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Model Definition
Trial Design
Modelling Steps

Short description:

PK/PD model for Fc-OPG and urinary NTx bone marker. This model was coded from the original publication to be run in mrgsolve (https://www.github.com/metrumresearchgroup/mrgsolve).

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Population PK-PD model for Fc-osteoprotegerin in healthy postmenopausal women. Zierhut ML, Gastonguay MR, Martin SW, Vicini P, Bekker PJ, Holloway D, Leese PT, Peterson MC Journal of pharmacokinetics and pharmacodynamics, 8/2008, Volume 35, Issue 4, pages: 379-399 Affiliation: Department of Bioengineering, University of Washington, Seattle, WA 98195-2255, USA. Abstract: Osteoporosis is a metabolic bone disease resulting from increased bone resorption and characterized by low bone mass that leads to increased bone fragility and risk of fracture, particularly of the hip, spine and wrist. Bone resorption is dependent on receptor activator of NF-kappa B ligand (RANKL), which binds to RANK receptor on preosteoclasts to initiate osteoclastogenesis and maintains osteoclast function and survival. To neutralize the effects of RANKL, the body naturally produces the protein osteoprotegerin (OPG), which acts as a decoy receptor for RANKL and contributes to bone homeostasis. We describe the piecewise development of a three-compartment pharmacokinetic model with both linear and Michaelis-Menten eliminations, and an indirect pharmacodynamic response model to describe the pharmacokinetics and pharmacodynamics, respectively, of the fusion protein, Fc-osteoprotegerin (Fc-OPG), in healthy postmenopausal women. Subsequently, model verification was performed and used to address study design questions via simulation. The model was developed using data from eight cohorts (n = 13 subjects/cohort; Fc-OPG:placebo = 10:3) classified by dose level (0.1, 0.3, 1.0, or 3.0 mg/kg) and route of administration (intravenous [IV] or subcutaneous [SC]). Fc-OPG serum concentrations and urinary N-telopeptide/creatinine ratios (NTX) following both IV and SC administration were available. The model provided an adequate fit to the observed data and physiologically plausible parameter estimates. Model robustness was tested via a posterior predictive check with the model performing well in most cases. Subsequent clinical trial simulations demonstrated that a single 3.0-mg/kg SC dose of Fc-OPG would be expected to produce, at 14 days post-dose, a median NTX percentage change from baseline of -45% (with a 95% prediction interval ranging from -34% to -60%). Lastly, model ruggedness was evaluated using local and global sensitivity analysis methods. In conclusion, the model selection and simulation strategies we applied were rigorous, useful, and easily generalizable.
Contributors:	Kyle Baron, Mike K Smith

Context of model development:	Dose & Schedule Selection and Label Recommendation; Clinical end-point;
Discrepancy between implemented model and original publication:	None that I know of.;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	Early dose selection.;
Modelling task in scope:	simulation;
Nature of research:	Early clinical development (Phases I and II);
Therapeutic/disease area:	Endocrinology;

Validation Status:	Annotations are correct.
Certification Comment:	This model is not certified.

Mandatory file
- Fc_opg_uNTx_PKPD.xml

Additional Files

Model owner: Kyle Baron
Submitted: Nov 18, 2016 9:56:30 PM
Last Modified: Jul 13, 2018 8:37:51 AM

Revisions

Version: 52
- Submitted on: Jul 13, 2018 8:37:51 AM
- Submitted by: Mike K Smith
- With comment: Edited model metadata online.
Version: 48
- Submitted on: Mar 27, 2017 3:59:11 PM
- Submitted by: Mike K Smith
- With comment: Edited model metadata online.
Version: 46
- Submitted on: Feb 9, 2017 11:04:54 AM
- Submitted by: Mike K Smith
- With comment: Model revised without commit message
Version: 45
- Submitted on: Nov 19, 2016 6:05:58 PM
- Submitted by: Kyle Baron
- With comment: Edited model metadata online.
Version: 43
- Submitted on: Nov 19, 2016 2:07:09 PM
- Submitted by: Kyle Baron
- With comment: Edited model metadata online.
Version: 41
- Submitted on: Nov 18, 2016 11:55:33 PM
- Submitted by: Kyle Baron
- With comment: Edited model metadata online.
Version: 23
- Submitted on: Nov 18, 2016 9:56:30 PM
- Submitted by: Kyle Baron
- With comment: Model revised without commit message

