[LONGITUDINAL]
input = {V, k}
EQUATION:
Cc = pkmodel(V, k)
[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}
#-------------------------------------------------------------------------
# This application is governed by the CeCILL-B license.
# You can use, modify and/ or redistribute this code under the terms
# of the CeCILL license: http://www.cecill.info/index.en.html
#
# Marc Lavielle, Inria Saclay
# April 29th, 2015
#-------------------------------------------------------------------------
shinyUI(fluidPage(
# titlePanel(
# list(HTML('<p style="color:#4C0B5F; font-size:24px" fontsize=14>
# PK model with inter individual variability</p>' )),
# windowTitle="PK model with IIV"),
navbarPage("PK model with inter individual variability", selected="Plot", id="nav", inverse="FALSE",
tabPanel("Plot",
tabsetPanel( id="tabs", type="pills",
tabPanel("dosage"),
tabPanel("parameters"),
tabPanel("outputs"),
tabPanel("settings")
),
fluidRow(
column(3,
br(), br(),
conditionalPanel(condition="input.tabs=='dosage'",
sliderInput("tfd", "Time of first dose:", value=0, min=0, max = 20, step=1),
sliderInput("nd", "Number of doses:", value=6, min=1, max = 10, step=1),
sliderInput("ii", "Interdose interval:", value = 3, min = 0.5, max = 10, step=0.5),
sliderInput("tinf", "Infusion time:", value = 1, min = 0, max = 5, step=0.5),
sliderInput("amt", "Amount:", value = 5, min = 0, max = 20, step=1),
br()
),
conditionalPanel(condition="input.tabs=='parameters'",
sliderInput("V_pop", "V_pop :", value = 10, min = 1, max = 20, step=1),
sliderInput("k_pop", "k_pop :", value = 0.2, min = 0, max = 1, step=0.05),
sliderInput("omega_V", "omega_V :", value = 0.3, min = 0, max = 2, step=0.1),
sliderInput("omega_k", "omega_k :", value = 0.2, min = 0, max = 2, step=0.1),
br()
),
conditionalPanel(condition="input.tabs=='outputs'",
br(),
selectInput("output","",c("concentration (Cc)" = "Cc","amount (Ac)" = "Ac")),
br(),
sliderInput("range", "time range", min = -5, max = 50, value = c(0,20), step=5),
br(),
sliderInput("ngp", "grid size", min = 11, max = 501, value = 101, step=10),
br()
),
conditionalPanel(condition="input.tabs=='settings'",
sliderInput("level", "level (%)", min = 5, max = 95, value = 80, step=5),
sliderInput("nband", "number of bands", min = 1, max = 20, value = 8, step=1),
sliderInput("nbsim", "number of simulations", min = 500, max = 5000, value = 1000, step=500),
br()
)
),
column(9,
plotOutput("plot1", height="500px"))
)),
tabPanel("Table", tableOutput("table")),
navbarMenu("Codes",
tabPanel("Mlxtran", pre(includeText("pkiiv1_model.txt"))),
tabPanel("Simulx", verbatimTextOutput("simulx")),
tabPanel("ui.R", pre(includeText("ui.R"))),
tabPanel("server.R", pre(includeText("server.R")))
),
tabPanel("ReadMe", withMathJax(), includeMarkdown("readMe.Rmd")),
tabPanel("About", includeMarkdown("../../about/about.Rmd"))
)
))
#-------------------------------------------------------------------------
# This application is governed by the CeCILL-B license.
# You can use, modify and/ or redistribute this code under the terms
# of the CeCILL license: http://www.cecill.info/index.en.html
#
# Marc Lavielle, Inria Saclay
# April 30th, 2015
#-------------------------------------------------------------------------
library(mlxR)
shinyServer(function(input, output, session) {
r <- reactive({
if (input$tinf>input$ii)
stop("The infusion time should not exceed the interdose interval")
param.value=c(input$V_pop,input$k_pop,input$omega_V,input$omega_k)
t.value=seq(input$range[1],input$range[2],length.out=input$ngp)
t1=input$tfd
t2=input$ii*(input$nd-1)+t1
if (t2>=t1){
t.dose=seq(t1,t2,by=input$ii)
adm <- list(time=t.dose, amount=input$amt, rate=input$amt/input$tinf)
}else{
adm <- list(time=t1, amount=0)
}
f <- list(name=input$output,time=t.value)
p <- list(name=c('V_pop','k_pop','omega_V','omega_k'), value=param.value)
g <- list(size=input$nbsim,level='individual')
res <- simulx( model = 'pkiiv1_model.txt',
treatment = adm,
group = g,
parameter = p,
output = f)
ro <- res[[input$output]]
})
t <- reactive({
time1=input$tfd
time2=input$ii*(input$nd-1)+time1
t1 <- paste0("adm <- list(time=seq(",time1,",",time2,",by=",input$ii,"), amount=",input$amt,", rate=",input$amt/input$tinf,")\n")
t2 <- paste0("Cc <- list(name='Cc', time=seq(from=",input$range[1],", to=",input$range[2],", length.out=",input$ngp,"))\n")
t3 <- paste0("p <- c(V_pop=",input$V_pop,",k_pop=",input$k_pop,",omega_V=",input$omega_V,",omega_k=",input$omega_k,")\n")
t4 <- paste0("g <- list(size=",input$nbsim,", level='individual')\n")
t5 <- "res <- simulx(model='pkiiv1_model.txt', parameter=p, output=Cc, treatment=adm, group=g)\n\n"
t6 <- paste0("prctilemlx(res$Cc, band=list(number=",input$nband,", level=",input$level,"))")
txt <-paste0(t1, t2, t3, t4, t5, t6)
return(txt)
})
output$plot1 <- renderPlot({
withProgress(message = 'Creating plot', detail='Wait...', value = 0.1, expr={
r=r()
qr <- prctilemlx(r,band=list(level=input$level,number=input$nband))
print(qr)
})
})
output$table <- renderTable({
r=r()
rq <- prctilemlx(r,band=list(level=input$level,number=input$nband),plot=FALSE)
y=rq$y
})
output$simulx <- renderText(t())
})
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 dosage:
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.
This application is governed by the CeCILL-B license.
You can use, modify and/or redistribute these codes under the terms of the
CeCILL license.
This Shiny application requires the mlxR package.
Marc Lavielle
Inria Saclay, Popix team
April 29th, 2015