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Short description:

Minimal model describing glucose kinetics during an intravenous glucose tolerance test to estimate glucose effectiveness and insulin sensitivity in reduced sampling schedules via Bayesian approach.

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Reduced sampling schedule for the glucose minimal model: importance of Bayesian estimation. Sparacino G, Bellazzi R, Cobelli C, Magni Paolo American journal of physiology. Endocrinology and metabolism, 1/2006, Volume 290, Issue 1, pages: E177-E184 Affiliation: Dipartimento di Informatica e Sistemica, Università degli Studi di Pavia,Pavia, Italy. Università degli Studi di Padova, Italy. paolo.magni@unipv.it Abstract: The minimal model (MM) of glucose kinetics during an intravenous glucose tolerance test (IVGTT) is widely used in clinical studies to measure metabolic indexes such as glucose effectiveness (S(G)) and insulin sensitivity (S(I)). The standard (frequent) IVGTT sampling schedule (FSS) for MM identification consists of 30 points over 4 h. To facilitate clinical application of the MM, reduced sampling schedules (RSS) of 13-14 samples have also been derived for normal subjects. These RSS are especially appealing in large-scale studies. However, with RSS, the precision of S(G) and S(I) estimates deteriorates and, in certain cases, becomes unacceptably poor. To overcome this difficulty, population approaches such as the iterative two-stage (ITS) approach have been recently proposed, but, besides leaving some theoretical issues open, they appear to be oversized for the problem at hand. Here, we show that a Bayesian methodology operating at the single individual level allows an accurate determination of MM parameter estimates together with a credible measure of their precision. Results of 16 subjects show that, in passing from FSS to RSS, there are no significant changes of point estimates in nearly all of the subjects and that only a limited deterioration of parameter precision occurs. In addition, in contrast with the previously proposed ITS method, credible confidence intervals (e.g., excluding negative values) are obtained. They can be crucial for a subsequent use of the estimated MM parameters, such as in classification, clustering, regression, or risk analysis.
Contributors:	Paolo Magni

Context of model development:	Mechanistic Understanding; Clinical end-point; Variability sources in PK and PD (CYP, Renal, Biomarkers);
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	The minimal model (MM) of glucose kinetics during an intravenous glucose tolerance test (IVGTT) is widely used in clinical studies to measure metabolic indexes such as glucose effectiveness (S(G)) and insulin sensitivity (S(I)). The standard (frequent) IVGTT sampling schedule (FSS) for MM identification consists of 30 points over 4 h. To facilitate clinical application of the MM, reduced sampling schedules (RSS) of 13-14 samples have also been derived for normal subjects. These RSS are especially appealing in large-scale studies. However, with RSS, the precision of S(G) and S(I) estimates deteriorates and, in certain cases, becomes unacceptably poor. To overcome this difficulty, population approaches such as the iterative two-stage (ITS) approach have been recently proposed, but, besides leaving some theoretical issues open, they appear to be oversized for the problem at hand. Here, we show that a Bayesian methodology operating at the single individual level allows an accurate determination of MM parameter estimates together with a credible measure of their precision. Results of 16 subjects show that, in passing from FSS to RSS, there are no significant changes of point estimates in nearly all of the subjects and that only a limited deterioration of parameter precision occurs. In addition, in contrast with the previously proposed ITS method, credible confidence intervals (e.g., excluding negative values) are obtained. They can be crucial for a subsequent use of the estimated MM parameters, such as in classification, clustering, regression, or risk analysis.;
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
- Executable_Magni_2006_diabetes_MinimalModel.xml

Additional Files

Model owner: Paolo Magni
Submitted: Dec 11, 2015 11:52:30 PM
Last Modified: Oct 13, 2016 6:56:17 PM

Revisions

Version: 17
- Submitted on: Oct 13, 2016 6:56:17 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.
Version: 15
- Submitted on: Oct 11, 2016 4:29:11 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.
Version: 8
- Submitted on: Jun 2, 2016 8:06:03 PM
- Submitted by: Paolo Magni
- With comment: Model revised without commit message
Version: 4
- Submitted on: Dec 11, 2015 11:52:30 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.

Name

Generated from MDL. MOG ID: magni2006

Independent Variables

Function Definitions

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

Covariate Model: $cm$

Continuous Covariates

INS

Parameter Model: $pm$

Random Variables

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

Population Parameters

MU_SG_POP = - 3.7

MU_SI_POP = - 7.5

MU_P2_POP = - 3.0

MU_G0_POP = 5.6

SIGMA_SG_POP = 0.45

SIGMA_SI_POP = 0.71

SIGMA_P2_POP = 0.63

SIGMA_G0_POP = 0.12

{logSG_POP}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_SG_POP, stdev = pm.SIGMA_SG_POP)

{logSI_POP}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_SI_POP, stdev = pm.SIGMA_SI_POP)

{logP2_POP}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_P2_POP, stdev = pm.SIGMA_P2_POP)

{logG0_POP}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_G0_POP, stdev = pm.SIGMA_G0_POP)

pop_SG = ⅇ^{pm.logSG_POP}

pop_SI = ⅇ^{pm.logSI_POP}

pop_P2 = ⅇ^{pm.logP2_POP}

pop_G0 = ⅇ^{pm.logG0_POP}

SIGMA_RES_G = 1

CV = 0.02

pop_GB = 82

pop_IB = 7

Individual Parameters

SG = pm.pop_SG

SI = pm.pop_SI

P2 = pm.pop_P2

G0 = pm.pop_G0

GB = pm.pop_GB

IB = pm.pop_IB

Structural Model: $sm$

Variables

\begin{matrix} \frac{ⅆ}{ⅆ T} GLUC = - (pm.SG + sm.X_REMOTE) \cdot sm.GLUC + pm.SG \cdot pm.GB \\ GLUC (T = 0) = pm.G0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} X_REMOTE = - pm.P2 \cdot (sm.X_REMOTE - pm.SI \cdot (cm.INS - pm.IB)) \\ X_REMOTE (T = 0) = 0 \end{matrix}

Observation Model: $om1$

Continuous Observation

Y_G = sm.GLUC + proportionalError (proportional = pm.CV, f = sm.GLUC) + pm.EPS_RES_G

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_magni_2006_data.csv

Column Definitions

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

Column Mappings

Column Ref	Modelling Mapping
$TIME$	$T$
$DV$	$om1.Y_G$
$INS$	$cm.INS$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Fixed?	Limits
pm.logSG_POP	false	$()$
pm.logSI_POP	false	$()$
pm.logP2_POP	false	$()$
pm.logG0_POP	false	$()$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$mcmc$

Operation: $2$

Op Type

BUGS

Operation Properties

Name	Value
nchains	$1$
burnin	$1000$
niter	$5000$
winbugsgui	$true$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000112: Magni_2006_diabetes_MinimalModel

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

External Dataset

File Specification

Column Definitions

Column Mappings

Estimation Step

Parameters To Estimate

Operations

Operation: 1

Operation Properties

Operation: 2

Operation Properties

Step Dependencies

Covariate Model: $cm$

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Operation: $1$

Operation: $2$