Name

Zierhut_2008_Population PKPD model for Fc-osteoprotegerin in healthy postmenopausal women

Independent Variables

Function Definitions

additiveError : real (additive : real) = additive

combinedError1 : real (additive : real, proportional : real, f : real) = additive + proportional \cdot f

Covariate Model: $cm$

Continuous Covariates

IV

Parameter Model: $pm$

Random Variables

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

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

{EVP1}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.PPV_VP1)

{EVP2}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.PPV_VP2)

{EQ1}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.PPV_Q1)

{EKA}_{vm_mdl.ID} ~ Normal1 (mean = 0, stdev = pm.PPV_KA)

{EFSC}_{vm_mdl.ID} ~ Normal1 (mean = 0, stdev = pm.PPV_FSC)

{ETA_KSYN_KDEG_IC50}_{vm_mdl.ID} ~ MultivariateNormal1 (mean = (0, 0, 0), covariancematrix = pm.PPV_KSYN_KDEG_IC50)

{EPS_PK}_{vm_err.DV} ~ Normal2 (mean = 0, var = 1)

{EPS_PD}_{vm_err.DV} ~ Normal2 (mean = 0, var = 1)

Population Parameters

TVCL

TVVC

TVVP1

TVVP2

TVQ1

TVQ2

TVKA

TVVMAX

TVKM

TVFSC

TVKSYN

TVKDEG

TVIC50

PPV_CL

PPV_VC

PPV_VP1

PPV_VP2

PPV_Q1

PPV_KA

PPV_FSC

PPV_KSYN_KDEG_IC50

ADDIV

ADDSC

PDPROP

PDADD

MDL__ETA_KSYN_KDEG_IC50_1 = pm.ETA_KSYN_KDEG_IC50 (1)

MDL__ETA_KSYN_KDEG_IC50_2 = pm.ETA_KSYN_KDEG_IC50 (2)

MDL__ETA_KSYN_KDEG_IC50_3 = pm.ETA_KSYN_KDEG_IC50 (3)

