DDMoRe Model Repository

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Model Definition
Estimation Steps

Short description:

Sunitinib is a potent inhibitor of receptor tyrosine kinases, including VEGFR-1, -2, and -3, stem cell factor receptor and others, which have been implicated in tumor cell growth indirectly via tumor-dependent angiogenesis. This is a semi-mechanistic PK/PD model developed and validated using clinical trail data.

Format:	PharmML (0.6.1)
Contributors:	Moran Optimata

Context of model development:	Disease Progression model; Dose & Schedule Selection and Label Recommendation; Clinical end-point; Mechanistic Understanding;
Model implementation requiring submitter’s additional knowledge:	Yes;
Modelling context description:	This is a semi-mechanistic PK/PD model for sunitinib therapy in non-small cell lung cancer patients. It was developed and validated using clinical trail data provided by the drug developer.;
Modelling task in scope:	estimation; simulation;
Nature of research:	Early clinical development (Phases I and II);
Therapeutic/disease area:	Oncology;

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

Mandatory file
- Sunitinib_MPD6_model.xml

Additional Files
- Sunitinib_MPD6_model.mdl
- DDMODEL00000231.rdf

Model owner: Moran Optimata
Submitted: Oct 27, 2016 9:32:06 AM
Last Modified: Oct 27, 2016 9:32:06 AM

Revisions

Version: 3
- Submitted on: Oct 27, 2016 9:32:06 AM
- Submitted by: Moran Optimata
- With comment: Updated model annotations.

Independent variable T

Function Definitions

proportionalError (proportional, f) = (proportional \times f)

combinedError1 (additive, proportional, f) = (additive + (proportional \times f))

Structural Model sm

Variable definitions

D

dres = 0

fp = 0.21

th1 = 1

th2 = 1

th3 = 1

th4 = 1

thettum = 1

Kah = (Ka \times 24)

Kamh = (Kam \times 24)

q = \frac{(24 \times Cl)}{V1}

qm = \frac{(24 \times Clm)}{Vm1}

k12 = \frac{(24 \times QQ)}{V1}

k21 = \frac{(24 \times QQ)}{V2}

km12 = \frac{(24 \times QQm)}{Vm1}

km21 = \frac{(24 \times QQm)}{Vm2}

stst1 = exp (st1)

stst2 = exp (st2)

stst3 = exp (st3)

stst4 = exp (st4)

kin1 = (stst1 \times d1)

kin2 = (stst2 \times d2)

kin3 = (stst3 \times d3)

kin4 = (stst4 \times d4)

maxgr = \frac{log (2)}{30}

\frac{dA1}{dT} = (((((Kah \times A14) \times (1 - fp)) - (k12 \times A1)) + (k21 \times A2)) - (q \times A1))

\frac{dA2}{dT} = ((k12 \times A1) - (k21 \times A2))

\frac{dA3}{dT} = (((((Kamh \times A15) \times fp) - (km12 \times A3)) + (km21 \times A4)) - (qm \times A3))

\frac{dA4}{dT} = ((km12 \times A3) - (km21 \times A4))

\frac{dA5}{dT} = (kin1 - \frac{(d1 \times A5)}{(1 + (pd1 \times (\frac{(th1 \times A1)}{V1} + \frac{((1 - th1) \times A3)}{Vm1})))})

\frac{dA6}{dT} = (\frac{kin2}{(1 + (pd2 \times (\frac{(th2 \times A1)}{V1} + \frac{((1 - th2) \times A3)}{Vm1})))} - (d2 \times A6))

\frac{dA7}{dT} = (\frac{kin3}{(1 + (pd3 \times (\frac{(th3 \times A1)}{V1} + \frac{((1 - th3) \times A3)}{Vm1})))} - (d3 \times A7))

\frac{dA8}{dT} = (\frac{kin4}{(1 + (pd4 \times (\frac{(th4 \times A1)}{V1} + \frac{((1 - th4) \times A3)}{Vm1})))} - (d4 \times A8))

RATEIN = {\begin{matrix} (((min (maxgr, A13) - (\frac{lam0}{pdr} \times A12)) + (lam0 \times A11)) \times A9) & if & (A9 > 0) \\ 0 & otherwise \end{matrix}

\frac{dA9}{dT} = RATEIN

\frac{dA10}{dT} = ((pdr \times ((thettum \times max (0, \frac{A1}{V1})) + ((1 - thettum) \times max (0, \frac{A3}{Vm1})))) - (dres \times max (0, A10)))

\frac{dA11}{dT} = (A12 - (pdr \times A11))

\frac{dA12}{dT} = (\frac{A1}{V1} - (pdm \times A12))

\frac{dA13}{dT} = (alphres \times A13)

\frac{dA14}{dT} = (- Kah \times A14)

