# DDMODEL00000004: DeWinter_2006_diabetes

Short description:
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
 Format: PharmML 0.8.x (0.8.1) Related Publication: .hiddenContent {display:none;} 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. de Winter W, DeJongh J, Post T, Ploeger B, Urquhart R, Moules I, Eckland D, Danhof M Journal of pharmacokinetics and pharmacodynamics, 6/2006, Volume 33, Issue 3, pages: 313-343 Affiliation: LAP&P Consultants BV, Leiden, The Netherlands. Abstract: Effective long-term treatment of Type 2 Diabetes Mellitus (T2DM) implies modification of the disease processes that cause this progressive disorder. This paper proposes a mechanism-based approach to disease progression modeling of T2DM that aims to provide the ability to describe and quantify the effects of treatment on the time-course of the progressive loss of beta-cell function and insulin-sensitivity underlying T2DM. It develops a population pharmacodynamic model that incorporates mechanism-based representations of the homeostatic feedback relationships between fasting levels of plasma glucose (FPG) and fasting serum insulin (FSI), and the physiological feed-forward relationship between FPG and glycosylated hemoglobin A1c (HbA1c). This model was developed on data from two parallel one-year studies comparing the effects of pioglitazone relative to metformin or sulfonylurea treatment in 2,408 treatment-naïve T2DM patients. It was found that the model provided accurate descriptions of the time-courses of FPG and HbA1c for different treatment arms. It allowed the identification of the long-term effects of different treatments on loss of beta-cell function and insulin-sensitivity, independently from their immediate anti-hyperglycemic effects modeled at their specific sites of action. Hence it avoided the confounding of these effects that is inherent in point estimates of beta-cell function and insulin-sensitivity such as the widely used HOMA-%B and HOMA-%S. It was also found that metformin therapy did not result in a reduction in FSI levels in conjunction with reduced FPG levels, as expected for an insulin-sensitizer, whereas pioglitazone therapy did. It is concluded that, although its current implementation leaves room for further improvement, the mechanism-based approach presented here constitutes a promising conceptual advance in the study of T2DM disease progression and disease modification. Contributors: Paolo Magni
 Context of model development: Clinical end-point; Mechanistic Understanding; Discrepancy between implemented model and original publication: However, because the original code was not available, this implementation might be different from the one used in the original publication in model parts that are not described in detail. In addition, initial value expressions for FPG0 and FSI0 are derived from the differential equations at the steady-state (Eq.1-2 in the paper), since the reported expressions (Eq.6-7 in the paper) contain an error: from Eq.7 S0=22.5/(FPG0*FSI0) should be obtained instead of S0=FPG0*FSI0/22.5.); Model compliance with original publication: Yes; Model implementation requiring submitter’s additional knowledge: No; Modelling context description: Effective long-term treatment of Type 2 Diabetes Mellitus (T2DM) implies modification of the disease processes that cause this progressive disorder. This paper proposes a mechanism-based approach to disease progression modeling of T2DM that aims to provide the ability to describe and quantify the effects of treatment on the time-course of the progressive loss of beta-cell function and insulin-sensitivity underlying T2DM. It develops a population pharmacodynamic model that incorporates mechanism-based representations of the homeostatic feedback relationships between fasting levels of plasma glucose (FPG) and fasting serum insulin (FSI), and the physiological feed-forward relationship between FPG and glycosylated hemoglobin A1c (HbA1c). This model was developed on data from two parallel one-year studies comparing the effects of pioglitazone relative to metformin or sulfonylurea treatment in 2,408 treatment-naïve T2DM patients. It was found that the model provided accurate descriptions of the time-courses of FPG and HbA1c for different treatment arms. It allowed the identification of the long-term effects of different treatments on loss of beta-cell function and insulin-sensitivity, independently from their immediate anti-hyperglycemic effects modeled at their specific sites of action. Hence it avoided the confounding of these effects that is inherent in point estimates of beta-cell function and insulin-sensitivity such as the widely used HOMA-%B and HOMA-%S. It was also found that metformin therapy did not result in a reduction in FSI levels in conjunction with reduced FPG levels, as expected for an insulin-sensitizer, whereas pioglitazone therapy did. It is concluded that, although its current implementation leaves room for further improvement, the mechanism-based approach presented here constitutes a promising conceptual advance in the study of T2DM disease progression and disease modification; Modelling task in scope: estimation; Nature of research: Clinical research & Therapeutic use; Therapeutic/disease area: Endocrinology;
 Validation Status: Annotations are correct. Certification Comment: This model is not certified.
• Model owner: Paolo Magni
• Submitted: Sep 25, 2014 5:20:22 PM
##### Revisions
• Version: 7
• Submitted on: Oct 10, 2016 9:56:13 PM
• Submitted by: Paolo Magni
• With comment: Update MDL syntax to the version 1.0 and R script to SEE version 2.0.0. Code automatically generated for NONMEM and MONOLIX
• Version: 6
• Submitted on: Jul 16, 2016 4:24:05 PM
• Submitted by: Paolo Magni
• With comment: Updated model annotations.
• Version: 3
• Submitted on: Dec 11, 2015 3:32:36 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.
• Version: 1
• Submitted on: Sep 25, 2014 5:20:22 PM
• Submitted by: Paolo Magni
• With comment: Import of DeWinter_2006_diabetes

