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Short description:

Population model of glycosylation of red blood cells to simulate the longitudinal relationship between HbA1c and mean plasma glucose in normal and diabetic subjects.

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	A semi-mechanistic model of the relationship between average glucose and HbA1c in healthy and diabetic subjects. Lledó-García R, Mazer NA, Karlsson MO Journal of pharmacokinetics and pharmacodynamics, 4/2013, Volume 40, Issue 2, pages: 129-142 Affiliation: Pharmacometrics Research Group, Department of Pharmaceutical Biosciences, Uppsala University, Box 591, SE 751 24, Uppsala, Sweden. rocio.lledo@gmail.com Abstract: HbA1c is the most commonly used biomarker for the adequacy of glycemic management in diabetic patients and a surrogate endpoint for anti-diabetic drug approval. In spite of an empirical description for the relationship between average glucose (AG) and HbA1c concentrations, obtained from the A1c-derived average glucose (ADAG) study by Nathan et al., a model for the non-steady-state relationship is still lacking. Using data from the ADAG study, we here develop such models that utilize literature information on (patho)physiological processes and assay characteristics. The model incorporates the red blood cell (RBC) aging description, and uses prior values of the glycosylation rate constant (KG), mean RBC life-span (LS) and mean RBC precursor LS obtained from the literature. Different hypothesis were tested to explain the observed non-proportional relationship between AG and HbA1c. Both an inverse dependence of LS on AG and a non-specificity of the National Glycohemoglobin Standardization Program assay used could well describe the data. Both explanations have mechanistic support and could be incorporated, alone or in combination, in models allowing prediction of the time-course of HbA1c changes associated with changes in AG from, for example dietary or therapeutic interventions, and vice versa, to infer changes in AG from observed changes in HbA1c. The selection between the alternative mechanistic models require gathering of new information.
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:	HbA1c is the most commonly used biomarker for the adequacy of glycemic management in diabetic patients and a surrogate endpoint for anti-diabetic drug approval. In spite of an empirical description for the relationship between average glucose (AG) and HbA1c concentrations, obtained from the A1c-derived average glucose (ADAG) study by Nathan et al., a model for the non-steady-state relationship is still lacking. Using data from the ADAG study, we here develop such models that utilize literature information on (patho)physiological processes and assay characteristics. The model incorporates the red blood cell (RBC) aging description, and uses prior values of the glycosylation rate constant (KG), mean RBC life-span (LS) and mean RBC precursor LS obtained from the literature. Different hypothesis were tested to explain the observed non-proportional relationship between AG and HbA1c. Both an inverse dependence of LS on AG and a non-specificity of the National Glycohemoglobin Standardization Program assay used could well describe the data. Both explanations have mechanistic support and could be incorporated, alone or in combination, in models allowing prediction of the time-course of HbA1c changes associated with changes in AG from, for example dietary or therapeutic interventions, and vice versa, to infer changes in AG from observed changes in HbA1c. The selection between the alternative mechanistic models require gathering of new information.;
Modelling task in scope:	simulation;
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
- Lledo-Garcia_2013_diabetes.xml

Additional Files

Model owner: Paolo Magni
Submitted: Sep 26, 2014 3:32:40 PM
Last Modified: Oct 10, 2016 9:42:06 PM

Revisions

Version: 12
- Submitted on: Oct 10, 2016 9:42:06 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: 11
- Submitted on: Jun 2, 2016 8:27:17 PM
- Submitted by: Paolo Magni
- With comment: Model revised without commit message
Version: 10
- Submitted on: Jun 2, 2016 8:24:02 PM
- Submitted by: Paolo Magni
- With comment: Updated model annotations.
Version: 7
- Submitted on: Dec 11, 2015 12:36:07 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.
Version: 3
- Submitted on: Sep 26, 2014 3:32:40 PM
- Submitted by: Paolo Magni
- With comment: Model revised without commit message

Name

Generated from MDL. MOG ID: lledo2013_mog

Independent Variables

Function Definitions

proportionalError : real (proportional : real, f : real) = proportional \cdot f

Covariate Model: $cm$

Continuous Covariates

AG

Parameter Model: $pm$

Random Variables

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

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

{eps_HBA1C}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.SIGMA_RES)