Individual Parameters

\ln (CL) = \ln (pm.TVCL) + pm.ECL

\ln (VC) = \ln (pm.TVVC) + pm.EVC

\ln (VP1) = \ln (pm.TVVP1) + pm.EVP1

\ln (VP2) = \ln (pm.TVVP2) + pm.EVP2

\ln (Q1) = \ln (pm.TVQ1) + pm.EQ1

Q2 = pm.TVQ2

\ln (KA) = \ln (pm.TVKA) + pm.EKA

VMAX = pm.TVVMAX

KM = pm.TVKM

\ln (FSC) = \ln (pm.TVFSC) + pm.EFSC

\ln (KSYN) = \ln (pm.TVKSYN) + pm.MDL__ETA_KSYN_KDEG_IC50_1

\ln (KDEG) = \ln (pm.TVKDEG) + pm.MDL__ETA_KSYN_KDEG_IC50_2

\ln (IC50) = \ln (pm.TVIC50) + pm.MDL__ETA_KSYN_KDEG_IC50_3

Structural Model: $sm$

Variables

NTX_0 = \frac{pm.KSYN}{pm.KDEG}

F_SC = \frac{pm.FSC}{(1.0 + pm.FSC)}

\begin{matrix} \frac{ⅆ}{ⅆ T} SC = - pm.KA \cdot sm.SC \\ SC (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} CENT = pm.KA \cdot sm.SC - \frac{(pm.CL + pm.Q1 + pm.Q2 + sm.CLNL) \cdot sm.CENT}{pm.VC} + \frac{pm.Q1 \cdot sm.P1}{pm.VP1} + \frac{pm.Q2 \cdot sm.P2}{pm.VP2} \\ CENT (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} P1 = \frac{sm.CENT \cdot pm.Q1}{pm.VC} - \frac{sm.P1 \cdot pm.Q1}{pm.VP1} \\ P1 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} P2 = \frac{sm.CENT \cdot pm.Q2}{pm.VC} - \frac{sm.P2 \cdot pm.Q2}{pm.VP2} \\ P2 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} CLNL = \frac{pm.VMAX}{(sm.CP + pm.KM)} \\ CLNL (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} NTX = pm.KSYN \cdot (1.0 - \frac{sm.CP}{(pm.IC50 + sm.CP)}) - pm.KDEG \cdot sm.NTX \\ NTX (T = 0) = sm.NTX_0 \end{matrix}

CP = \frac{sm.CENT}{\frac{pm.VC}{1000000.0}}

Observation Model: $om1$

Continuous Observation

\ln (PK) = \ln (sm.CP) + additiveError (additive = {\begin{cases} pm.ADDIV & if & cm.IV = 2 \\ pm.ADDSC & otherwise \end{cases}) + pm.EPS_PK

Observation Model: $om2$

Continuous Observation

PD = sm.NTX + combinedError1 (additive = pm.PDADD, proportional = pm.PDPROP, f = sm.NTX) + pm.EPS_PD

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_opg.txt

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$CMT$	$3$	$cmt$	$int$
$AMT$	$4$	$dose$	$real$
$DVID$	$5$	$dvid$	$int$
$DV$	$6$	$dv$	$real$

Column Mappings

Column Ref	Modelling Mapping
$ID$	$vm_mdl.ID$
$TIME$	$T$
$AMT$	${\begin{cases} sm.SC & if & CMT = 1 \land AMT > 0 \\ sm.CENT & if & CMT = 2 \land AMT > 0 \end{cases}$
$DV$	${\begin{cases} om1.PK & if & DVID = 1 \\ om2.PD & if & DVID = 2 \end{cases}$
$CMT$	$cm.IV$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Initial Value	Fixed?	Limits
pm.TVCL	$168$	false	$()$
pm.TVVC	$2800$	false	$()$
pm.TVVP1	$443$	false	$()$
pm.TVVP2	$269$	false	$()$
pm.TVQ1	$15.5$	false	$()$
pm.TVQ2	$3.02$	false	$()$
pm.TVKA	$0.0131$	false	$()$
pm.TVVMAX	$13300$	false	$()$
pm.TVKM	$6.74$	false	$()$
pm.TVFSC	$0.0719$	false	$()$
pm.TVKSYN	$0.864$	false	$()$
pm.TVKDEG	$0.0204$	false	$()$
pm.TVIC50	$5.38$	false	$()$
pm.PPV_CL	$0.0391$	false	$()$
pm.PPV_VC	$0.0102$	false	$()$
pm.PPV_VP1	$0.0144$	false	$()$
pm.PPV_VP2	$0.0333$	false	$()$
pm.PPV_Q1	$0.0379$	false	$()$
pm.PPV_KA	$0.0457$	false	$()$
pm.PPV_FSC	$0.263$	false	$()$
pm.PPV_KSYN_KDEG_IC50	$(\begin{matrix} 0.281 \\ 0.0867 & 0.0325 \\ 0.0 & 0.0 & 1.18 \end{matrix})$	false	$()$
pm.ADDIV	$0.0193$	false	$()$
pm.ADDSC	$0.733$	false	$()$
pm.PDPROP	$0.0407$	false	$()$
pm.PDADD	$20.7$	false	$()$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$saem$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000233: Zierhut_2008_Population PKPD model for Fc-osteoprotegerin in healthy postmenopausal women

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

Observation Model: om2

Continuous Observation

External Dataset

File Specification

Column Definitions

Column Mappings

Estimation Step

Parameters To Estimate

Operations

Operation: 1

Operation Properties

Step Dependencies

Covariate Model: $cm$

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Observation Model: $om2$

Operation: $1$