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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:	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/(FPG0FSI0) should be obtained instead of S0=FPG0FSI0/22.5.);
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.

Mandatory file
- DeWinter_2006_diabetes.xml

Additional Files

Model owner: Paolo Magni
Submitted: Sep 25, 2014 5:20:22 PM
Last Modified: Oct 10, 2016 9:56:13 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

Independent Variables

Function Definitions

additiveError : real (additive : real) = additive

Covariate Model: $cm$

Continuous Covariates

STEP

TREAT

Parameter Model: $pm$

Random Variables

{eta_EFF}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_EFF)

{eta_RB}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_RB)

{eta_RS}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_RS)

{eta_B0}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_B0)

{eta_S0}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_S0)

{eta_FRHB0}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_FRHB0)

{eps_RES_FSI}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.SIGMA_RES_FSI)

{eps_RES_FPG}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.SIGMA_RES_FPG)

{eps_RES_HB}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.SIGMA_RES_HB)

Population Parameters

K_OUT_FPG

K_OUT_HB

POP_FRHB0

POP_B0

POP_RB_G

POP_S0

POP_RS_G

EF_B_G

EF_S_M

EF_S_P

BETA_RB_P

BETA_RB_M

BETA_RS_P

BETA_RS_M

RES_FSI

RES_FSI30

RES_FPG

RES_HB

OMEGA_EFF

OMEGA_RB

OMEGA_RS

OMEGA_B0

OMEGA_S0

OMEGA_FRHB0

COV_B0_S0

COV_B0_FRHB0

COV_S0_FRHB0

SIGMA_RES_FSI

SIGMA_RES_FPG

SIGMA_RES_HB

TRT_M = {\begin{cases} 1 & if & cm.TREAT = 0 \\ 0 & otherwise \end{cases}

TRT_P = {\begin{cases} 1 & if & cm.TREAT = 1 \\ 0 & otherwise \end{cases}

TRT_G = {\begin{cases} 1 & if & cm.TREAT = 2 \\ 0 & otherwise \end{cases}

Individual Parameters

SHIFT_EF_B_G = pm.EF_B_G \cdot ⅇ^{pm.eta_EFF}

SHIFT_EF_S_M = pm.EF_S_M \cdot ⅇ^{pm.eta_EFF}

SHIFT_EF_S_P = pm.EF_S_P \cdot ⅇ^{pm.eta_EFF}

FRHB0 = pm.POP_FRHB0 \cdot ⅇ^{pm.eta_FRHB0}

B0 = pm.POP_B0 \cdot ⅇ^{pm.eta_B0}

S0 = pm.POP_S0 \cdot ⅇ^{pm.eta_S0}

RB = pm.POP_RB_G \cdot (1 + pm.TRT_P \cdot pm.BETA_RB_P + pm.TRT_M \cdot pm.BETA_RB_M) + pm.eta_RB

RS = pm.POP_RS_G \cdot (1 + pm.TRT_P \cdot pm.BETA_RS_P + pm.TRT_M \cdot pm.BETA_RS_M) + pm.eta_RS

K_OUT_FSI = 1

BB0 = \frac{1}{(1 + ⅇ^{pm.B0})}

SS0 = \frac{1}{(1 + ⅇ^{pm.S0})}

FSI0 = \frac{(- 5 \cdot 3.5 \cdot pm.BB0 + \sqrt{({(5 \cdot 3.5 \cdot pm.BB0)}^{2} + \frac{4 \cdot 5 \cdot 22.5 \cdot pm.BB0}{pm.SS0})})}{2}

FPG0 = \frac{22.5}{pm.SS0 \cdot pm.FSI0}

HB0 = pm.FRHB0 \cdot pm.FPG0

K_IN_FSI = 5 \cdot pm.K_OUT_FSI

K_IN_FPG = 22.5 \cdot pm.K_OUT_FPG

K_IN_HB = pm.FRHB0 \cdot pm.K_OUT_HB

Random Variable Correlation

cov (eta_B0, eta_S0) = pm.COV_B0_S0

cov (eta_B0, eta_FRHB0) = pm.COV_B0_FRHB0

cov (eta_S0, eta_FRHB0) = pm.COV_S0_FRHB0

Structural Model: $sm$

Variables

BB = \frac{1}{(1 + ⅇ^{(pm.B0 + \frac{pm.RB \cdot T}{365})})}

SS = \frac{1}{(1 + ⅇ^{(pm.S0 + \frac{pm.RS \cdot T}{365})})}

EF_B = 1 + pm.TRT_G \cdot cm.STEP \cdot pm.SHIFT_EF_B_G

EF_S = 1 + pm.TRT_M \cdot cm.STEP \cdot pm.SHIFT_EF_S_M + pm.TRT_P \cdot cm.STEP \cdot pm.SHIFT_EF_S_P

\begin{matrix} \frac{ⅆ}{ⅆ T} FSI = sm.EF_B \cdot sm.BB \cdot (sm.FPG - 3.5) \cdot pm.K_IN_FSI - sm.FSI \cdot pm.K_OUT_FSI \\ FSI (T = 0) = pm.FSI0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} FPG = \frac{pm.K_IN_FPG}{sm.EF_S \cdot sm.SS \cdot sm.FSI} - sm.FPG \cdot pm.K_OUT_FPG \\ FPG (T = 0) = pm.FPG0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} HB = sm.FPG \cdot pm.K_IN_HB - sm.HB \cdot pm.K_OUT_HB \\ HB (T = 0) = pm.HB0 \end{matrix}

logFSI = \ln (sm.FSI)

logFPG = \ln (sm.FPG)

logHB = \ln (sm.HB)

RES_FSI_IND = {\begin{cases} pm.RES_FSI & if & sm.FSI \leq 30 \\ {({pm.RES_FSI}^{2} + {pm.RES_FSI30}^{2})}^{0.5} & otherwise \end{cases}

Observation Model: $om1$

Continuous Observation

Y1 = sm.logFSI + additiveError (additive = sm.RES_FSI_IND) + pm.eps_RES_FSI

Observation Model: $om2$

Continuous Observation

Y2 = sm.logFPG + additiveError (additive = pm.RES_FPG) + pm.eps_RES_FPG

Observation Model: $om3$

Continuous Observation

Y3 = sm.logHB + additiveError (additive = pm.RES_HB) + pm.eps_RES_HB

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_winter2006_data.csv

Column Definitions

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

Column Mappings

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

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

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

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$focei$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000004: DeWinter_2006_diabetes

Revisions

Name

Independent Variables

Function Definitions

Covariate Model: cm

Continuous Covariates

Parameter Model: pm

Random Variables

Population Parameters

Individual Parameters

Random Variable Correlation

Structural Model: sm

Variables

Observation Model: om1

Continuous Observation

Observation Model: om2

Continuous Observation

Observation Model: om3

Continuous Observation

External Dataset

File Specification

Column Definitions

Column Mappings

Estimation Step

Parameters To Estimate

Operations

Operation: 1

Operation Properties

Step Dependencies

Covariate Model: $cm$

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Observation Model: $om2$

Observation Model: $om3$

Operation: $1$