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

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: Dose & Schedule Selection and Label Recommendation; Clinical end-point; Disease Progression model; 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: simulation; estimation; 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.
• Model owner: Moran Optimata
• Submitted: 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

$proportionalError(proportional,f)=(proportional ×f)$
$combinedError1(additive,proportional,f)=(additive+(proportional ×f))$

### Structural Model sm

Variable definitions

$D$
$dres=0$
$fp=0.21$
$th1=1$
$th2=1$
$th3=1$
$th4=1$
$thettum=1$
$Kah=(Ka ×24)$
$Kamh=(Kam ×24)$
$q=(24 ×Cl)V1$
$qm=(24 ×Clm)Vm1$
$k12=(24 ×QQ)V1$
$k21=(24 ×QQ)V2$
$km12=(24 ×QQm)Vm1$
$km21=(24 ×QQm)Vm2$
$stst1=exp(st1)$
$stst2=exp(st2)$
$stst3=exp(st3)$
$stst4=exp(st4)$
$kin1=(stst1 ×d1)$
$kin2=(stst2 ×d2)$
$kin3=(stst3 ×d3)$
$kin4=(stst4 ×d4)$
$maxgr=log(2)30$
$dA1dT=(((((Kah ×A14) ×(1-fp))-(k12 ×A1))+(k21 ×A2))-(q ×A1))$
$dA2dT=((k12 ×A1)-(k21 ×A2))$
$dA3dT=(((((Kamh ×A15) ×fp)-(km12 ×A3))+(km21 ×A4))-(qm ×A3))$
$dA4dT=((km12 ×A3)-(km21 ×A4))$
$dA5dT=(kin1-(d1 ×A5)(1+(pd1 ×((th1 ×A1)V1+((1-th1) ×A3)Vm1))))$
$dA6dT=(kin2(1+(pd2 ×((th2 ×A1)V1+((1-th2) ×A3)Vm1)))-(d2 ×A6))$
$dA7dT=(kin3(1+(pd3 ×((th3 ×A1)V1+((1-th3) ×A3)Vm1)))-(d3 ×A7))$
$dA8dT=(kin4(1+(pd4 ×((th4 ×A1)V1+((1-th4) ×A3)Vm1)))-(d4 ×A8))$
$dA9dT=RATEIN$
$dA10dT=((pdr ×((thettum ×max(0,A1V1))+((1-thettum) ×max(0,A3Vm1))))-(dres ×max(0,A10)))$
$dA11dT=(A12-(pdr ×A11))$
$dA12dT=(A1V1-(pdm ×A12))$
$dA13dT=(alphres ×A13)$
$dA14dT=(-Kah ×A14)$
$dA15dT=(-Kamh ×A15)$
$output1=A1V1$
$output2=A3Vm1$
$output3=A5$
$output4=A6$
$output5=A7$
$output6=A8$
$output7=(3(4 ×3.1416) ×max(A9,0))13$

Initial conditions

$A1=0$
$A2=0$
$A3=0$
$A4=0$
$A5=stst1$
$A6=stst2$
$A7=stst3$
$A8=stst4$
$A9=((43 ×3.1416) ×exp(x0)3)$
$A10=0$
$A11=0$
$A12=0$
$A13=lam$
$A14=D$
$A15=D$

