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Short description:

Population PK/PD model describing the interplay between tesaglitazar and fasting plasma glucose, hemoglobin, and glycosylated hemoglobin in type 2 diabetic patients.

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Models for plasma glucose, HbA1c, and hemoglobin interrelationships in patients with type 2 diabetes following tesaglitazar treatment. Hamrén B, Björk E, Sunzel M, Karlsson M Clinical pharmacology and therapeutics, 8/2008, Volume 84, Issue 2, pages: 228-235 Affiliation: Department of Medical Science, Clinical Pharmacology, AstraZeneca R&D Mölndal, Mölndal, Sweden. bengt.hamren@astrazeneca.com Abstract: Pharmacokinetic (PK) pharmacodynamic (PD) modeling was applied to understand and quantitate the interplay between tesaglitazar (a peroxisome proliferator-activated receptor alpha/gamma agonist) exposure, fasting plasma glucose (FPG), hemoglobin (Hb), and glycosylated hemoglobin (HbA1c) in type 2 diabetic patients. Data originated from a 12-week dose-ranging study with tesaglitazar. The primary objective was to develop a mechanism-based PD model for the FPG-HbA1c relationship. The secondary objective was to investigate possible mechanisms for the tesaglitazar effect on Hb. Following initiation of tesaglitazar therapy, time to new FPG steady state was approximately 9 weeks, and tesaglitazar potency in females was twice that in males. The model included aging of red blood cells (RBCs) using a transit compartment approach. The RBC life span was estimated to 135 days. The transformation from RBC to HbA1c was modeled as an FPG-dependent process. The model indicated that the tesaglitazar effect on Hb was caused by hemodilution of RBCs.
Contributors:	Paolo Magni

Context of model development:	Clinical end-point; Mechanistic Understanding;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	Pharmacokinetic (PK) pharmacodynamic (PD) modeling was applied to understand and quantitate the interplay between tesaglitazar (a peroxisome proliferator-activated receptor alpha/gamma agonist) exposure, fasting plasma glucose (FPG), hemoglobin (Hb), and glycosylated hemoglobin (HbA1c) in type 2 diabetic patients. Data originated from a 12-week dose-ranging study with tesaglitazar. The primary objective was to develop a mechanism-based PD model for the FPG-HbA1c relationship. The secondary objective was to investigate possible mechanisms for the tesaglitazar effect on Hb. Following initiation of tesaglitazar therapy, time to new FPG steady state was approximately 9 weeks, and tesaglitazar potency in females was twice that in males. The model included aging of red blood cells (RBCs) using a transit compartment approach. The RBC life span was estimated to 135 days. The transformation from RBC to HbA1c was modeled as an FPG-dependent process. The model indicated that the tesaglitazar effect on Hb was caused by hemodilution of RBCs.;
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
- Hamren_2008_diabetes_tesaglitazar.xml

Additional Files

Model owner: Paolo Magni
Submitted: Dec 10, 2015 10:16:55 AM
Last Modified: Oct 10, 2016 9:31:51 PM

Revisions

Version: 10
- Submitted on: Oct 10, 2016 9:31:51 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: 9
- Submitted on: Jun 2, 2016 8:37:50 PM
- Submitted by: Paolo Magni
- With comment: Updated model annotations.
Version: 6
- Submitted on: Dec 11, 2015 7:47:09 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.
Version: 4
- Submitted on: Dec 10, 2015 10:16:55 AM
- Submitted by: Paolo Magni
- With comment: Updated simulated data set

Name

Generated from MDL. MOG ID: hamren2008_mog

Independent Variables

Function Definitions

additiveError : real (additive : real) = additive

Covariate Model: $cm$

Continuous Covariates

SEX

TREAT

CL

V

Parameter Model: $pm$

Random Variables

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

{eta_EC_50_FPG}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_EC_50_FPG)

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

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

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

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

{eta_EC_50_DILUTION}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_EC_50_DILUTION)

{eta_RES_HBA1C}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.OMEGA_RES_HBA1C)