### Name

Generated from MDL. MOG ID: dewinter2006_mog

 T

### Function Definitions

 $\mathrm{additiveError}:\mathrm{real}\left(\mathrm{additive}:\mathrm{real}\right)=\mathrm{additive}$

### Covariate Model: $\mathrm{cm}$

#### Continuous Covariates

$\mathrm{STEP}$
$\mathrm{TREAT}$

### Parameter Model: $\mathrm{pm}$

#### Random Variables

${\mathrm{eta_EFF}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_EFF}\right)$
${\mathrm{eta_RB}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_RB}\right)$
${\mathrm{eta_RS}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_RS}\right)$
${\mathrm{eta_B0}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_B0}\right)$
${\mathrm{eta_S0}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_S0}\right)$
${\mathrm{eta_FRHB0}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_FRHB0}\right)$
${\mathrm{eps_RES_FSI}}_{\mathrm{vm_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.SIGMA_RES_FSI}\right)$
${\mathrm{eps_RES_FPG}}_{\mathrm{vm_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.SIGMA_RES_FPG}\right)$
${\mathrm{eps_RES_HB}}_{\mathrm{vm_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.SIGMA_RES_HB}\right)$

#### Population Parameters

$\mathrm{K_OUT_FPG}$
$\mathrm{K_OUT_HB}$
$\mathrm{POP_FRHB0}$
$\mathrm{POP_B0}$
$\mathrm{POP_RB_G}$
$\mathrm{POP_S0}$
$\mathrm{POP_RS_G}$
$\mathrm{EF_B_G}$
$\mathrm{EF_S_M}$
$\mathrm{EF_S_P}$
$\mathrm{BETA_RB_P}$
$\mathrm{BETA_RB_M}$
$\mathrm{BETA_RS_P}$
$\mathrm{BETA_RS_M}$
$\mathrm{RES_FSI}$
$\mathrm{RES_FSI30}$
$\mathrm{RES_FPG}$
$\mathrm{RES_HB}$
$\mathrm{OMEGA_EFF}$
$\mathrm{OMEGA_RB}$
$\mathrm{OMEGA_RS}$
$\mathrm{OMEGA_B0}$
$\mathrm{OMEGA_S0}$
$\mathrm{OMEGA_FRHB0}$
$\mathrm{COV_B0_S0}$
$\mathrm{COV_B0_FRHB0}$
$\mathrm{COV_S0_FRHB0}$
$\mathrm{SIGMA_RES_FSI}$
$\mathrm{SIGMA_RES_FPG}$
$\mathrm{SIGMA_RES_HB}$
$\mathrm{TRT_M}=\left\{\begin{array}{lll}1& \text{if}& \mathrm{cm.TREAT}=0\\ 0& \text{otherwise}& \end{array}$
$\mathrm{TRT_P}=\left\{\begin{array}{lll}1& \text{if}& \mathrm{cm.TREAT}=1\\ 0& \text{otherwise}& \end{array}$
$\mathrm{TRT_G}=\left\{\begin{array}{lll}1& \text{if}& \mathrm{cm.TREAT}=2\\ 0& \text{otherwise}& \end{array}$

