impact of HbA1c on insulin‐dependent glucose clearance	–0.744	0.9	−
HBA1c ~ SINCR	Impact of HbA1c on slope of incretin effect	–2.25	1.1	−
BMI ~ ISS	Impact of BMI on baseline insulin concentration	2.02	1.1	−
RESG	Residual error – glucose	0.102	0.2	−
RESI	Residual error – insulin	0.276	0.1	−

Estimated parameters are in bold, while all other parameters were fixed to the values determined during previously published experiments 13.

BMI, body mass index; HbA1c, glycosylated haemoglobin; IIV, interindividual variability

Figure 1.

Visual predictive check of the final model, stratified by patient glycosylated haemoglobin (HbA1c) group. Grey data points corresponds to individual observations; the red line represents the median of the observed data; the black line represents the median model simulation; the shaded area corresponds to the 90% prediction interval

Figure 2.

Estimated effects of patient‐specific covariates, baseline glycosylated haemoglobin (HbA1c) and body mass index (BMI) on integrated glucose–insulin model parameters. CLGI, insulin‐dependent glucose clearance; GSS, steady‐state glucose concentration; ISS, steady‐state insulin concentration; SINCR, magnitude of the incretin effect

Simulated glucose and insulin profiles in different patient groups

As HbA1c at baseline was found to be a good predictor of patients' response to a glucose challenge, the final model was used to make simulations for four groups of T2DM patients, with different HbA1c baselines. Simulated glucose and insulin concentration–time profiles for the four groups of patients are presented in Figure 3. The first group (i.e. patients with an HbA1c baseline less than 7.3%) can be classed as patients with good glycaemic control, while the fourth group (patients with an HbA1c baseline above 8.8%) would correspond to the patients with the poorest glycaemic control. It can be seen that the glycaemic profiles progressively deteriorated for patients from group 1 through to group 4 (Figure 3, left‐hand panel). The differences can also be observed in the insulin levels between patient types, with well‐controlled diabetics (in group 1) displaying the highest insulin levels, and the poorly controlled patients (in group 4) having much lower concentrations, following the same glucose load (Figure 3, right‐hand panel).

Figure 3.

Simulations from the final model of glucose (left‐hand panel) and insulin (right‐hand panel) concentration–time profiles in four groups of type 2 diabetes mellitus patients, following standard mixed‐meal test

Details of each patient group can be found in the Supporting Information in Table S3. It can be seen that the disease duration progressively increased in patients from HbA1c group 1 to group 4 (average of 4.9 years, 5.9 years, 6.5 years and 7.8 years in groups 1, 2, 3 and 4, respectively), suggesting a link between the level of glycaemic control and the duration of the disease. BMI, body weight and average daily metformin dose was observed to be similar across all HbA1c patient groups.

Discussion

Data from four different clinical studies were included in the analysis presented here. It was noted that the patients who took part in those studies displayed a wide range of baseline characteristics. Therefore, an adequate range of disease severity was seen in the data to allow a comprehensive identification of patient‐specific covariates. Disease duration ranged from 2.5 months to 36 years across the patients, and baseline HbA1c between 6.5% and 11.6%. This indicates that the study populations consisted of various types of patients: early diabetics, who had recently been diagnosed with the disease; advanced diabetics with many years of diabetes duration; and patients with a wide range of glycaemic control – from well to poorly controlled. It is anticipated that such different patients would respond differently to an oral glucose challenge, such as a mixed‐meal tolerance test. The aim of the analysis presented here was to apply the semi‐mechanistic IGI model to characterize quantitatively those potential differences between patients.

In the current analysis, we successfully developed an IGI model that contained covariate effects that can link certain patients' characteristics with the IGI model parameters. The final model appeared to fit all data well, and final parameter estimates were comparable with those available from previously published IGI models 11, 12, 13, 14, 19, 22; details of the comparison can be found in the Supporting Information (Table S7).

Surprisingly, it was not T2DM duration but baseline HbA1c levels that were found to be a good predictor of several model parameters: GSS, CLGI and the magnitude of the incretin effect. We found that baseline HbA1c was positively correlated with GSS, which was expected as it is well known that the baseline glucose concentration and HbA1c level are highly correlated 27, 28. Baseline HbA1c was also found to be negatively correlated with CLGI and the magnitude of the incretin effect. CLGI is the parameter in the IGI model that is an indicator of total insulin resistance – i.e. the lower the CLGI value, the less glucose can be cleared from the plasma through insulin‐dependent mechanisms (predominantly skeletal muscle glucose uptake 29), and hence the higher the insulin resistance. A reduction in the incretin effect was previously observed in T2DM patients compared with healthy subjects 30. Similar results were also reported when the IGI model was applied to describe progression from prediabetes to overt diabetes 22. Ghadzi and colleagues also reported a gradual decline in first‐phase insulin secretion in the prediabetic state 22; in our analysis, this parameter was not included in the IGI model as it was not supported by the data. The reason for this may be that the first‐phase insulin secretion gradually declines in glucose‐impaired subjects but appears to be completely lost at the time that subjects are diagnosed with diabetes. However, it was previously observed that first‐phase insulin secretion could not be identified using the IGI model, even in healthy volunteers during the oral glucose challenge 11, despite it being present during the intravenous provocations 12; therefore, it was difficult to know whether the patients used in the current analysis lacked first‐phase insulin secretion because they were diabetics or because an oral glucose challenge was used.

