This vignette shows how a model can be appended to another. This is particularly useful when appending a PD model to a existing PK model. In this vignette, we’ll demonstrate how an effect compartment model can be appended to a 2-compartment model.
The following code will load our reference 2-compartment PK model.
The effect-compartment model can be loaded from the model library as follows:
## [MAIN]
## EMAX=THETA_EMAX*exp(ETA_EMAX)
## EC50=THETA_EC50*exp(ETA_EC50)
## GAMMA=THETA_GAMMA*exp(ETA_GAMMA)
## E0=THETA_E0*exp(ETA_E0)
## KE0=THETA_KE0*exp(ETA_KE0)
##
## [ODE]
## PK_CONC=10
## d/dt(A_ECONC)=KE0*(PK_CONC - A_ECONC)
## EFFECT=E0 + EMAX*pow(A_ECONC, GAMMA)/(pow(EC50, GAMMA) + pow(A_ECONC, GAMMA))
##
##
## THETA's:
## name index value fix label unit
## 1 EMAX 1 100.0 FALSE Maximum effect <NA>
## 2 EC50 2 10.0 FALSE Concentration at 50% of EMAX ng/mL
## 3 GAMMA 3 1.5 FALSE Hill coefficient <NA>
## 4 E0 4 20.0 FALSE Baseline <NA>
## 5 KE0 5 0.5 FALSE Effect compartment delay rate 1/h
## OMEGA's:
## name index index2 value fix type
## 1 EMAX 1 1 10 FALSE cv%
## 2 EC50 2 2 10 FALSE cv%
## 3 GAMMA 3 3 10 FALSE cv%
## 4 E0 4 4 10 FALSE cv%
## 5 KE0 5 5 10 FALSE cv%
## SIGMA's:
## # A tibble: 0 × 0
## No variance-covariance matrix
##
## Compartments:
## A_ECONC (CMT=1)This PD model has a variable PK_CONC, that needs to be
linked with the PK concentration.
Therefore, we need to adapt it as follows:
Appending the PD model to the PK model is done using the
add function:
## [MAIN]
## TVBIO=THETA_BIO
## TVKA=THETA_KA
## TVVC=THETA_VC
## TVVP=THETA_VP
## TVQ=THETA_Q
## TVCL=THETA_CL
##
## BIO=TVBIO
## KA=TVKA * exp(ETA_KA)
## VC=TVVC * exp(ETA_VC)
## VP=TVVP * exp(ETA_VP)
## Q=TVQ * exp(ETA_Q)
## CL=TVCL * exp(ETA_CL)
## EMAX=THETA_EMAX*exp(ETA_EMAX)
## EC50=THETA_EC50*exp(ETA_EC50)
## GAMMA=THETA_GAMMA*exp(ETA_GAMMA)
## E0=THETA_E0*exp(ETA_E0)
## KE0=THETA_KE0*exp(ETA_KE0)
##
## [ODE]
## d/dt(A_ABS)=-KA*A_ABS
## d/dt(A_CENTRAL)=KA*A_ABS + Q/VP*A_PERIPHERAL - Q/VC*A_CENTRAL - CL/VC*A_CENTRAL
## d/dt(A_PERIPHERAL)=Q/VC*A_CENTRAL - Q/VP*A_PERIPHERAL
## PK_CONC=A_CENTRAL/VC
## d/dt(A_ECONC)=KE0*(PK_CONC - A_ECONC)
## EFFECT=E0 + EMAX*pow(A_ECONC, GAMMA)/(pow(EC50, GAMMA) + pow(A_ECONC, GAMMA))
##
## [F]
## A_ABS=BIO
##
## [ERROR]
## CONC=A_CENTRAL/VC
## if (CONC <= 0.001) CONC=0.001
## CONC_ERR=CONC*(1 + EPS_PROP_RUV)
##
##
## THETA's:
## name index value fix label unit
## 1 BIO 1 1.0 FALSE Bioavailability <NA>
## 2 KA 2 1.0 FALSE Absorption rate 1/h
## 3 VC 3 10.0 FALSE Volume of central compartment L
## 4 VP 4 40.0 FALSE Volume of peripheral compartment L
## 5 Q 5 20.0 FALSE Inter-compartment flow L/h
## 6 CL 6 3.0 FALSE Clearance L/h
## 7 EMAX 7 100.0 FALSE Maximum effect <NA>
## 8 EC50 8 10.0 FALSE Concentration at 50% of EMAX ng/mL
## 9 GAMMA 9 1.5 FALSE Hill coefficient <NA>
## 10 E0 10 20.0 FALSE Baseline <NA>
## 11 KE0 11 0.5 FALSE Effect compartment delay rate 1/h
## OMEGA's:
## name index index2 value fix type
## 1 KA 1 1 25 FALSE cv%
## 2 VC 2 2 25 FALSE cv%
## 3 VP 3 3 25 FALSE cv%
## 4 Q 4 4 25 FALSE cv%
## 5 CL 5 5 25 FALSE cv%
## 6 EMAX 6 6 10 FALSE cv%
## 7 EC50 7 7 10 FALSE cv%
## 8 GAMMA 8 8 10 FALSE cv%
## 9 E0 9 9 10 FALSE cv%
## 10 KE0 10 10 10 FALSE cv%
## SIGMA's:
## name index index2 value fix type
## 1 PROP_RUV 1 1 0.1 FALSE sd
## No variance-covariance matrix
##
## Compartments:
## A_ABS (CMT=1)
## A_CENTRAL (CMT=2)
## A_PERIPHERAL (CMT=3)
## A_ECONC (CMT=4)Let’s now simulate our PK/PD model:
library(campsis)
dataset <- Dataset(25) %>%
add(Bolus(time=0, amount=1000, compartment=1, ii=12, addl=2)) %>%
add(Observations(times=0:36))
results <- pkpd_model %>% simulate(dataset=dataset, seed=1)
shadedPlot(results, "CONC")
