DDMODEL00000112: Magni_2006_diabetes_MinimalModel

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: .hiddenContent {display:none;} 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; Variability sources in PK and PD (CYP, Renal, Biomarkers); Clinical end-point; 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.
• Model owner: Paolo Magni
• Submitted: Dec 11, 2015 11:52:30 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

 T

Function Definitions

 $\mathrm{proportionalError}:\mathrm{real}\left(\mathrm{proportional}:\mathrm{real},f:\mathrm{real}\right)=\mathrm{proportional}\cdot f$

Covariate Model: $\mathrm{cm}$

Continuous Covariates

$\mathrm{INS}$

Parameter Model: $\mathrm{pm}$

Random Variables

${\mathrm{EPS_RES_G}}_{\mathrm{vm_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.SIGMA_RES_G}\right)$

Population Parameters

$\mathrm{MU_SG_POP}=-3.7$
$\mathrm{MU_SI_POP}=-7.5$
$\mathrm{MU_P2_POP}=-3.0$
$\mathrm{MU_G0_POP}=5.6$
$\mathrm{SIGMA_SG_POP}=0.45$
$\mathrm{SIGMA_SI_POP}=0.71$
$\mathrm{SIGMA_P2_POP}=0.63$
$\mathrm{SIGMA_G0_POP}=0.12$
${\mathrm{logSG_POP}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Normal1}\left(\mathrm{mean}=\mathrm{pm.MU_SG_POP},\mathrm{stdev}=\mathrm{pm.SIGMA_SG_POP}\right)$
${\mathrm{logSI_POP}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Normal1}\left(\mathrm{mean}=\mathrm{pm.MU_SI_POP},\mathrm{stdev}=\mathrm{pm.SIGMA_SI_POP}\right)$
${\mathrm{logP2_POP}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Normal1}\left(\mathrm{mean}=\mathrm{pm.MU_P2_POP},\mathrm{stdev}=\mathrm{pm.SIGMA_P2_POP}\right)$
${\mathrm{logG0_POP}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Normal1}\left(\mathrm{mean}=\mathrm{pm.MU_G0_POP},\mathrm{stdev}=\mathrm{pm.SIGMA_G0_POP}\right)$
$\mathrm{pop_SG}={e}^{\mathrm{pm.logSG_POP}}$
$\mathrm{pop_SI}={e}^{\mathrm{pm.logSI_POP}}$
$\mathrm{pop_P2}={e}^{\mathrm{pm.logP2_POP}}$
$\mathrm{pop_G0}={e}^{\mathrm{pm.logG0_POP}}$
$\mathrm{SIGMA_RES_G}=1$
$\mathrm{CV}=0.02$
$\mathrm{pop_GB}=82$
$\mathrm{pop_IB}=7$

Individual Parameters

$\mathrm{SG}=\mathrm{pm.pop_SG}$
$\mathrm{SI}=\mathrm{pm.pop_SI}$
$\mathrm{P2}=\mathrm{pm.pop_P2}$
$\mathrm{G0}=\mathrm{pm.pop_G0}$
$\mathrm{GB}=\mathrm{pm.pop_GB}$
$\mathrm{IB}=\mathrm{pm.pop_IB}$

Structural Model: $\mathrm{sm}$

Variables

$\begin{array}{c}\frac{d}{dT}\mathrm{GLUC}=-\left(\mathrm{pm.SG}+\mathrm{sm.X_REMOTE}\right)\cdot \mathrm{sm.GLUC}+\mathrm{pm.SG}\cdot \mathrm{pm.GB}\\ \mathrm{GLUC}\left(T=0\right)=\mathrm{pm.G0}\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X_REMOTE}=-\mathrm{pm.P2}\cdot \left(\mathrm{sm.X_REMOTE}-\mathrm{pm.SI}\cdot \left(\mathrm{cm.INS}-\mathrm{pm.IB}\right)\right)\\ \mathrm{X_REMOTE}\left(T=0\right)=0\end{array}$

Observation Model: $\mathrm{om1}$

Continuous Observation

$\mathrm{Y_G}=\mathrm{sm.GLUC}+\mathrm{proportionalError}\left(\mathrm{proportional}=\mathrm{pm.CV},f=\mathrm{sm.GLUC}\right)+\mathrm{pm.EPS_RES_G}$

External Dataset

 OID $\mathrm{nm_ds}$ Tool Format NONMEM

File Specification

 Format $\mathrm{csv}$ Delimiter comma File Location Simulated_magni_2006_data.csv

Column Definitions

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

Column Mappings

Column Ref Modelling Mapping
$TIME$
$T$
$DV$
$\mathrm{om1.Y_G}$
$INS$
$\mathrm{cm.INS}$

Estimation Step

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

Parameters To Estimate

Parameter Initial Value Fixed? Limits
pm.logSG_POP
false
$\left(,\right)$
pm.logSI_POP
false
$\left(,\right)$
pm.logP2_POP
false
$\left(,\right)$
pm.logG0_POP
false
$\left(,\right)$

Operations

Operation: $1$

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

Operation: $2$

 Op Type BUGS
Operation Properties
Name Value
nchains
$1$
burnin
$1000$
niter
$5000$
winbugsgui
$\text{true}$

Step Dependencies

Step OID Preceding Steps
$\mathrm{estimStep_1}$