PK model with inter individual variability




[LONGITUDINAL]
input = {V, k}

PK:
depot(target=Ac)

EQUATION:
ddt_Ac = -k*Ac
Cc=Ac/V

;-----------------------
[INDIVIDUAL]
input = {V_pop, k_pop, omega_V, omega_k}

DEFINITION:
V = {distribution=lognormal, reference=V_pop, sd=omega_V}
k = {distribution=lognormal, reference=k_pop, sd=omega_k}
source('prctilemlx.R')

adm <- list(time=1, amount=40)
Cc  <- list(name='Cc',time=seq(from=0, to=20, by=1))
p   <- list(name=c('V_pop','k_pop','omega_V','omega_k'), value=c(10,0.2,0.3,0.2))
g <- list(size=1000,level='individual')
res <- simulx(model='pk1b_model.txt', parameter=p, output=Cc, treatment=adm, group=g)

band.level=80
band.nb=8

qr <- prctilemlx(res$Cc,band.level,band.nb)

#----------------------------------

PK model with inter individual variability (IIV)

The amount \(A_c\) in the central compartment is solution of the ODE \(\ \ \dot{A_c}(t) = - k \, A_c(t)\)

The concentration \(C_c\) in the central compartment is defined by \(\ \ C_c(t) = A_c(t)/V\)

\(V\) and \(k\) are both log-normally distributed: \[ \begin{aligned} \log(V) & \sim {\cal N}(\log(V_{\rm pop}), \omega^2_V) \\ \log(k) & \sim {\cal N}(\log(k_{\rm pop}), \omega^2_k) \end{aligned} \]

  • Define the dosage regimen in the tab iv: time of first dose, number of doses, interdose interval, infusion time, amount.

  • select the PK parameters in the tab parameters:
    • \(k_{\rm pop}\), the population value of the elimination rate constant \(k\),
    • \(V_{\rm pop}\), the population value of the volume \(V\),
    • \(\omega_k\), the standard deviation of \(\log(k)\),
    • \(\omega_V\), the standard deviation of \(\log(V)\).

  • define the outputs in the tab outputs :
    • select the output to display: the amount \(A_c\) or the concentration \(C_c\),
    • select the time range where the prediction is computed,
    • select the number of time points of the grid where the prediction is computed.

  • define the prediction distribution to display in the tab settings:
    • select the level of the prediction interval (between 5% and 95%),
    • select the number of bands which form this prediction interval
    • the number of simulations used for estimating this prediction distribution.

By default a 80% prediction interval decomposed in 8 bands is used. Then, the 10th, 20th, 30th, …, 70th and 90th percentiles are displayed.