Another significant correlation that was identified was a relationship between BMI and ISS. It was observed that patients with a higher BMI had increased baseline insulin levels. Interestingly, BMI, rather than baseline HbA1c or T2DM duration, was a better predictor of insulin levels; this suggests that while GSS gradually rised when patients lost their glycaemic control (i.e. from HbA1c group 1 to group 4 patients), the insulin levels were related to the level of obesity of the patient, rather than their disease duration or their level of glycaemic control. In this way, the insulin levels would reflect total insulin resistance, which is known to increase with the magnitude of obesity. This finding is also in agreement with a recently published weight–HbA1c–insulin‐glucose model 31.

Interestingly, neither glucose absorption nor glucose bioavailability was found to be significantly different across T2DM patients. This is surprising, given that a well‐known complication is progressive autonomic gastrointestinal dysfunction, which manifests in both delayed gastric emptying and altered intestinal transit 32. Initial data exploration suggested that baseline HbA1c and/or diabetes duration may be related to either of these two parameters; however, the model‐based covariate search did not support this relationship. This lack of relationship may be potentially linked to the high variability in the data, known to be present during oral glucose provocations and associated with differences in gastric emptying 33, 34. It is also likely that the potential differences between liquid meals and standardized meals may contribute to the observed variability. More data, especially with dedicated gastric transit measurements, would be needed fully to understand and characterize the potential effects of patient‐specific covariates on glucose absorption and/or bioavailability. Unsurprisingly, however, glucose absorption was found to be affected by the glucose dose. The amount of glucose in the duodenum is known to affect gastric emptying, which in this model would translate to a lower glucose absorption rate with increasing glucose dose 34. This was also our finding: patients who received a higher dose of glucose had a lower absorption rate compared with patients receiving a lower glucose dose. This finding explains, in part, of the prolonged glucose profiles and late glucose t_max observed in patients from the D6420C00001 study (see Supporting Information, S4), where the highest glucose dose was used. Another factor that may contribute to these prolonged profiles is the estimate of the CLGI parameter, which is an indicator of insulin resistance. Patients from the D6420C00001 study were found to have lower estimates of CLGI compared with those from other studies (data not shown), and hence higher insulin resistance. High insulin resistance would cause the glucose elimination to be slow and that would consequently affect the shape of the profiles.

Overall, the IGI model was found accurately to characterize the glucose–insulin system following oral glucose provocations in a wide range of patients, from early diabetics to patients with many years of disease duration, as well as patients with various levels of glycaemic control. It was possible to characterize how different patients responded to the glucose test, depending on their baseline characteristics. This is best illustrated in Figure 2; it can be seen that with a gradual increase in HbA1c baseline, which reflects the loss of glycaemic control, there is a gradual increase in GSS and in insulin resistance. This is also accompanied by a gradual decrease in the incretin effect. It was interesting to find that baseline HbA1c was a better predictor of changes in the IGI model parameters than disease duration. This indicates that it is not primarily the total disease duration but the level of glycaemic control that is more predictive of the patients' response to a glucose challenge. However, it is important to note that the disease duration may not be an accurate biological or clinical estimate, and should be used with caution, given the high rate of long‐term undiagnosed T2DM in the population 35, 36.

As we were able to identify a number of patient‐specific covariates of the IGI model, it is expected that the model‐predicted population profiles following the glucose challenge will be different for different T2DM patients. Specifically, as HbA1c is a good predictor of a number of IGI parameters, it is expected that patients with different HbA1c baselines, and therefore different levels of glycaemic control, will respond differently to the same glucose challenge. This can be seen in glucose and insulin concentration–time profiles simulated for T2DM patients with various levels of glycaemic control; the glycaemic profiles deteriorate from group 1 to group 4 patients – i.e. from well‐ to poorly controlled diabetics. Such deterioration is consistent with previously reported glycaemic profiles in different groups of T2DM patients 37. The differences in the response to the glucose challenge between different patient populations may have potential implications for the design and simulation of future clinical studies in which antidiabetic drug effects are tested. For example, different patient population may be enrolled in the study (this can be controlled by modifying the inclusion/exclusion criteria) – e.g. mostly diabetics with low baseline HbA1c (well controlled), diabetics with high baseline HbA1c (poorly controlled) or patients with lower or higher BMI values. It is then expected that these patient groups will have different glucose and insulin concentration–time profiles, which can be easily simulated using the IGI model with added patient‐specific covariates. It should be highlighted that the extended IGI model presented here was developed for patients who are on metformin only, and it has not yet been validated in patients using other background therapies. The inclusion of patients on different therapies would be a valuable addition to the current model, and a potential next step of the work presented here.

