# DDMODEL00000110: Magni_2000_diabetes_C-peptide

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: .hiddenContent {display:none;} 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: 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: 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: simulation; 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 13, 2015 12:54:20 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

 T

### Function Definitions

 $\mathrm{additiveError}:\mathrm{real}\left(\mathrm{additive}:\mathrm{real}\right)=\mathrm{additive}$

### Covariate Model: $\mathrm{cm}$

#### Continuous Covariates

$\mathrm{HSTATUS}$
$\mathrm{FEMALE}$
$\mathrm{AGE}$
$\mathrm{WEIGHT}$
$\mathrm{HEIGHT}$

### Parameter Model: $\mathrm{pm}$

#### Random Variables

${\mathrm{EPS}}_{\mathrm{vm_err.DV}}~\mathrm{MultivariateNormal2}\left(\mathrm{mean}=\left(0,0,0,0\right),\mathrm{precisionmatrix}=\mathrm{pm.invOMEGA_PAR}\right)$

#### Population Parameters

$\mathrm{data1}$
$\mathrm{data_par_joint}$
${\mathrm{par_joint}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{RandomSample}\left(\right)$
$\mathrm{mtsn}=\mathrm{pm.par_joint}\left(1\right)$
$\mathrm{mtso}=\mathrm{pm.par_joint}\left(2\right)$
$\mathrm{mtsd}=\mathrm{pm.par_joint}\left(3\right)$
$\mathrm{mFn}=\mathrm{pm.par_joint}\left(4\right)$
$\mathrm{mFo}=\mathrm{pm.par_joint}\left(5\right)$
$\mathrm{mFd}=\mathrm{pm.par_joint}\left(6\right)$
$\mathrm{atl}=\mathrm{pm.par_joint}\left(7\right)$
$\mathrm{btl}=\mathrm{pm.par_joint}\left(8\right)$
$\mathrm{aVm}=\mathrm{pm.par_joint}\left(9\right)$
$\mathrm{bVm}=\mathrm{pm.par_joint}\left(10\right)$
$\mathrm{aVf}=\mathrm{pm.par_joint}\left(11\right)$
$\mathrm{bVf}=\mathrm{pm.par_joint}\left(12\right)$
$\mathrm{invVAR_ts}=\mathrm{pm.par_joint}\left(13\right)$
$\mathrm{invVAR_F}=\mathrm{pm.par_joint}\left(14\right)$
$\mathrm{invVAR_tl}=\mathrm{pm.par_joint}\left(15\right)$
$\mathrm{invVAR_V}=\mathrm{pm.par_joint}\left(16\right)$
$\mathrm{invCOV_ts_F}=\mathrm{pm.par_joint}\left(17\right)$
$\mathrm{invCOV_ts_tl}=\mathrm{pm.par_joint}\left(18\right)$
$\mathrm{invCOV_F_tl}=\mathrm{pm.par_joint}\left(19\right)$
$\mathrm{invCOV_ts_V}=\mathrm{pm.par_joint}\left(20\right)$
$\mathrm{invCOV_F_V}=\mathrm{pm.par_joint}\left(21\right)$
$\mathrm{invCOV_tl_V}=\mathrm{pm.par_joint}\left(22\right)$
$\mathrm{invOMEGA_PAR}=\left(\begin{array}{cccc}\mathrm{pm.invVAR_ts}& \mathrm{pm.invCOV_ts_F}& \mathrm{pm.invCOV_ts_tl}& \mathrm{pm.invCOV_ts_V}\\ \mathrm{pm.invCOV_ts_F}& \mathrm{pm.invVAR_F}& \mathrm{pm.invCOV_F_tl}& \mathrm{pm.invCOV_F_V}\\ \mathrm{pm.invCOV_ts_tl}& \mathrm{pm.invCOV_F_tl}& \mathrm{pm.invVAR_tl}& \mathrm{pm.invCOV_tl_V}\\ \mathrm{pm.invCOV_ts_V}& \mathrm{pm.invCOV_F_V}& \mathrm{pm.invCOV_tl_V}& \mathrm{pm.invVAR_V}\end{array}\right)$
$\mathrm{BSA}={\mathrm{cm.WEIGHT}}^{0.425}\cdot {\mathrm{cm.HEIGHT}}^{0.725}\cdot 0.20247$
$\mathrm{GROUP_tl}=\mathrm{pm.atl}+\mathrm{pm.btl}\cdot \mathrm{cm.AGE}$
$\mathrm{GROUP_ts}=\left\{\begin{array}{lll}\mathrm{pm.mtsn}& \text{if}& \mathrm{cm.HSTATUS}=0\\ \mathrm{pm.mtso}& \text{if}& \mathrm{cm.HSTATUS}=1\\ \mathrm{pm.mtsd}& \text{if}& \mathrm{cm.HSTATUS}=2\end{array}$
$\mathrm{GROUP_F}=\left\{\begin{array}{lll}\mathrm{pm.mFn}& \text{if}& \mathrm{cm.HSTATUS}=0\\ \mathrm{pm.mFo}& \text{if}& \mathrm{cm.HSTATUS}=1\\ \mathrm{pm.mFd}& \text{if}& \mathrm{cm.HSTATUS}=2\end{array}$
$\mathrm{GROUP_V}=\left\{\begin{array}{lll}\mathrm{pm.aVm}+\mathrm{pm.bVm}\cdot \mathrm{pm.BSA}& \text{if}& \mathrm{cm.FEMALE}=0\\ \mathrm{pm.aVf}+\mathrm{pm.bVf}\cdot \mathrm{pm.BSA}& \text{otherwise}& \end{array}$