#### Individual Parameters

$\mathrm{SHIFT_EF_B_G}=\mathrm{pm.EF_B_G}\cdot {e}^{\mathrm{pm.eta_EFF}}$
$\mathrm{SHIFT_EF_S_M}=\mathrm{pm.EF_S_M}\cdot {e}^{\mathrm{pm.eta_EFF}}$
$\mathrm{SHIFT_EF_S_P}=\mathrm{pm.EF_S_P}\cdot {e}^{\mathrm{pm.eta_EFF}}$
$\mathrm{FRHB0}=\mathrm{pm.POP_FRHB0}\cdot {e}^{\mathrm{pm.eta_FRHB0}}$
$\mathrm{B0}=\mathrm{pm.POP_B0}\cdot {e}^{\mathrm{pm.eta_B0}}$
$\mathrm{S0}=\mathrm{pm.POP_S0}\cdot {e}^{\mathrm{pm.eta_S0}}$
$\mathrm{RB}=\mathrm{pm.POP_RB_G}\cdot \left(1+\mathrm{pm.TRT_P}\cdot \mathrm{pm.BETA_RB_P}+\mathrm{pm.TRT_M}\cdot \mathrm{pm.BETA_RB_M}\right)+\mathrm{pm.eta_RB}$
$\mathrm{RS}=\mathrm{pm.POP_RS_G}\cdot \left(1+\mathrm{pm.TRT_P}\cdot \mathrm{pm.BETA_RS_P}+\mathrm{pm.TRT_M}\cdot \mathrm{pm.BETA_RS_M}\right)+\mathrm{pm.eta_RS}$
$\mathrm{K_OUT_FSI}=1$
$\mathrm{BB0}=\frac{1}{\left(1+{e}^{\mathrm{pm.B0}}\right)}$
$\mathrm{SS0}=\frac{1}{\left(1+{e}^{\mathrm{pm.S0}}\right)}$
$\mathrm{FSI0}=\frac{\left(-5\cdot 3.5\cdot \mathrm{pm.BB0}+\sqrt{\left({\left(5\cdot 3.5\cdot \mathrm{pm.BB0}\right)}^{2}+\frac{4\cdot 5\cdot 22.5\cdot \mathrm{pm.BB0}}{\mathrm{pm.SS0}}\right)}\right)}{2}$
$\mathrm{FPG0}=\frac{22.5}{\mathrm{pm.SS0}\cdot \mathrm{pm.FSI0}}$
$\mathrm{HB0}=\mathrm{pm.FRHB0}\cdot \mathrm{pm.FPG0}$
$\mathrm{K_IN_FSI}=5\cdot \mathrm{pm.K_OUT_FSI}$
$\mathrm{K_IN_FPG}=22.5\cdot \mathrm{pm.K_OUT_FPG}$
$\mathrm{K_IN_HB}=\mathrm{pm.FRHB0}\cdot \mathrm{pm.K_OUT_HB}$

#### Random Variable Correlation

$\mathrm{cov}\left(\mathrm{eta_B0},\mathrm{eta_S0}\right)=\mathrm{pm.COV_B0_S0}$
$\mathrm{cov}\left(\mathrm{eta_B0},\mathrm{eta_FRHB0}\right)=\mathrm{pm.COV_B0_FRHB0}$
$\mathrm{cov}\left(\mathrm{eta_S0},\mathrm{eta_FRHB0}\right)=\mathrm{pm.COV_S0_FRHB0}$