Population Parameters

GAMMA

POP_LS

IIV_LS

POP_KG

POP_LSP

IIV_LSP

CV_HBA1C

OMEGA_LS

OMEGA_LSP

SIGMA_RES

Individual Parameters

KIN = 1

AGLS = {\frac{149}{cm.AG}}^{pm.GAMMA}

LS = pm.POP_LS \cdot pm.AGLS \cdot ⅇ^{(pm.IIV_LS \cdot pm.eta_LS)}

NC = 12

KTR = \frac{pm.NC}{pm.LS}

KG = \frac{pm.POP_KG}{1000}

LSP = pm.POP_LSP \cdot ⅇ^{(pm.IIV_LSP \cdot pm.eta_LSP)}

PREC = ⅇ^{(- pm.KG \cdot cm.AG \cdot pm.LSP)}

A2_0 = \frac{pm.PREC \cdot pm.KIN}{(pm.KTR + pm.KG \cdot cm.AG)}

A3_0 = \frac{pm.A2_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A4_0 = \frac{pm.A3_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A5_0 = \frac{pm.A4_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A6_0 = \frac{pm.A5_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A7_0 = \frac{pm.A6_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A8_0 = \frac{pm.A7_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A9_0 = \frac{pm.A8_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A10_0 = \frac{pm.A9_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A11_0 = \frac{pm.A10_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A12_0 = \frac{pm.A11_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A13_0 = \frac{pm.A12_0 \cdot pm.KTR}{(pm.KTR + pm.KG \cdot cm.AG)}

A14_0 = \frac{(pm.A2_0 \cdot pm.KG \cdot cm.AG + pm.KIN \cdot (1 - pm.PREC))}{pm.KTR}

A15_0 = \frac{(pm.A14_0 \cdot pm.KTR + pm.A3_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A16_0 = \frac{(pm.A15_0 \cdot pm.KTR + pm.A4_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A17_0 = \frac{(pm.A16_0 \cdot pm.KTR + pm.A5_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A18_0 = \frac{(pm.A17_0 \cdot pm.KTR + pm.A6_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A19_0 = \frac{(pm.A18_0 \cdot pm.KTR + pm.A7_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A20_0 = \frac{(pm.A19_0 \cdot pm.KTR + pm.A8_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A21_0 = \frac{(pm.A20_0 \cdot pm.KTR + pm.A9_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A22_0 = \frac{(pm.A21_0 \cdot pm.KTR + pm.A10_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A23_0 = \frac{(pm.A22_0 \cdot pm.KTR + pm.A11_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A24_0 = \frac{(pm.A23_0 \cdot pm.KTR + pm.A12_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

A25_0 = \frac{(pm.A24_0 \cdot pm.KTR + pm.A13_0 \cdot pm.KG \cdot cm.AG)}{pm.KTR}

