EMA: Waiving MD study [Regulatives / Guidelines]

posted by Helmut Homepage – Vienna, Austria, 2020-09-09 16:21 (504 d 05:52 ago) – Posting: # 21912
Views: 2,909

Dear all,

at the end an [image] script to play with.

For any elimination half life longer than ~7 hours and an intended dosing interval of 24 hours it will be impossible to get the MD study waived. Red are formulations with flip-flop PK (kakel).

last <- 72
ke   <- log(2)/7
tlag <- 0


[image]


If the half life is short (say, 3 hours) you don’t have to dive deep into flip-flop PK and may succeed. However, such a limited extension might not match your development target.

last <- 36
ke   <- log(2)/3
tlag <- 1


[image]




C.t <- function(f, D, V, ka, ke, t, tlag) { # 1-compartment
  if (any(c(length(f) > 1, length(D) > 1, length(V) > 1,
            length(ka) > 1, length(ke) > 1)))
    stop("f, D, V, ka, ke have to be scalars.")
  if (f <= 0 | f > 1) stop("f has to be positive <= 1.")
  if (any(c(D <= 0, V <= 0, ka <= 0, ke <= 0)))
    stop("D, V, ka, ke have to be positive.")
  if (missing(tlag)) tlag <- 0
  if (tlag < 0) stop("tlag has to be >= 0.")
  if (ka != ke) {
    C <- f*D*ka/(V*(ka-ke))*(exp(-ke*(t-tlag))-exp(-ka*(t-tlag)))
  } else { # flip-flop PK
    k <- ka
    C <- f*D*k*(t-tlag)/V*exp(-k*(t-tlag))
  }
  C[C < 0] <- NA # negatives due to lag-time
  return(C)
}
AUC.t <- function(C, t, tau) { # lin-up/log-down method
  t <- t[t <= tau]             # for AUC until tau
  AUC.t <- 0
  for (j in 2:length(t)) {
    if (!is.na(C[j-1])) {
      if (C[j] >= C[j-1]) { # linear-up
        AUC.t <- AUC.t+0.5*(t[j]-t[j-1])*(C[j]+C[j-1])
      } else {              # logarithmic-down
        AUC.t <- AUC.t+(t[j]-t[j-1])*(C[j]-C[j-1])/log(C[j]/C[j-1])
      }
    }
  }
  return(AUC.t)
}
AUC.i <- function(AUC.tau, C, t, last, tau) { # extrapolation
  tlast.3  <- tail(t[t <= last], 3)
  Clast.3  <- tail(C[t <= last], 3)
  Clast    <- tail(Clast.3, 1)
  Ctau     <- C[t == tau]
  mod      <- lm(log(Clast.3) ~ tlast.3)
  lambda.z <- -coef(mod)[[2]]
  if (lambda.z <= 0) stop("increasing concentrations")
  AUC.inf  <- AUC.tau+Ctau/lambda.z
  return(AUC.inf)
}
last  <- 72
tau   <- 24
f     <- 1
D     <- 100
V     <- 5
ke    <- log(2)/7       # moderate elimination half life
tlag  <- 0              # optional >= 0
forms <- 15             # no. of formulations
ka    <- log(2)/1:forms # vary absorption
t     <- seq(0, last, 0.1)
AUC.ext <- numeric()
windows(width = 6, height = 6)
op    <- par(no.readonly = TRUE)
par(mar = c(4, 4, 0.2, 0) + 0.1, family = "sans")
split.screen(c(2, 1))
screen(1)
  for (j in 1:forms) {
    C <- C.t(f, D, V, ka[j], ke, t, tlag)
    if (j == 1) {
      plot(t, C, type = "l", col = "blue", axes = FALSE,
           xlab = "time", ylab = "concentration")
      abline(v = tau, lty = 3)
      axis(1, labels = seq(0, last, 6), at = seq(0, last, 6))
      axis(2, las = 1)
    } else {
      if (ka[j] > ke) {
        lines(t, C, col = "blue")
      } else { # flip-flop
        lines(t, C, col = "red")
      }
    }
    AUC.tau    <- AUC.t(C, t, tau)
    AUC.inf    <- AUC.i(AUC.tau, C, t, last, tau)
    AUC.ext[j] <- (AUC.inf-AUC.tau)/AUC.inf
  }
  clr <- ifelse (ka/ke > 1, clr <- "blue", clr <- "red")
  par(family = "mono")
  legend("topright", title = "ka / kel", box.lty = 0,
         legend = sprintf("%.4f", ka/ke), title.col = "black",
         text.col = clr, cex = 0.75, ncol = 3); box()
screen(2)
  par(family = "sans")
  plot(ka/ke, 100*AUC.ext, ylim = c(0, max(100*AUC.ext)), log = "x",
       axes = FALSE, xlab = "ka / kel", ylab = "extrapolated AUC",
       pch = 19, col = clr)
  points(rev(ka/ke)[which(rev(AUC.ext) <= 0.1)],
         rev(100*AUC.ext)[rev(AUC.ext) <= 0.1], pch = 21, col = "#00C000",
         bg = "transparent", cex = 1.55)
  xticks <- c(axTicks(side = 1, log = TRUE), max(ka/ke))
  axis(1, at = xticks, labels = xticks)
  axis(2, las = 1, at = c(0, pretty(100*AUC.ext)),
       labels = sprintf("%.0f%%", c(0, pretty(100*AUC.ext))))
  abline(v = 1, lty = 3)  # flip-flop limit
  abline(h = 10, lty = 3) # MD waiver limit
  par(family = "mono")
  legend("topright", title = "ka / kel, extrapolated AUC", box.lty = 0,
         legend = sprintf("%.4f %.2f%%", rev(ka/ke), rev(100*AUC.ext)),
         title.col = "black", text.col = rev(clr), cex = 0.75, ncol = 3,
         bg = "white"); box()
close.screen(all = TRUE)
par(op)


Dif-tor heh smusma 🖖
Helmut Schütz
[image]

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Complete thread:

Activity
 Admin contact
21,854 posts in 4,573 threads, 1,554 registered users;
online 25 (0 registered, 25 guests [including 18 identified bots]).
Forum time: Wednesday 21:13 CET (Europe/Vienna)

The real purpose of the scientific method is to make sure
nature hasn’t misled you into thinking you know something
you actually don’t know.    Robert M. Pirsig

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5