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Short description:

Regression model relating the parameters of a two-compartment model of C-peptide kinetics with anthropometric parameters of normal, obese and diabetic subjects via a Bayesian approach.

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Bayesian identification of a population compartmental model of C-peptide kinetics. Magni P, Bellazzi R, Sparacino G, Cobelli C Annals of biomedical engineering, 7/2000, Volume 28, Issue 7, pages: 812-823 Affiliation: Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, Italy. paolo.magni@unipv.it Abstract: When models are used to measure or predict physiological variables and parameters in a given individual, the experiments needed are often complex and costly. A valuable solution for improving their cost effectiveness is represented by population models. A widely used population model in insulin secretion studies is the one proposed by Van Cauter et al. (Diabetes 41:368-377, 1992), which determines the parameters of the two compartment model of C-peptide kinetics in a given individual from the knowledge of his/her age, sex, body surface area, and health condition (i.e., normal, obese, diabetic). This population model was identified from the data of a large training set (more than 200 subjects) via a deterministic approach. This approach, while sound in terms of providing a point estimate of C-peptide kinetic parameters in a given individual, does not provide a measure of their precision. In this paper, by employing the same training set of Van Cauter et al., we show that the identification of the population model into a Bayesian framework (by using Markov chain Monte Carlo) allows, at the individual level, the estimation of point values of the C-peptide kinetic parameters together with their precision. A successful application of the methodology is illustrated in the estimation of C-peptide kinetic parameters of seven subjects (not belonging to the training set used for the identification of the population model) for which reference values were available thanks to an independent identification experiment.
Contributors:	Paolo Magni

Context of model development:	Clinical end-point; Mechanistic Understanding; 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:	When models are used to measure or predict physiological variables and parameters in a given individual, the experiments needed are often complex and costly. A valuable solution for improving their cost effectiveness is represented by population models. A widely used population model in insulin secretion studies is the one proposed by Van Cauter et al. (Diabetes 41:368-377, 1992), which determines the parameters of the two compartment model of C-peptide kinetics in a given individual from the knowledge of his/her age, sex, body surface area, and health condition (i.e., normal, obese, diabetic). This population model was identified from the data of a large training set (more than 200 subjects) via a deterministic approach. This approach, while sound in terms of providing a point estimate of C-peptide kinetic parameters in a given individual, does not provide a measure of their precision. In this paper, by employing the same training set of Van Cauter et al., we show that the identification of the population model into a Bayesian framework (by using Markov chain Monte Carlo) allows, at the individual level, the estimation of point values of the C-peptide kinetic parameters together with their precision. A successful application of the methodology is illustrated in the estimation of C-peptide kinetic parameters of seven subjects (not belonging to the training set used for the identification of the population model) for which reference values were available thanks to an independent identification experiment.;
Modelling task in scope:	estimation; 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
- Executable_Magni_2000_diabetes_C-peptide.xml

Additional Files

Model owner: Paolo Magni
Submitted: Dec 13, 2015 12:54:20 PM
Last Modified: Nov 8, 2017 5:24:11 PM

Revisions

Version: 18
- Submitted on: Nov 8, 2017 5:24:11 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.
Version: 16
- Submitted on: Oct 13, 2016 3:31:43 PM
- Submitted by: Paolo Magni
- With comment: Wrong command file in the previous version. Now updated
Version: 15
- Submitted on: Oct 11, 2016 5:18:02 PM
- Submitted by: Paolo Magni
- With comment: Update MDL syntax to the version 1.0 and R script to SEE version 2.0.0. Added prior distributions Code automatically generated/manually modified for WinBUGS
Version: 12
- Submitted on: Jun 2, 2016 7:07:01 PM
- Submitted by: Paolo Magni
- With comment: Updated model annotations.
Version: 4
- Submitted on: Dec 13, 2015 12:54:20 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.