The existence of patient‐specific covariates that describe differences between T2DM patients may also have an implication for estimation of potential drug effects – e.g. the same drug may have a different effect (i.e. of a different magnitude), depending on whether it is tested in patients with a low or high HbA1c baseline. Additionally, potential differences in the drug response may vary depending on the mechanism of action of the drug – a different impact may be expected for drugs targeting the incretin system compared with those that target glucose production or elimination. The expanded IGI model presented here, with the addition of patient‐specific covariates that can characterize different patient populations, may therefore be a valuable tool for simulation in future clinical studies. Such a framework can potentially be used for future optimization of drug treatments, including the assessment of different mechanisms of action across various patient groups.

Competing Interests

The authors declare no competing interests. J.P., B.H. and S.S. are employees/shareholders of AstraZeneca. M.C.K. is employed by Uppsala University, Sweden. All authors have completed the Unified Competing Interest form at http://www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declare: J.P., B.H. and S.S. had support from AstraZeneca for the submitted work; J.P., B.H. and S.S. have been shareholders of AstraZeneca in the previous 3 years; no other relationships or activities that could appear to have influenced the submitted work.

The authors would like to thank Hans Ericsson and Susanne Johansson for their help with data access and valuable discussions.

Supporting information

Figure S1 Schematic representation of the mechanistic integrated glucose–insulin model. Adapted from Silber et al. [11]

Figure S2 Correlations between diabetes duration (x‐axis) and selected patients’ baseline characteristics (y‐axis). Blue line corresponds to the loess smoothing (locally weighted polynomial regression, computed and plotted using R)

Figure S3 Correlations between baseline HbA1c (x‐axis) and selected patients baseline characteristics (y‐axis). Blue line corresponds to the loess smoothing (locally weighted polynomial regression, computed and plotted using R)

Figure S4 Time course of glucose levels in each of the studies. Grey data points correspond to the individual observations and the red line corresponds to the mean. The dotted line represents the time of maximum glucose levels (glucose tmax)

Figure S5 Time course of insulin levels in each of the studies. Grey data points correspond to the individual observations and the red line corresponds to the mean. The dotted line represents the time of maximum insulin levels (insulin tmax)

Figure S6 Etas of parameters of interest vs. diabetes duration (years). The blue line corresponds to the loess smoothing (computed and plotted using R)

Figure S7 Etas of parameters of interest vs. baseline HbA1c (%). The blue line corresponds to the loess smoothing (computed and plotted using R)

Figure S8 Etas of parameters of interest vs. baseline body mass index (BMI). The blue line corresponds to the loess smoothing (computed and plotted using R)

Figure S9 Goodness‐of‐fit plots of the final model: (Top) Glucose data only: (Bottom) Insulin data only.

Figure S10 Visual predictive check of the final model, stratified by patient disease duration group. Grey data points correspond to individual observations; the red line represents the median of the observed data; the black line represents the median model simulation; the shaded area corresponds to the 90% prediction interval

Figure S11 Visual predictive check of the final model, stratified by study. Grey data points correspond to individual observations; the red line represents the median of the observed data; the black line represents the median model simulation; the shaded area corresponds to the 90% prediction interval

Figure S12 Visual predictive check of the final model, stratified by glucose dose. Grey data points correspond to individual observations; the red line represents the median of the observed data; the black line represents the median model simulation; the shaded area corresponds to the 90% prediction interval

Figure S13 Visual predictive check of the final model, stratified by additional glycosylated haemoglobin (HbA1c) groups. Grey data points correspond to individual observations; the red line represents the median of the observed data; the black line represents the median model simulation; the shaded area corresponds to the 90% prediction interval

Table S. Summary statistics and patient‐specific parameter estimates from the integrated glucose–insulin model for the four glycosylated haemoglobin groups of type 2 diabetes mellitus patients used in the simulations

Table S2 Summary statistics and patient‐specific parameter estimates from the integrated glucose–insulin I model for the four diabetes duration groups of type 2 diabetes mellitus patients

Table S3 Summary statistics and patient‐specific parameter estimates from the integrated glucose–insulin model for the additional glycosylated haemoglobin groups of type 2 diabetes mellitus patients

Table S4 Correlation matrix for baseline characteristics

Table S5 Eta‐shrinkage for the estimated integrated glucose–insulin parameters (baseline model)

Table S6 Covariate model development

Table S7 Comparison of the parameter estimates from the current integrated glucose–insulin (IGT) model with the previously published data from healthy, IGT and type 2 diabetes patients

Supporting info item

Parkinson, J. , Hamrén, B. , Kjellsson, M. C. , and Skrtic, S. (2016) Application of the integrated glucose–insulin model for cross‐study characterization of T2DM patients on metformin background treatment. Br J Clin Pharmacol, 82: 1613–1624. doi: 10.1111/bcp.13069.