Structural Model: $sm$

Variables

\begin{matrix} \frac{ⅆ}{ⅆ T} A1 = 0 \\ A1 (T = 0) = cm.AG \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A2 = pm.KIN \cdot pm.PREC - sm.A2 \cdot (pm.KTR + pm.KG \cdot cm.AG) \\ A2 (T = 0) = pm.A2_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A3 = (sm.A2 - sm.A3) \cdot pm.KTR - sm.A3 \cdot pm.KG \cdot cm.AG \\ A3 (T = 0) = pm.A3_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A4 = (sm.A3 - sm.A4) \cdot pm.KTR - sm.A4 \cdot pm.KG \cdot cm.AG \\ A4 (T = 0) = pm.A4_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A5 = (sm.A4 - sm.A5) \cdot pm.KTR - sm.A5 \cdot pm.KG \cdot cm.AG \\ A5 (T = 0) = pm.A5_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A6 = (sm.A5 - sm.A6) \cdot pm.KTR - sm.A6 \cdot pm.KG \cdot cm.AG \\ A6 (T = 0) = pm.A6_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A7 = (sm.A6 - sm.A7) \cdot pm.KTR - sm.A7 \cdot pm.KG \cdot cm.AG \\ A7 (T = 0) = pm.A7_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A8 = (sm.A7 - sm.A8) \cdot pm.KTR - sm.A8 \cdot pm.KG \cdot cm.AG \\ A8 (T = 0) = pm.A8_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A9 = (sm.A8 - sm.A9) \cdot pm.KTR - sm.A9 \cdot pm.KG \cdot cm.AG \\ A9 (T = 0) = pm.A9_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A10 = (sm.A9 - sm.A10) \cdot pm.KTR - sm.A10 \cdot pm.KG \cdot cm.AG \\ A10 (T = 0) = pm.A10_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A11 = (sm.A10 - sm.A11) \cdot pm.KTR - sm.A11 \cdot pm.KG \cdot cm.AG \\ A11 (T = 0) = pm.A11_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A12 = (sm.A11 - sm.A12) \cdot pm.KTR - sm.A12 \cdot pm.KG \cdot cm.AG \\ A12 (T = 0) = pm.A12_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A13 = (sm.A12 - sm.A13) \cdot pm.KTR - sm.A13 \cdot pm.KG \cdot cm.AG \\ A13 (T = 0) = pm.A13_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A14 = pm.KIN \cdot (1 - pm.PREC) - sm.A14 \cdot pm.KTR + sm.A2 \cdot pm.KG \cdot cm.AG \\ A14 (T = 0) = pm.A14_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A15 = (sm.A14 - sm.A15) \cdot pm.KTR + sm.A3 \cdot pm.KG \cdot cm.AG \\ A15 (T = 0) = pm.A15_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A16 = (sm.A15 - sm.A16) \cdot pm.KTR + sm.A4 \cdot pm.KG \cdot cm.AG \\ A16 (T = 0) = pm.A16_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A17 = (sm.A16 - sm.A17) \cdot pm.KTR + sm.A5 \cdot pm.KG \cdot cm.AG \\ A17 (T = 0) = pm.A17_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A18 = (sm.A17 - sm.A18) \cdot pm.KTR + sm.A6 \cdot pm.KG \cdot cm.AG \\ A18 (T = 0) = pm.A18_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A19 = (sm.A18 - sm.A19) \cdot pm.KTR + sm.A7 \cdot pm.KG \cdot cm.AG \\ A19 (T = 0) = pm.A19_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A20 = (sm.A19 - sm.A20) \cdot pm.KTR + sm.A8 \cdot pm.KG \cdot cm.AG \\ A20 (T = 0) = pm.A20_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A21 = (sm.A20 - sm.A21) \cdot pm.KTR + sm.A9 \cdot pm.KG \cdot cm.AG \\ A21 (T = 0) = pm.A21_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A22 = (sm.A21 - sm.A22) \cdot pm.KTR + sm.A10 \cdot pm.KG \cdot cm.AG \\ A22 (T = 0) = pm.A22_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A23 = (sm.A22 - sm.A23) \cdot pm.KTR + sm.A11 \cdot pm.KG \cdot cm.AG \\ A23 (T = 0) = pm.A23_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A24 = (sm.A23 - sm.A24) \cdot pm.KTR + sm.A12 \cdot pm.KG \cdot cm.AG \\ A24 (T = 0) = pm.A24_0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A25 = (sm.A24 - sm.A25) \cdot pm.KTR + sm.A13 \cdot pm.KG \cdot cm.AG \\ A25 (T = 0) = pm.A25_0 \end{matrix}

NON = sm.A2 + sm.A3 + sm.A4 + sm.A5 + sm.A6 + sm.A7 + sm.A8 + sm.A9 + sm.A10 + sm.A11 + sm.A12 + sm.A13

GLY = sm.A14 + sm.A15 + sm.A16 + sm.A17 + sm.A18 + sm.A19 + sm.A20 + sm.A21 + sm.A22 + sm.A23 + sm.A24 + sm.A25

TOT = sm.NON + sm.GLY

HBA1C = \frac{sm.GLY}{sm.TOT} \cdot 100

Observation Model: $om1$

Continuous Observation

Y = sm.HBA1C + proportionalError (proportional = pm.CV_HBA1C, f = sm.HBA1C) + pm.eps_HBA1C

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_Dynamic_MPG.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$DV$	$3$	$dv$	$real$
$AG$	$4$	$covariate$	$real$
$EV$	$5$	$undefined$	$real$

Column Mappings

Column Ref	Modelling Mapping
$ID$	$vm_mdl.ID$
$TIME$	$T$
$DV$	$om1.Y$
$AG$	$cm.AG$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Initial Value	Fixed?	Limits
pm.GAMMA	$0.381$	true	$()$
pm.POP_LS	$91.7$	true	$()$
pm.IIV_LS	$0.0822$	true	$()$
pm.POP_KG	$0.00837$	true	$()$
pm.POP_LSP	$8.2$	true	$()$
pm.IIV_LSP	$0.115$	true	$()$
pm.CV_HBA1C	$0.0227$	true	$()$
pm.OMEGA_LS	$1$	true	$()$
pm.OMEGA_LSP	$1$	true	$()$
pm.SIGMA_RES	$1$	true	$()$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$saem$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000005: Lledo-Garcia_2013_diabetes