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

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

{eps_RES_HBA1C}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.SIGMA_RES_HBA1C)

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

Population Parameters

BETA_FPG_BASELINE

POP_FPG_BASELINE_N

K_OUT_FPG

E_MAX_FPG

BETA_EC_50_FPG

POP_EC_50_FPG_F

BETA_FPG_WASHOUT

POP_FPG_WASHOUT_N

POP_RES_FPG

POP_GAMMA

K_GLUCOSE

RBC_LIFESPAN

BETA_K_IN_RBC

POP_K_IN_RBC_F

E_MAX_DILUTION

POP_EC_50_DILUTION

K_OUT_DILUTION

POP_RES_HBA1C

POP_RES_HB

OMEGA_FPG_BASELINE

OMEGA_EC_50_FPG

OMEGA_FPG_WASHOUT

OMEGA_RES_FPG

OMEGA_GAMMA

OMEGA_K_IN_RBC

OMEGA_EC_50_DILUTION

OMEGA_RES_HBA1C

OMEGA_RES_HB

SIGMA_RES_FPG

SIGMA_RES_HBA1C

SIGMA_RES_HB

POP_EC_50_FPG = {\begin{cases} pm.POP_EC_50_FPG_F & if & cm.SEX = 2 \\ pm.POP_EC_50_FPG_F + pm.BETA_EC_50_FPG & otherwise \end{cases}

POP_K_IN_RBC = {\begin{cases} pm.POP_K_IN_RBC_F & if & cm.SEX = 2 \\ pm.POP_K_IN_RBC_F + pm.BETA_K_IN_RBC & otherwise \end{cases}

POP_FPG_BASELINE = {\begin{cases} pm.POP_FPG_BASELINE_N & if & cm.TREAT = 1 \\ pm.POP_FPG_BASELINE_N + pm.BETA_FPG_BASELINE & otherwise \end{cases}

POP_FPG_WASHOUT = {\begin{cases} pm.POP_FPG_WASHOUT_N & if & cm.TREAT = 1 \\ pm.POP_FPG_WASHOUT_N + pm.BETA_FPG_WASHOUT & otherwise \end{cases}

Individual Parameters

FPG_BASELINE = pm.POP_FPG_BASELINE \cdot ⅇ^{pm.eta_FPG_BASELINE}

EC_50_FPG = pm.POP_EC_50_FPG \cdot ⅇ^{pm.eta_EC_50_FPG}

FPG_WASHOUT = pm.POP_FPG_WASHOUT \cdot ⅇ^{pm.eta_FPG_WASHOUT}

RES_FPG = pm.POP_RES_FPG \cdot ⅇ^{pm.eta_RES_FPG}

GAMMA = pm.POP_GAMMA \cdot ⅇ^{pm.eta_GAMMA}

K_IN_RBC = pm.POP_K_IN_RBC \cdot ⅇ^{pm.eta_K_IN_RBC}

EC_50_DILUTION = pm.POP_EC_50_DILUTION \cdot ⅇ^{pm.eta_EC_50_DILUTION}

RES_HBA1C = pm.POP_RES_HBA1C \cdot ⅇ^{pm.eta_RES_HBA1C}

RES_HB = pm.POP_RES_HB \cdot ⅇ^{pm.eta_RES_HB}

K_IN_FPG = pm.K_OUT_FPG \cdot pm.FPG_BASELINE

K_TR = \frac{4}{pm.RBC_LIFESPAN}

NON_RBC10 = \frac{pm.K_IN_RBC}{(pm.K_TR + pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA})}

NON_RBC20 = \frac{pm.K_TR \cdot pm.NON_RBC10}{(pm.K_TR + pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA})}

NON_RBC30 = \frac{pm.K_TR \cdot pm.NON_RBC20}{(pm.K_TR + pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA})}

NON_RBC40 = \frac{pm.K_TR \cdot pm.NON_RBC30}{(pm.K_TR + pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA})}

RBC10 = \frac{pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA} \cdot pm.NON_RBC10}{pm.K_TR}