### Variability Model

Level Type

DV

residualError

ID

parameterVariability

### Parameter Model

Parameters
$POP_d1$ $POP_d2$ $POP_d3$ $POP_d4$ $POP_QQm$ $POP_pdr$ $POP_st1$ $POP_st2$ $POP_st3$ $POP_st4$ $POP_x0$ $POP_pdm$ $POP_lam$ $POP_lam0$ $POP_alphres$ $POP_pd1$ $POP_pd2$ $POP_pd3$ $POP_pd4$ $POP_Cl$ $POP_V1$ $POP_QQ$ $POP_V2$ $POP_Clm$ $POP_Vm1$ $POP_Vm2$ $POP_Ka$ $POP_Kam$ $b_1$ $b_2$ $b_3$ $b_4$ $b_5$ $b_6$ $a_7$ $b_7$ $omega_d1$ $omega_d2$ $omega_d3$ $omega_d4$ $omega_QQm$ $omega_pdr$ $omega_st1$ $omega_st2$ $omega_st3$ $omega_st4$ $omega_x0$ $omega_pdm$ $omega_lam$ $omega_lam0$ $omega_alphres$ $omega_pd1$ $omega_pd2$ $omega_pd3$ $omega_pd4$ $omega_Cl$ $omega_V1$ $omega_QQ$ $omega_V2$ $omega_Clm$ $omega_Vm1$ $omega_Vm2$ $omega_Ka$ $omega_Kam$
$ETA_d1∼N(0.0,omega_d1)$ — ID
$ETA_d2∼N(0.0,omega_d2)$ — ID
$ETA_d3∼N(0.0,omega_d3)$ — ID
$ETA_d4∼N(0.0,omega_d4)$ — ID
$ETA_QQm∼N(0.0,omega_QQm)$ — ID
$ETA_pdr∼N(0.0,omega_pdr)$ — ID
$ETA_st1∼N(0.0,omega_st1)$ — ID
$ETA_st2∼N(0.0,omega_st2)$ — ID
$ETA_st3∼N(0.0,omega_st3)$ — ID
$ETA_st4∼N(0.0,omega_st4)$ — ID
$ETA_x0∼N(0.0,omega_x0)$ — ID
$ETA_pdm∼N(0.0,omega_pdm)$ — ID
$ETA_lam∼N(0.0,omega_lam)$ — ID
$ETA_lam0∼N(0.0,omega_lam0)$ — ID
$ETA_alphres∼N(0.0,omega_alphres)$ — ID
$ETA_pd1∼N(0.0,omega_pd1)$ — ID
$ETA_pd2∼N(0.0,omega_pd2)$ — ID
$ETA_pd3∼N(0.0,omega_pd3)$ — ID
$ETA_pd4∼N(0.0,omega_pd4)$ — ID
$ETA_Cl∼N(0.0,omega_Cl)$ — ID
$ETA_V1∼N(0.0,omega_V1)$ — ID
$ETA_QQ∼N(0.0,omega_QQ)$ — ID
$ETA_V2∼N(0.0,omega_V2)$ — ID
$ETA_Clm∼N(0.0,omega_Clm)$ — ID
$ETA_Vm1∼N(0.0,omega_Vm1)$ — ID
$ETA_Vm2∼N(0.0,omega_Vm2)$ — ID
$ETA_Ka∼N(0.0,omega_Ka)$ — ID
$ETA_Kam∼N(0.0,omega_Kam)$ — ID
$EPS_Y∼N(0.0,1.0)$ — 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
$( 1 0 0 1 )$

### Observation Model

#### Observation Y1Continuous / Residual Data

Parameters
$Y1=(output1+(proportionalError(b_1,output1) ×EPS_Y))$

#### Observation Y2Continuous / Residual Data

Parameters
$Y2=(output2+(proportionalError(b_2,output2) ×EPS_Y))$

#### Observation Y3Continuous / Residual Data

Parameters
$Y3=(output3+(proportionalError(b_3,output3) ×EPS_Y))$

#### Observation Y4Continuous / Residual Data

Parameters
$Y4=(output4+(proportionalError(b_4,output4) ×EPS_Y))$

#### Observation Y5Continuous / Residual Data

Parameters
$Y5=(output5+(proportionalError(b_5,output5) ×EPS_Y))$

#### Observation Y6Continuous / Residual Data

Parameters
$Y6=(output6+(proportionalError(b_6,output6) ×EPS_Y))$

#### Observation Y7Continuous / Residual Data

Parameters
$Y7=(output7+(combinedError1(a_7,b_7,output7) ×EPS_Y))$

### 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