Simulation framework [NCA / SHAM]

posted by mittyri – Russia, 2019-04-17 01:21  – Posting: # 20179
Views: 2,234

Hi Helmut,

» If t½ of active metabolite > t½ of parent, assess only the metabolite.

Could you please explain a little bit? When did I miss that good old times?

ready for simulation:

library(ggplot2)
# input paraemeters
Nsub <- 1000 # number of subjects to simulate
D        <- 400
ka       <- 1.39  # 1/h
ka.omega <- 0.1
Vd       <- 1     # L
Vd.omega <- 0.2
CL       <- 0.347 # L/h
CL.omega <- 0.15
t<- c(seq(0, 1, 0.25), seq(2,6,1), 8,10,12,16,24) # some realistic sequence
ratio <- 2^(seq(-3,3,0.2)) # ratios of ka(T)/ka/R)

# helper functions
C.sd <- function(F=1, D, Vd, ka, ke, t) {
  if (!identical(ka, ke)) { # common case ka != ke
    C <- F*D/Vd*(ka/(ka - ke))*(exp(-ke*t) - exp(-ka*t))
  } else {                  # equal input & output
    C <- F*D/Vd*ke*t*exp(-ke*t)
  }
  return(C)
}
AUCcalc <- function(t,C){
  linlogflag <- C[-length(C)] <= C[-1]
  AUCsegments <- ifelse(linlogflag,
                   diff(t)*(C[-1]+C[-length(C)])/2,
                   (C[-length(C)] - C[-1])*diff(t)/(log(C[-length(C)]) - log(C[-1])))
  return(sum(AUCsegments))
}

AbsorptionDF <- function(D, ka, Vd, CL,t,ratio){
  # Reference
  ke       <- CL/Vd
  C        <- C.sd(D=D, Vd=Vd, ka=ka, ke=ke, t=t)
  tmax     <- t[C == max(C)][1]
  Cmax     <- C.sd(D=D, Vd=Vd, ka=ka, ke=ke, t=tmax)
  AUC.t    <- AUCcalc(t, C)
  t.1      <- t[which(t <= tmax)]
  t.cut    <- max(t.1)
  C.1      <- C[which(t <= t.cut)]
  pAUC     <- AUCcalc(t.1, C.1)
  Cmax.AUC <- Cmax/AUC.t
 
  # Tests
  ka.t  <- ka*ratio                           # Tests' ka
  res   <- data.frame(kaR=ka, kaT_kaR=ratio, kaT=signif(ka.t, 5),
                      Cmax=NA, Cmax.r=NA, pAUC=NA, pAUC.r=NA,
                      Cmax_AUC=NA, Cmax_AUC.r=NA)
 
  for (j in seq_along(ratio)) {
    # full internal precision, 4 significant digits for output
    C.tmp    <- C.sd(D=D, Vd=Vd, ka=ka.t[j], ke=ke, t=t)
    if (!identical(ka.t[j], ke)) { # ka != ke
      tmax.tmp <- log(ka.t[j]/ke)/(ka.t[j] - ke)
    } else {                       # ka = ke
      tmax.tmp <- 1/ke
    }
    Cmax.tmp <- C.sd(D=D, Vd=Vd, ka=ka.t[j], ke=ke, t=tmax.tmp)
    res[j, "Cmax"]   <- signif(Cmax.tmp, 4)
    res[j, "Cmax.r"] <- signif(Cmax.tmp/Cmax, 4)
    AUC.t.tmp <- AUCcalc(t,C.tmp)
    t.1.tmp   <- t[which(t <= t.cut)]
    C.1.tmp   <- C.tmp[which(t <= t.cut)] # cut at tmax of R!
    pAUC.tmp  <- AUCcalc(t.1.tmp, C.1.tmp)
    res[j, "pAUC"]       <- signif(pAUC.tmp, 4)
    res[j, "pAUC.r"]     <- signif(pAUC.tmp/pAUC, 4)
    res[j, "Cmax_AUC"]   <- signif(Cmax.tmp/AUC.t.tmp, 4)
    res[j, "Cmax_AUC.r"] <- signif((Cmax.tmp/AUC.t.tmp)/Cmax.AUC, 4)
  }
  return(res)
}

SubjectsDF <- data.frame()
for(isub in 1:Nsub){
  # sampling parameters
  ka.sub       <- ka * exp(rnorm(1, sd = sqrt(ka.omega)))
  Vd.sub       <- Vd * exp(rnorm(1,sd = sqrt(Vd.omega)))
  CL.sub       <- CL * exp(rnorm(1,sd = sqrt(CL.omega)))
  DF.sub <- cbind(Subject = isub, V = Vd.sub, CL = CL.sub, AbsorptionDF(D, ka.sub, Vd.sub, CL.sub, t, ratio))
  SubjectsDF <- rbind(SubjectsDF, DF.sub)
}

SubjectsDFstack <-
  reshape(SubjectsDF[, -c(2,3,4,6,7,9,11)],
        direction = 'long', varying = 3:5, v.names = "ratio", timevar = "metric", times = names(SubjectsDF)[3:5]) # hate this one!

ggplot(SubjectsDFstack, aes(x=kaT_kaR, y=ratio, color=factor(metric)) ) +
  theme_bw() +
  geom_point(size=.3) +
  geom_smooth(method = 'loess', se = FALSE) +
  stat_density_2d(data = subset(SubjectsDFstack, metric == unique(SubjectsDFstack$metric)[1]), geom = "raster", aes(alpha = ..density..), fill = "#F8766D" , contour = FALSE) +
  stat_density_2d(data = subset(SubjectsDFstack, metric == unique(SubjectsDFstack$metric)[2]), geom = "raster", aes(alpha = ..density..), fill = "#6daaf8" , contour = FALSE) +
  stat_density_2d(data = subset(SubjectsDFstack, metric == unique(SubjectsDFstack$metric)[3]), geom = "raster", aes(alpha = ..density..), fill = "#6df876" , contour = FALSE) +
  scale_alpha(range = c(0, 0.7)) +
  scale_x_continuous(trans='log2') +
  scale_y_continuous(trans='log')


[image]

Kind regards,
Mittyri

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