RBC20 = \frac{(pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA} \cdot pm.NON_RBC20 + pm.K_TR \cdot pm.RBC10)}{pm.K_TR}

RBC30 = \frac{(pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA} \cdot pm.NON_RBC30 + pm.K_TR \cdot pm.RBC20)}{pm.K_TR}

RBC40 = \frac{(pm.K_GLUCOSE \cdot {pm.FPG_BASELINE}^{pm.GAMMA} \cdot pm.NON_RBC40 + pm.K_TR \cdot pm.RBC30)}{pm.K_TR}

Kout = \frac{cm.CL}{cm.V}

Structural Model: $sm$

Variables

CP = \frac{sm.QP}{cm.V}

\begin{matrix} \frac{ⅆ}{ⅆ T} QP = - pm.Kout \cdot sm.QP \\ QP (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} FPG = pm.K_IN_FPG \cdot (1 + pm.FPG_WASHOUT) - pm.K_OUT_FPG \cdot sm.FPG \cdot (1 + \frac{pm.E_MAX_FPG \cdot sm.CP}{(pm.EC_50_FPG + sm.CP)}) \\ FPG (T = 0) = pm.FPG_BASELINE \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} NON_RBC1 = pm.K_IN_RBC - (pm.K_TR + pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA}) \cdot sm.NON_RBC1 \\ NON_RBC1 (T = 0) = pm.NON_RBC10 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} NON_RBC2 = pm.K_TR \cdot sm.NON_RBC1 - (pm.K_TR + pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA}) \cdot sm.NON_RBC2 \\ NON_RBC2 (T = 0) = pm.NON_RBC20 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} NON_RBC3 = pm.K_TR \cdot sm.NON_RBC2 - (pm.K_TR + pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA}) \cdot sm.NON_RBC3 \\ NON_RBC3 (T = 0) = pm.NON_RBC30 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} NON_RBC4 = pm.K_TR \cdot sm.NON_RBC3 - (pm.K_TR + pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA}) \cdot sm.NON_RBC4 \\ NON_RBC4 (T = 0) = pm.NON_RBC40 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} RBC1 = pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA} \cdot sm.NON_RBC1 - pm.K_TR \cdot sm.RBC1 \\ RBC1 (T = 0) = pm.RBC10 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} RBC2 = pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA} \cdot sm.NON_RBC2 + pm.K_TR \cdot sm.RBC1 - pm.K_TR \cdot sm.RBC2 \\ RBC2 (T = 0) = pm.RBC20 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} RBC3 = pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA} \cdot sm.NON_RBC3 + pm.K_TR \cdot sm.RBC2 - pm.K_TR \cdot sm.RBC3 \\ RBC3 (T = 0) = pm.RBC30 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} RBC4 = pm.K_GLUCOSE \cdot {sm.FPG}^{pm.GAMMA} \cdot sm.NON_RBC4 + pm.K_TR \cdot sm.RBC3 - pm.K_TR \cdot sm.RBC4 \\ RBC4 (T = 0) = pm.RBC40 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} VHB = pm.K_OUT_DILUTION \cdot (1 + \frac{pm.E_MAX_DILUTION \cdot sm.CP}{(pm.EC_50_DILUTION + sm.CP)} - sm.VHB) \\ VHB (T = 0) = 1 \end{matrix}

TOTRBC = sm.NON_RBC1 + sm.NON_RBC2 + sm.NON_RBC3 + sm.NON_RBC4 + sm.RBC1 + sm.RBC2 + sm.RBC3 + sm.RBC4

GLYRBC = sm.RBC1 + sm.RBC2 + sm.RBC3 + sm.RBC4

HBA1C = \frac{100 \cdot sm.GLYRBC}{sm.TOTRBC}

HB = \frac{sm.TOTRBC}{sm.VHB}

logHBA1C = \ln (sm.HBA1C)

logFPG = \ln (sm.FPG)

logHB = \ln (sm.HB)