\frac{dA15}{dT} = (- Kamh \times A15)

output1 = \frac{A1}{V1}

output2 = \frac{A3}{Vm1}

output3 = A5

output4 = A6

output5 = A7

output6 = A8

output7 = {(\frac{3}{(4 \times 3.1416)} \times max (A9, 0))}^{\frac{1}{3}}

Initial conditions

A1 = 0

A2 = 0

A3 = 0

A4 = 0

A5 = stst1

A6 = stst2

A7 = stst3

A8 = stst4

A9 = ((\frac{4}{3} \times 3.1416) \times {exp (x0)}^{3})

A10 = 0

A11 = 0

A12 = 0

A13 = lam

A14 = D

A15 = D

Variability Model

Level	Type
DV	residualError
ID	parameterVariability

Parameter Model

Parameters

POP_d1

;

POP_d2

;

POP_d3

;

POP_d4

;

POP_QQm

;

POP_pdr

;

POP_st1

;

POP_st2

;

POP_st3

;

POP_st4

;

POP_x0

;

POP_pdm

;

POP_lam

;

POP_lam0

;

POP_alphres

;

POP_pd1

;

POP_pd2

;

POP_pd3

;

POP_pd4

;

POP_Cl

;

POP_V1

;

POP_QQ

;

POP_V2

;

POP_Clm

;

POP_Vm1

;

POP_Vm2

;

POP_Ka

;

POP_Kam

;

b_1

;

b_2

;

b_3

;

b_4

;

b_5

;

b_6

;

a_7

;

b_7

;

omega_d1

;

omega_d2

;

omega_d3

;

omega_d4

;

omega_QQm

;

omega_pdr

;

omega_st1

;

omega_st2

;

omega_st3

;

omega_st4

;

omega_x0

;

omega_pdm

;

omega_lam

;

omega_lam0

;

omega_alphres

;

omega_pd1

;

omega_pd2

;

omega_pd3

;

omega_pd4

;

omega_Cl

;

omega_V1

;

omega_QQ

;

omega_V2

;

omega_Clm

;

omega_Vm1

;

omega_Vm2

;

omega_Ka

;

omega_Kam

;

ETA_d1 \sim N (0.0, omega_d1)

— ID

ETA_d2 \sim N (0.0, omega_d2)

— ID

ETA_d3 \sim N (0.0, omega_d3)

— ID

ETA_d4 \sim N (0.0, omega_d4)

— ID

ETA_QQm \sim N (0.0, omega_QQm)

— ID

ETA_pdr \sim N (0.0, omega_pdr)

— ID

ETA_st1 \sim N (0.0, omega_st1)

— ID

ETA_st2 \sim N (0.0, omega_st2)

— ID

ETA_st3 \sim N (0.0, omega_st3)

— ID

ETA_st4 \sim N (0.0, omega_st4)

— ID

ETA_x0 \sim N (0.0, omega_x0)

— ID

ETA_pdm \sim N (0.0, omega_pdm)

— ID

ETA_lam \sim N (0.0, omega_lam)

— ID

ETA_lam0 \sim N (0.0, omega_lam0)

— ID

ETA_alphres \sim N (0.0, omega_alphres)

— ID

ETA_pd1 \sim N (0.0, omega_pd1)

— ID

ETA_pd2 \sim N (0.0, omega_pd2)

— ID

ETA_pd3 \sim N (0.0, omega_pd3)

— ID

ETA_pd4 \sim N (0.0, omega_pd4)

— ID

ETA_Cl \sim N (0.0, omega_Cl)

— ID

ETA_V1 \sim N (0.0, omega_V1)

— ID

ETA_QQ \sim N (0.0, omega_QQ)

— ID

ETA_V2 \sim N (0.0, omega_V2)

— ID

ETA_Clm \sim N (0.0, omega_Clm)

— ID

ETA_Vm1 \sim N (0.0, omega_Vm1)

— ID

ETA_Vm2 \sim N (0.0, omega_Vm2)

— ID

ETA_Ka \sim N (0.0, omega_Ka)

— ID

ETA_Kam \sim N (0.0, omega_Kam)

— ID

EPS_Y \sim N (0.0, 1.0)

— DV

log (d1) = (log (POP_d1) + ETA_d1)

log (d2) = (log (POP_d2) + ETA_d2)

log (d3) = (log (POP_d3) + ETA_d3)

log (d4) = (log (POP_d4) + ETA_d4)

log (QQm) = (log (POP_QQm) + ETA_QQm)

log (pdr) = (log (POP_pdr) + ETA_pdr)

log (st1) = (log (POP_st1) + ETA_st1)

log (st2) = (log (POP_st2) + ETA_st2)

log (st3) = (log (POP_st3) + ETA_st3)

log (st4) = (log (POP_st4) + ETA_st4)

log (x0) = (log (POP_x0) + ETA_x0)

log (pdm) = (log (POP_pdm) + ETA_pdm)

log (lam) = (log (POP_lam) + ETA_lam)

log (lam0) = (log (POP_lam0) + ETA_lam0)

log (alphres) = (log (POP_alphres) + ETA_alphres)

log (pd1) = (log (POP_pd1) + ETA_pd1)

log (pd2) = (log (POP_pd2) + ETA_pd2)

log (pd3) = (log (POP_pd3) + ETA_pd3)

log (pd4) = (log (POP_pd4) + ETA_pd4)

log (Cl) = (log (POP_Cl) + ETA_Cl)

log (V1) = (log (POP_V1) + ETA_V1)

log (QQ) = (log (POP_QQ) + ETA_QQ)

log (V2) = (log (POP_V2) + ETA_V2)

log (Clm) = (log (POP_Clm) + ETA_Clm)

log (Vm1) = (log (POP_Vm1) + ETA_Vm1)

log (Vm2) = (log (POP_Vm2) + ETA_Vm2)

log (Ka) = (log (POP_Ka) + ETA_Ka)

log (Kam) = (log (POP_Kam) + ETA_Kam)

