[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("", selected="Plot", id="nav", inverse="FALSE", 
             title="PK model with inter individual variability",
             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, list(number=",input$nband,", level=",input$level,"))")
    
    txt <-paste0(t1, t2, t3, t4, t5, t6)
    return(txt)
  })
  
  output$plot1 <- renderPlot({
    withProgress(message = 'Creating plot', detail='Wait...', value = 0.1, expr={
      r=r()
      qr <- prctilemlx(r,list(level=input$level,number=input$nband))
      print(qr)
    })
  })
  
  
  output$table <- renderTable({ 
    r=r()
    rq <- prctilemlx(r,list(level=input$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