How to choose the most appropriate options to interpolate concentrations between measurements or extrapolate concentrations after the last measurement

[ChunLIU001]

Hi Bill,

I want to calculate partial AUC (e.g., AUC0-28d) by using PKNCA. I see there are 3 methods ('lin up/log down', 'lin-log', or 'linear') to interpolate the missing observations and 3 methods to extrapolate concentrations after the last measurement ('AUCinf', 'AUClast', and 'AUCall'). Is there any guidance to help me select the most appropriate method to fit my data (e.g., drug was given by a 10min iv infusion, single dose), please?

Best regards,
Chun

[billdenney]

Hi Chun,

In my experience, "lin up/log down" works best for exogenous substances (most medications) while "linear" works best for endogenous substances (proteins or other substances typically in the body).

The three different AUCs give different answers for how concentrations are extrapolated after the last observed concentration. Most often for single doses, people will calculate AUClast and AUCinf. They estimate a simpler "what concentrations did you directly observe without extrapolation" (AUClast) and "what is the estimated total exposure over all time" (AUCinf). AUCall is not used often; it occasionally is used as a substitute for AUCinf when the half-life is not estimable.

[ChunLIU001]

Hi Bill,

Many thanks for your prompt reply! Yes, the logarithmic method fits my data well at the eliminating phase. I noticed that the default option "lin up/log down" doesn't consider Tmax while some commercial software like Winnonlin uses a different approach before or after Tmax. I wonder in which case you would suggest "lin up/log down" and in which case you would suggest "lin-log", please?

[billdenney]

I don't have access to WinNonlin, so I don't know its defaults. I do know that it implements at least the same three interpolation methods. (There could be others that I don't know.)

"lin-log" does linear interpolation before Tmax and logarithmic after. So, if that is your preference, you can use it. In my own work, I don't use "lin-log" because it makes assumptions that I don't prefer. (I implemented "lin-log" for completeness since some users requested it and other software uses it.) "lin up/log down" assumes that when concentrations are increasing between two measures the best approximation is a line while when concentrations are decreasing the best approximation is first-order exponential elimination. In my opinion, in cases when the absorption profile is unclear or variable (not a simple, smooth first-order absorption), I don't know what the absorption would look like, and more often in my experience logarithmic interpolation while increasing after observed Tmax will under-estimate the exposure.

Several years ago (and very briefly just now), I looked for references giving rationale for choosing one method over the other, and I did not find an paper supporting the rationale for using "lin-log". If you know of one, I'd love to read it.

Here is an example of what could be a more challenging dataset for lin-log.

library(ggplot2)

d <- data.frame(conc = c(0, 1, 2, 4, 2, 3, 2, 1, 0.5, 0), time = c(0, 1, 2, 3, 4, 6, 8, 12, 24, 48))

ggplot(d, aes(x = time, y = conc)) +
  geom_line() +
  geom_point()

[ChunLIU001]

I don't see any regulatory recommendations either. I found a study randomly that calculated AUC0-28d with very bumpy data by using WinNonlin (https://pubmed.ncbi.nlm.nih.gov/36794354/). In the "Method-Noncompartmental analyses of pharmacokinetics" you can see that the logarithmic interpolation method was used to interpolate the concentration of day 28 (a timepoint after Tmax) without considering the trends of two adjacent observation points. But yes I agree as you said this may be a user‘s preference instead of a recommended option.

I would highly appreciate it if you could send me some regulatory recommendations (or anything you found) to support the rationale of using "lin-up/log down" method. (BTW, I have a scenario like your example)

[billdenney]

With a quick read of the paper you linked, I think that they are just referring to interpolation during or after the last interval which could either be "lin up/log down" or "lin-log".

I don't know of regulations requiring one method or another. Sometimes, people have cited older guidances that indicate linear trapezoidal is required, but I don't think that they apply anymore.

[ChunLIU001]

Thanks Bill!