Correlation matrix for level ID and random effects: ETA_d1, ETA_d2

(\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})

Observation Model

Observation Y1
Continuous / Residual Data

Parameters

Y1 = (output1 + (proportionalError (b_1, output1) \times EPS_Y))

Observation Y2
Continuous / Residual Data

Parameters

Y2 = (output2 + (proportionalError (b_2, output2) \times EPS_Y))

Observation Y3
Continuous / Residual Data

Parameters

Y3 = (output3 + (proportionalError (b_3, output3) \times EPS_Y))

Observation Y4
Continuous / Residual Data

Parameters

Y4 = (output4 + (proportionalError (b_4, output4) \times EPS_Y))

Observation Y5
Continuous / Residual Data

Parameters

Y5 = (output5 + (proportionalError (b_5, output5) \times EPS_Y))

Observation Y6
Continuous / Residual Data

Parameters

Y6 = (output6 + (proportionalError (b_6, output6) \times EPS_Y))

Observation Y7
Continuous / Residual Data

Parameters

Y7 = (output7 + (combinedError1 (a_7, b_7, output7) \times EPS_Y))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Initial estimates for non-fixed parameters

$POP_d1 = 0.111$
$POP_d2 = 0.101$
$POP_d3 = 0.169$
$POP_d4 = 0.00659$
$POP_QQm = 159$
$POP_pdr = 0.0286$
$POP_st1 = 0$
$POP_st2 = 0$
$POP_st3 = 0$
$POP_st4 = 0$
$POP_x0 = 0$
$POP_pdm = 0.129$
$POP_lam = 1.93E-4$
$POP_lam0 = 0.00189$
$POP_alphres = 0.0102$
$POP_pd1 = 144$
$POP_pd2 = 22$
$POP_pd3 = 36.4$
$POP_pd4 = 98.1$
$POP_Cl = 26.9$
$POP_V1 = 3220$
$POP_QQ = 17.5$
$POP_V2 = 127$
$POP_Clm = 15.6$
$POP_Vm1 = 3710$
$POP_Vm2 = 156$
$POP_Ka = 0.0715$
$POP_Kam = 0.177$
$b_1 = 0.512$
$b_2 = 0.429$
$b_3 = 0.503$
$b_4 = 0.137$
$b_5 = 0.28$
$b_6 = 0.135$
$a_7 = 0.241$
$b_7 = 0.0856$
$omega_d1 = 4.94$
$omega_d2 = 0.485$
$omega_d3 = 0.517$
$omega_d4 = 0.468$
$omega_QQm = 0$
$omega_pdr = 0$
$omega_st1 = 0.348$
$omega_st2 = 0$
$omega_st3 = 0$
$omega_st4 = 0$
$omega_x0 = 0$
$omega_pdm = 1.74$
$omega_lam = 2.11$
$omega_lam0 = 0$
$omega_alphres = 0$
$omega_pd1 = 0$
$omega_pd2 = 0.468$
$omega_pd3 = 0.988$
$omega_pd4 = 0.384$
$omega_Cl = 0.297$
$omega_V1 = 1.3$
$omega_QQ = 0$
$omega_V2 = 0$
$omega_Clm = 0.444$
$omega_Vm1 = 0.908$
$omega_Vm2 = 0$
$omega_Ka = 0$
$omega_Kam = 0$

Estimation operations

1) Estimate the population parameters

Algorithm SAEM

Step Dependencies

estimStep_1

DDMODEL00000231: PK/PD model of sunitinib in non-small cell lung cancer patients

Revisions

Function Definitions

Structural Model sm

Variability Model

Parameter Model

Observation Model

Observation Y1Continuous / Residual Data

Observation Y2Continuous / Residual Data

Observation Y3Continuous / Residual Data

Observation Y4Continuous / Residual Data

Observation Y5Continuous / Residual Data

Observation Y6Continuous / Residual Data

Observation Y7Continuous / Residual Data

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Estimation operations

Step Dependencies

Observation Y1
Continuous / Residual Data

Observation Y2
Continuous / Residual Data

Observation Y3
Continuous / Residual Data

Observation Y4
Continuous / Residual Data

Observation Y5
Continuous / Residual Data

Observation Y6
Continuous / Residual Data

Observation Y7
Continuous / Residual Data