Append a model to another

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.

Prerequisite

The examples below require the package campismod.

library(campsismod)

Load your base PK model

The following code will load our reference 2-compartment PK model.

pk_model <- model_suite$pk$`2cpt_fo`

Load an effect-compartment model

The effect-compartment model can be loaded from the model library as follows:

pd_model <- model_suite$pd$effect_cmt_model
pd_model

## [MAIN]
## KE0=THETA_KE0*exp(ETA_KE0)
## 
## [ODE]
## PK_CONC=10
## d/dt(A_EFFECT)=KE0*(PK_CONC - A_EFFECT)
## 
## 
## THETA's:
##   name index value   fix
## 1  KE0     1  0.25 FALSE
## OMEGA's:
##   name index index2 value   fix type same
## 1  KE0     1      1    15 FALSE  cv%   NA
## SIGMA's:
## # A tibble: 0 × 0
## No variance-covariance matrix
## 
## Compartments:
## A_EFFECT (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:

pd_model <- pd_model %>% replace(Equation("PK_CONC", "A_CENTRAL/VC"))

Append PD model to PK model

Appending the PD model to the PK model is done using the add function:

pkpd_model <- pk_model %>% add(pd_model)
pkpd_model

## [MAIN]
## TVKA=THETA_KA
## TVVC=THETA_VC
## TVVP=THETA_VP
## TVQ=THETA_Q
## TVCL=THETA_CL
## TVPROP_RUV=THETA_PROP_RUV
## 
## 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)
## PROP_RUV=TVPROP_RUV
## 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_EFFECT)=KE0*(PK_CONC - A_EFFECT)
## 
## [ERROR]
## CONC=A_CENTRAL/VC
## if (CONC <= 0.001) CONC=0.001
## IPRED=log(CONC)
## W=PROP_RUV
## Y=IPRED + W*EPS_RUV_FIX
## 
## 
## THETA's:
##       name index value   fix
## 1       KA     1  1.00 FALSE
## 2       VC     2 60.00 FALSE
## 3       VP     3 10.00 FALSE
## 4        Q     4  2.00 FALSE
## 5       CL     5  3.00 FALSE
## 6 PROP_RUV     6  0.10 FALSE
## 7      KE0     7  0.25 FALSE
## OMEGA's:
##   name index index2 value   fix type same
## 1   KA     1      1    25 FALSE  cv%   NA
## 2   VC     2      2    25 FALSE  cv%   NA
## 3   VP     3      3    25 FALSE  cv%   NA
## 4    Q     4      4    25 FALSE  cv%   NA
## 5   CL     5      5    25 FALSE  cv%   NA
## 6  KE0     6      6    15 FALSE  cv%   NA
## SIGMA's:
##      name index index2 value  fix type
## 1 RUV_FIX     1      1     1 TRUE  var
## No variance-covariance matrix
## 
## Compartments:
## A_ABS (CMT=1)
## A_CENTRAL (CMT=2)
## A_PERIPHERAL (CMT=3)
## A_EFFECT (CMT=4)

Simulate our PK/PD model

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")

shadedPlot(results, "CONC")

PK concentration

shadedPlot(results, "A_EFFECT")

Showing the delayed effect