Name

Generated from MDL. MOG ID: outputMog

Independent Variables

Function Definitions

additiveError : real (additive : real) = additive

Covariate Model: $cm$

Continuous Covariates

HSTATUS

FEMALE

AGE

WEIGHT

HEIGHT

Parameter Model: $pm$

Random Variables

{EPS}_{vm_err.DV} ~ MultivariateNormal2 (mean = (0, 0, 0, 0), precisionmatrix = pm.invOMEGA_PAR)

Population Parameters

data1

data_par_joint

{par_joint}_{vm_mdl.MDL__prior} ~ RandomSample ()

mtsn = pm.par_joint (1)

mtso = pm.par_joint (2)

mtsd = pm.par_joint (3)

mFn = pm.par_joint (4)

mFo = pm.par_joint (5)

mFd = pm.par_joint (6)

atl = pm.par_joint (7)

btl = pm.par_joint (8)

aVm = pm.par_joint (9)

bVm = pm.par_joint (10)

aVf = pm.par_joint (11)

bVf = pm.par_joint (12)

invVAR_ts = pm.par_joint (13)

invVAR_F = pm.par_joint (14)

invVAR_tl = pm.par_joint (15)

invVAR_V = pm.par_joint (16)

invCOV_ts_F = pm.par_joint (17)

invCOV_ts_tl = pm.par_joint (18)

invCOV_F_tl = pm.par_joint (19)

invCOV_ts_V = pm.par_joint (20)

invCOV_F_V = pm.par_joint (21)

invCOV_tl_V = pm.par_joint (22)

invOMEGA_PAR = (\begin{matrix} pm.invVAR_ts & pm.invCOV_ts_F & pm.invCOV_ts_tl & pm.invCOV_ts_V \\ pm.invCOV_ts_F & pm.invVAR_F & pm.invCOV_F_tl & pm.invCOV_F_V \\ pm.invCOV_ts_tl & pm.invCOV_F_tl & pm.invVAR_tl & pm.invCOV_tl_V \\ pm.invCOV_ts_V & pm.invCOV_F_V & pm.invCOV_tl_V & pm.invVAR_V \end{matrix})

BSA = {cm.WEIGHT}^{0.425} \cdot {cm.HEIGHT}^{0.725} \cdot 0.20247

GROUP_tl = pm.atl + pm.btl \cdot cm.AGE

GROUP_ts = {\begin{cases} pm.mtsn & if & cm.HSTATUS = 0 \\ pm.mtso & if & cm.HSTATUS = 1 \\ pm.mtsd & if & cm.HSTATUS = 2 \end{cases}

GROUP_F = {\begin{cases} pm.mFn & if & cm.HSTATUS = 0 \\ pm.mFo & if & cm.HSTATUS = 1 \\ pm.mFd & if & cm.HSTATUS = 2 \end{cases}

GROUP_V = {\begin{cases} pm.aVm + pm.bVm \cdot pm.BSA & if & cm.FEMALE = 0 \\ pm.aVf + pm.bVf \cdot pm.BSA & otherwise \end{cases}

Individual Parameters

ts_IND = pm.GROUP_ts

F_IND = pm.GROUP_F

tl_IND = pm.GROUP_tl

V_IND = pm.GROUP_V

Structural Model: $sm$

Variables

ts_PRED = pm.ts_IND

F_PRED = pm.F_IND

tl_PRED = pm.tl_IND

V_PRED = pm.V_IND

Observation Model: $om1$

Variables

EPS_1 = pm.EPS (1)

Continuous Observation

Y1 = sm.ts_PRED + additiveError (additive = 1) + EPS_1

Observation Model: $om2$

Variables

EPS_2 = pm.EPS (2)

Continuous Observation

Y2 = sm.F_PRED + additiveError (additive = 1) + EPS_2

Observation Model: $om3$

Variables

EPS_3 = pm.EPS (3)

Continuous Observation

Y3 = sm.tl_PRED + additiveError (additive = 1) + EPS_3

Observation Model: $om4$

Variables

EPS_4 = pm.EPS (4)

