Bioequivalence and Bioavailability Forum

Hi Titus,

❝ ❝ Do you know more about the drug than its t_max?

❝ About the Drug - Since the study is a simulation-based experiment, I developed a hypothetical drug which is expected to have more colonic absorption to support my theoretical objective.

❝ I have pasted the Log-Conc profile of the drug for your reference below.

In your original post you talked about an SR formulation. Locally applied, locally acting drugs (LALAs) are delayed release (DR). The correct model is simple (one or two compartments but with a substantial lag-time), which is not your current one.
For an example see the profile of mesalazine (scroll down to Fig. 5 because what’s given in the NDA is crap).

❝ I totally agree with you point regarding Cmax. But also I want to be realistic in PK sampling time points to clinical setting. I mean, no over-sampling. therefore, according to US FDA guidance "Bio­equivalence Studies With Pharmacokinetic End­points for Drugs Submitted Under an ANDA Guidance for Industry, 2021", I can go upto 18 time points.

Guidelines are based on science in principle. 
However, they try to cover most of the ‘common’ cases, which might not be yours. For my approach see this presentation (slides 7–9). Unfortunately, lag-times in LALAs are terribly variable and you have to take that into account (in my simulations I use a truncated normal distribution and discretize it for the sampling times). See the -script at the end.

Not a LALA but a PPI with extremely variable lag-times. Due to the acid-sensitivity of PPIs, all formulations are gastric resistant coated. Here the variability is caused by physiology (gastric motility / emptying) and is not a property of the formulation. Do you see how difficult it is to ‘catch’ C_max?

❝ In my case, I do not see flip-flop kinetics, therefore I will assume the Tmax = 8.4 h as reliable parameter and add further more (3-5) time points.

Forget what I wrote about flip-flop PK. Anyhow, do you know that \(\small{k_\text{a}\gg k_\text{e}}\) (e.g., from IV or an IR formulation)?

❝ I also would like to know, what are the criteria to choose the PK sampling time points as best as possible to capture the PK estimates well? (All I know to describe the ADE phase and at least three or more terminal elimination half-lives of the drug).

My approach (if I have some real data beforehand):

• Find a suitable PK model.
  
• Define different sampling schedules.
  
• With the parameters of the model, simulate the schedules.
  
• Inspect the variance inflation factors (the lower is better).
  
• Inspect plots of partial derivatives of parameters vs. time (optimal are sampling times close to the minima). See also this post for an example.

---

library(truncnorm)
roundClosest <- function(x, y) {     # Round x to the closest multiple of y
  return(y * round(x / y))
}
npSummary <- function(x) {           # Nonparametric summary of x
  y                <- summary(x)[-4] # remove the mean
  attr(y, "names") <- c("Min", "Q I", "Median", "Q III", "Max")
  return(y)
}
delta    <- 1                        # sampling every hour
tlag.exp <- 6                        # expected lag-time
tlag.min <- 2                        # fast gastric passage
tlag.max <- 72                       # maximum possible gastric passage
tlag.sd  <- 4                        # standard deviation (pretty large)
n        <- 1e3                      # number of simulations
set.seed(123456)                     # for reproducibility
tlag     <- rtruncnorm(n = n, a = tlag.min, b = tlag.max,
                       mean = tlag.exp, sd = tlag.sd) # continuous
tlag     <- roundClosest(tlag, delta)                 # discrete
npSummary(tlag)
hist(tlag, breaks = "FD", freq = FALSE, , xlim = c(0, npSummary(tlag)[["Max"]]),
     main = "", las = 1, xlab = expression(italic(t)[lag]))

Gives

Min    Q I Median  Q III    Max
  2      5      7      9     18