### Structural Model: $\mathrm{sm}$

#### Variables

$\mathrm{BB}=\frac{1}{\left(1+{e}^{\left(\mathrm{pm.B0}+\frac{\mathrm{pm.RB}\cdot T}{365}\right)}\right)}$
$\mathrm{SS}=\frac{1}{\left(1+{e}^{\left(\mathrm{pm.S0}+\frac{\mathrm{pm.RS}\cdot T}{365}\right)}\right)}$
$\mathrm{EF_B}=1+\mathrm{pm.TRT_G}\cdot \mathrm{cm.STEP}\cdot \mathrm{pm.SHIFT_EF_B_G}$
$\mathrm{EF_S}=1+\mathrm{pm.TRT_M}\cdot \mathrm{cm.STEP}\cdot \mathrm{pm.SHIFT_EF_S_M}+\mathrm{pm.TRT_P}\cdot \mathrm{cm.STEP}\cdot \mathrm{pm.SHIFT_EF_S_P}$
$\begin{array}{c}\frac{d}{dT}\mathrm{FSI}=\mathrm{sm.EF_B}\cdot \mathrm{sm.BB}\cdot \left(\mathrm{sm.FPG}-3.5\right)\cdot \mathrm{pm.K_IN_FSI}-\mathrm{sm.FSI}\cdot \mathrm{pm.K_OUT_FSI}\\ \mathrm{FSI}\left(T=0\right)=\mathrm{pm.FSI0}\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{FPG}=\frac{\mathrm{pm.K_IN_FPG}}{\mathrm{sm.EF_S}\cdot \mathrm{sm.SS}\cdot \mathrm{sm.FSI}}-\mathrm{sm.FPG}\cdot \mathrm{pm.K_OUT_FPG}\\ \mathrm{FPG}\left(T=0\right)=\mathrm{pm.FPG0}\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{HB}=\mathrm{sm.FPG}\cdot \mathrm{pm.K_IN_HB}-\mathrm{sm.HB}\cdot \mathrm{pm.K_OUT_HB}\\ \mathrm{HB}\left(T=0\right)=\mathrm{pm.HB0}\end{array}$
$\mathrm{logFSI}=\mathrm{ln}\left(\mathrm{sm.FSI}\right)$
$\mathrm{logFPG}=\mathrm{ln}\left(\mathrm{sm.FPG}\right)$
$\mathrm{logHB}=\mathrm{ln}\left(\mathrm{sm.HB}\right)$
$\mathrm{RES_FSI_IND}=\left\{\begin{array}{lll}\mathrm{pm.RES_FSI}& \text{if}& \mathrm{sm.FSI}\le 30\\ {\left({\mathrm{pm.RES_FSI}}^{2}+{\mathrm{pm.RES_FSI30}}^{2}\right)}^{0.5}& \text{otherwise}& \end{array}$

### Observation Model: $\mathrm{om1}$

#### Continuous Observation

$\mathrm{Y1}=\mathrm{sm.logFSI}+\mathrm{additiveError}\left(\mathrm{additive}=\mathrm{sm.RES_FSI_IND}\right)+\mathrm{pm.eps_RES_FSI}$

### Observation Model: $\mathrm{om2}$

#### Continuous Observation

$\mathrm{Y2}=\mathrm{sm.logFPG}+\mathrm{additiveError}\left(\mathrm{additive}=\mathrm{pm.RES_FPG}\right)+\mathrm{pm.eps_RES_FPG}$

### Observation Model: $\mathrm{om3}$

#### Continuous Observation

$\mathrm{Y3}=\mathrm{sm.logHB}+\mathrm{additiveError}\left(\mathrm{additive}=\mathrm{pm.RES_HB}\right)+\mathrm{pm.eps_RES_HB}$

## External Dataset

 OID $\mathrm{nm_ds}$ Tool Format NONMEM

### File Specification

 Format $\mathrm{csv}$ Delimiter comma File Location Simulated_winter2006_data.csv