#### Individual Parameters

$\mathrm{ts_IND}=\mathrm{pm.GROUP_ts}$
$\mathrm{F_IND}=\mathrm{pm.GROUP_F}$
$\mathrm{tl_IND}=\mathrm{pm.GROUP_tl}$
$\mathrm{V_IND}=\mathrm{pm.GROUP_V}$

### Structural Model: $\mathrm{sm}$

#### Variables

$\mathrm{ts_PRED}=\mathrm{pm.ts_IND}$
$\mathrm{F_PRED}=\mathrm{pm.F_IND}$
$\mathrm{tl_PRED}=\mathrm{pm.tl_IND}$
$\mathrm{V_PRED}=\mathrm{pm.V_IND}$

### Observation Model: $\mathrm{om1}$

#### Variables

$\mathrm{EPS_1}=\mathrm{pm.EPS}\left(1\right)$

#### Continuous Observation

$\mathrm{Y1}=\mathrm{sm.ts_PRED}+\mathrm{additiveError}\left(\mathrm{additive}=1\right)+\mathrm{EPS_1}$

### Observation Model: $\mathrm{om2}$

#### Variables

$\mathrm{EPS_2}=\mathrm{pm.EPS}\left(2\right)$

#### Continuous Observation

$\mathrm{Y2}=\mathrm{sm.F_PRED}+\mathrm{additiveError}\left(\mathrm{additive}=1\right)+\mathrm{EPS_2}$

### Observation Model: $\mathrm{om3}$

#### Variables

$\mathrm{EPS_3}=\mathrm{pm.EPS}\left(3\right)$

#### Continuous Observation

$\mathrm{Y3}=\mathrm{sm.tl_PRED}+\mathrm{additiveError}\left(\mathrm{additive}=1\right)+\mathrm{EPS_3}$

### Observation Model: $\mathrm{om4}$

#### Variables

$\mathrm{EPS_4}=\mathrm{pm.EPS}\left(4\right)$

#### Continuous Observation

$\mathrm{Y4}=\mathrm{sm.V_PRED}+\mathrm{additiveError}\left(\mathrm{additive}=1\right)+\mathrm{EPS_4}$

## External Dataset

 OID $\mathrm{data1}$

### File Specification

 Format $\mathrm{csv}$ Delimiter comma File Location prior_magni2000.csv

### Column Definitions

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

### Column Mappings

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

## External Dataset

 OID $\mathrm{nm_ds}$ Tool Format NONMEM

### File Specification

 Format $\mathrm{csv}$ Delimiter comma File Location Simulated_magni2000_subjects.csv

### Column Definitions

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

### Column Mappings

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

## Simulation Step

 OID $\mathrm{simulStep_1}$

Variable Value

### Operations

#### Operation: $1$

 Op Type generic
Name Value

#### Operation: $2$

 Op Type BUGS
##### Operation Properties
Name Value
niter
$1000$

## Step Dependencies

Step OID Preceding Steps
$\mathrm{simulStep_1}$