Observation Model: $om1$

Continuous Observation

Y1 = sm.logHBA1C + additiveError (additive = pm.RES_HBA1C) + pm.eps_RES_HBA1C

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_hamren2008_data_DAY.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$DV$	$3$	$dv$	$real$
$AMT$	$4$	$dose$	$real$
$RATE$	$5$	$rate$	$real$
$CMT$	$6$	$cmt$	$int$
$CL$	$7$	$covariate$	$real$
$V$	$8$	$covariate$	$real$
$SEX$	$9$	$covariate$	$real$
$TREAT$	$10$	$covariate$	$real$
$ORIG$	$11$	$dvid$	$int$
$EVID$	$12$	$evid$	$real$
$DOSE$	$13$	$undefined$	$real$

Column Mappings

Column Ref	Modelling Mapping
$ID$	$vm_mdl.ID$
$TIME$	$T$
$DV$	${\begin{cases} om1.Y1 & if & ORIG = 1 \\ om2.Y2 & if & ORIG = 2 \\ om3.Y3 & if & ORIG = 3 \end{cases}$
$AMT$	${\begin{cases} sm.QP & if & AMT > 0 \end{cases}$
$CL$	$cm.CL$
$V$	$cm.V$
$SEX$	$cm.SEX$
$TREAT$	$cm.TREAT$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Initial Value	Fixed?	Limits
pm.BETA_FPG_BASELINE	$- 0.52$	false	$()$
pm.POP_FPG_BASELINE_N	$8.72$	false	$(6, 10)$
pm.K_OUT_FPG	$0.0367$	false	$(1.0E-4, 0.1)$
pm.E_MAX_FPG	$0.698$	false	$(0.4, 0.99)$
pm.BETA_EC_50_FPG	$0.6$	false	$(0)$
pm.POP_EC_50_FPG_F	$0.88$	false	$(0.2, 4)$
pm.BETA_FPG_WASHOUT	$0.164$	false	$(0.01, 1)$
pm.POP_FPG_WASHOUT_N	$0$	true	$()$
pm.POP_RES_FPG	$0.0964$	false	$(0.01, 0.2)$
pm.POP_GAMMA	$0.743$	false	$(0.4, 1.5)$
pm.K_GLUCOSE	$1.81E-4$	false	$(0)$
pm.RBC_LIFESPAN	$135$	false	$(1, 333)$
pm.BETA_K_IN_RBC	$0.09$	false	$(0)$
pm.POP_K_IN_RBC_F	$1.02$	false	$(0.1, 2)$
pm.E_MAX_DILUTION	$0.682$	false	$(0, 1)$
pm.POP_EC_50_DILUTION	$8.25$	false	$(0.01, 20)$
pm.K_OUT_DILUTION	$0.0305$	false	$(0)$
pm.POP_RES_HBA1C	$0.0495$	false	$(0, 0.1)$
pm.POP_RES_HB	$0.0298$	false	$(0, 0.1)$
pm.OMEGA_FPG_BASELINE	$0.0196$	false	$()$
pm.OMEGA_EC_50_FPG	$1.21$	false	$()$
pm.OMEGA_FPG_WASHOUT	$0.64$	false	$()$
pm.OMEGA_RES_FPG	$0.13$	false	$()$
pm.OMEGA_GAMMA	$0.0035$	false	$()$
pm.OMEGA_K_IN_RBC	$0.005$	false	$()$
pm.OMEGA_EC_50_DILUTION	$0.31$	false	$()$
pm.OMEGA_RES_HBA1C	$0.068$	false	$()$
pm.OMEGA_RES_HB	$0.029$	false	$()$
pm.SIGMA_RES_FPG	$1$	true	$()$
pm.SIGMA_RES_HBA1C	$1$	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
$estimStep_1$

DDMODEL00000003: Hamren_2008_diabetes_tesaglitazar

Revisions

Name

Independent Variables

Function Definitions

Covariate Model: cm

Continuous Covariates

Parameter Model: pm

Random Variables

Population Parameters

Individual Parameters

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: $1$