Continuous Observation

Y4 = sm.V_PRED + additiveError (additive = 1) + EPS_4

External Dataset

OID

data1

File Specification

Format	$csv$
Delimiter	comma
File Location	prior_magni2000.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$data_mtsn$	$1$	$undefined$	$real$
$data_mtso$	$2$	$undefined$	$real$
$data_mtsd$	$3$	$undefined$	$real$
$data_mFn$	$4$	$undefined$	$real$
$data_mFo$	$5$	$undefined$	$real$
$data_mFd$	$6$	$undefined$	$real$
$data_atl$	$7$	$undefined$	$real$
$data_btl$	$8$	$undefined$	$real$
$data_aVm$	$9$	$undefined$	$real$
$data_bVm$	$10$	$undefined$	$real$
$data_aVf$	$11$	$undefined$	$real$
$data_bVf$	$12$	$undefined$	$real$
$data_invVAR_ts$	$13$	$undefined$	$real$
$data_invVAR_F$	$14$	$undefined$	$real$
$data_invVAR_tl$	$15$	$undefined$	$real$
$data_invVAR_V$	$16$	$undefined$	$real$
$data_invCOV_ts_F$	$17$	$undefined$	$real$
$data_invCOV_ts_tl$	$18$	$undefined$	$real$
$data_invCOV_F_tl$	$19$	$undefined$	$real$
$data_invCOV_ts_V$	$20$	$undefined$	$real$
$data_invCOV_F_V$	$21$	$undefined$	$real$
$data_invCOV_tl_V$	$22$	$undefined$	$real$

Column Mappings

Column Ref	Modelling Mapping
$data_mtsn$	$pm.data_par_joint (1)$
$data_mtso$	$pm.data_par_joint (2)$
$data_mtsd$	$pm.data_par_joint (3)$
$data_mFn$	$pm.data_par_joint (4)$
$data_mFo$	$pm.data_par_joint (5)$
$data_mFd$	$pm.data_par_joint (6)$
$data_atl$	$pm.data_par_joint (7)$
$data_btl$	$pm.data_par_joint (8)$
$data_aVm$	$pm.data_par_joint (9)$
$data_bVm$	$pm.data_par_joint (10)$
$data_aVf$	$pm.data_par_joint (11)$
$data_bVf$	$pm.data_par_joint (12)$
$data_invVAR_ts$	$pm.data_par_joint (13)$
$data_invVAR_F$	$pm.data_par_joint (14)$
$data_invVAR_tl$	$pm.data_par_joint (15)$
$data_invVAR_V$	$pm.data_par_joint (16)$
$data_invCOV_ts_F$	$pm.data_par_joint (17)$
$data_invCOV_ts_tl$	$pm.data_par_joint (18)$
$data_invCOV_F_tl$	$pm.data_par_joint (19)$
$data_invCOV_ts_V$	$pm.data_par_joint (20)$
$data_invCOV_F_V$	$pm.data_par_joint (21)$
$data_invCOV_tl_V$	$pm.data_par_joint (22)$

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_magni2000_subjects.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$DV$	$3$	$dv$	$real$
$DVID$	$4$	$dvid$	$int$
$HSTATUS$	$5$	$covariate$	$real$
$FEMALE$	$6$	$covariate$	$real$
$AGE$	$7$	$covariate$	$real$
$HEIGHT$	$8$	$covariate$	$real$
$WEIGHT$	$9$	$covariate$	$real$
$BMI_DATASET$	$10$	$undefined$	$real$
$BSA_DATASET$	$11$	$undefined$	$real$

Column Mappings

Column Ref	Modelling Mapping
$TIME$	$T$
$DV$	${\begin{cases} om1.Y1 & if & DVID = 1 \\ om2.Y2 & if & DVID = 2 \\ om3.Y3 & if & DVID = 3 \\ om4.Y4 & if & DVID = 4 \end{cases}$
$HSTATUS$	$cm.HSTATUS$
$FEMALE$	$cm.FEMALE$
$AGE$	$cm.AGE$
$HEIGHT$	$cm.HEIGHT$
$WEIGHT$	$cm.WEIGHT$

Simulation Step

OID	$simulStep_1$

Variable Assignments

Variable	Value

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value

Operation: $2$

Op Type

BUGS

Operation Properties

Name	Value
niter	$1000$

Step Dependencies

Step OID	Preceding Steps
$simulStep_1$

DDMODEL00000110: Magni_2000_diabetes_C-peptide

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

Variables

Continuous Observation

Observation Model: om2

Variables

Continuous Observation

Observation Model: om3

Variables

Continuous Observation

Observation Model: om4

Variables

Continuous Observation

External Dataset

File Specification

Column Definitions

Column Mappings

External Dataset

File Specification

Column Definitions

Column Mappings

Simulation Step

Variable Assignments

Operations

Operation: 1

Operation Properties

Operation: 2

Operation Properties

Step Dependencies

Covariate Model: $cm$

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Observation Model: $om2$

Observation Model: $om3$

Observation Model: $om4$

Operation: $1$

Operation: $2$