### Column Definitions

Column ID Position Column Type Value Type
$\mathrm{ID}$
$1$
$\mathrm{id}$
$\mathrm{int}$
$\mathrm{TIME}$
$2$
$\mathrm{idv}$
$\mathrm{real}$
$\mathrm{DV}$
$3$
$\mathrm{dv}$
$\mathrm{real}$
$\mathrm{STEP}$
$4$
$\mathrm{covariate}$
$\mathrm{real}$
$\mathrm{TREAT}$
$5$
$\mathrm{covariate}$
$\mathrm{real}$
$\mathrm{ORIG}$
$6$
$\mathrm{dvid}$
$\mathrm{int}$
$\mathrm{EVID}$
$7$
$\mathrm{undefined}$
$\mathrm{real}$

### Column Mappings

Column Ref Modelling Mapping
$ID$
$\mathrm{vm_mdl.ID}$
$TIME$
$T$
$DV$
$\left\{\begin{array}{lll}\mathrm{om1.Y1}& \text{if}& \mathrm{ORIG}=1\\ \mathrm{om2.Y2}& \text{if}& \mathrm{ORIG}=2\\ \mathrm{om3.Y3}& \text{if}& \mathrm{ORIG}=3\end{array}$
$STEP$
$\mathrm{cm.STEP}$
$TREAT$
$\mathrm{cm.TREAT}$

## Estimation Step

 OID $\mathrm{estimStep_1}$ Dataset Reference $\mathrm{nm_ds}$

### Parameters To Estimate

Parameter Initial Value Fixed? Limits
pm.K_OUT_FPG
$0.021$
false
$\left(,\right)$
pm.K_OUT_HB
$0.0272$
false
$\left(,\right)$
pm.POP_FRHB0
$0.82$
false
$\left(,\right)$
pm.POP_B0
$0.635$
false
$\left(,\right)$
pm.POP_RB_G
$0.178$
false
$\left(,\right)$
pm.POP_S0
$1.38$
false
$\left(,\right)$
pm.POP_RS_G
$0.245$
false
$\left(,\right)$
pm.EF_B_G
$1.115$
false
$\left(,\right)$
pm.EF_S_M
$0.699$
false
$\left(,\right)$
pm.EF_S_P
$0.649$
false
$\left(,\right)$
pm.BETA_RB_P
$-2.24$
false
$\left(,\right)$
pm.BETA_RB_M
$-2.82$
false
$\left(,\right)$
pm.BETA_RS_P
$0.567$
false
$\left(,\right)$
pm.BETA_RS_M
$1.01$
false
$\left(,\right)$
pm.RES_FSI
$0.2985$
false
$\left(,\right)$
pm.RES_FSI30
$0.6124$
false
$\left(,\right)$
pm.RES_FPG
$0.1277$
false
$\left(,\right)$
pm.RES_HB
$0.0438$
false
$\left(,\right)$
pm.OMEGA_EFF
$0.13$
false
$\left(,\right)$
pm.OMEGA_RB
$0.0125$
false
$\left(,\right)$
pm.OMEGA_RS
$0.00805$
false
$\left(,\right)$
pm.OMEGA_B0
$0.967$
false
$\left(,\right)$
pm.OMEGA_S0
$0.519$
false
$\left(,\right)$
pm.OMEGA_FRHB0
$0.0158$
false
$\left(,\right)$
pm.COV_B0_S0
$-0.48$
false
$\left(,\right)$
pm.COV_B0_FRHB0
$-0.053$
false
$\left(,\right)$
pm.COV_S0_FRHB0
$-0.0185$
false
$\left(,\right)$
pm.SIGMA_RES_FSI
$1$
true
$\left(,\right)$
pm.SIGMA_RES_FPG
$1$
true
$\left(,\right)$
pm.SIGMA_RES_HB
$1$
true
$\left(,\right)$

### Operations

#### Operation: $1$

 Op Type generic
##### Operation Properties
Name Value
algo
$\text{focei}$

## Step Dependencies

Step OID Preceding Steps
$\mathrm{estimStep_1}$