Bioequivalence and Bioavailability Forum

Hello Farmacevt,

❝ Please advise what if the Lower limit of quantification for some of the subjects in the BE study is greater than 5% of Cmax (not for the pre-dose concentrations).

There should be a rule about it in your SOPs or in your protocol. Perhaps you are asking because that isn't the case?

For EU: My experience is that it happens now and then and some assessors are very vigilant about it, while others don't give two tiny mouse droppings.
At one extreme you may need to eliminate those subject periods that are affected, which may mean a complete loss of a subject for stats if this is a 222BE design, since only subjects who contribute with T and R should be in the stats analysis.
At the other extreme, no need for any action. You may land anywhere in between the two. It depends and it does not only depend on the RMS but also the actual assessor within the agency at the RMS.

If you have many such cases you can get flagged for inspection. It would be tremendously bad planning if your study is deemed futile due to this matter.

If you want a smooth process, don't submit with NL or DE as RMS. Submit in SE or DK or AT, if you can get a slot.

Dear Farmacevt,

❝ Please advise what if the Lower limit of quantification for some of the subjects in the BE study is greater than 5% of Cmax (not for the pre-dose concentrations).

There is always possibility that few subjects may have LLOQ of more than 5% Cmax as during the method development, the assumed Cmax is higher(compared to lower Cmax in observed) in current case. If the subjects are more than 20% having 1st time point of more than 5% Cmax, then there could be an issue with your CC range, but if less than 20% – it is generally good to submit the dossier.
To prevent the scenario in future, kindly take a range of Cmax for consideration of CC range. The lower Cmax can be considered for 5 or 6 half life consideration of LLOQ and upper Cmax for ULOQ consideration.
Regards,
dshah

Hi Farmacevt,

❝ Please advise what if the Lower limit of quantification for some of the subjects in the BE study is greater than 5% of Cmax (not for the pre-dose concentrations).

I agree with ElMaestro and dshah.

The LLOQ is fixed in a validated method based on an assumed C_max. It is not a good idea rely on a mean C_max (say, from the literature). You have to take the within- and between-subject variability into account. The former is esp. important for Highly Variable Drugs / Drug Products and the latter for drugs with polymorphic metabolism. For these drugs \(\small{CV_\textrm{inter}\gg CV_\textrm{intra}}\).
A stupid example (normal distribution for simplicity) of C_max with a mean of 100 and a standard deviation of 20. You plan the study with the Babylonian number of 24 subjects. If you set the LLOQ to 5 and, since \(\small{\mu\pm\sigma}\) covers \(\small{\approx 68.27\%}\) you can expect at least three subjects (\(\small{1-0.6827/2\times 24\approx 3.81}\)) with a concentration > LLOQ. Hence, aim lower.

However, concentrations follow a lognormal distribution. Therefore, it is more likely to see higher values than lower ones. A small simulation:

set.seed(123456)
n        <- 24
Cmax     <- setNames(c(100, 0.2), c("mu", "CV"))
pct.Cmax <- 5
LLOQ     <- pct.Cmax * Cmax[["mu"]] / 100
nsims    <- 1E6L
Cmax.sim <- rlnorm(n = nsims,
                   meanlog = log(Cmax[["mu"]]) - 0.5 * log(Cmax[["CV"]]^2 + 1),
                   sdlog = sqrt(log(Cmax[["CV"]]^2 + 1)))
pd       <- 0.05 * Cmax.sim
p.above  <- sum(pd > LLOQ) / nsims
cat(paste0("Assumed Cmax = ", Cmax[["mu"]], " (CV = ",
    sprintf("%.f%%),", 100 * Cmax[["CV"]])),
    "LLOQ set to", sprintf("%.f%%", pct.Cmax), "of Cmax.",
    paste0("\n", prettyNum(nsims, format = "i", big.mark = ",")),
    "simulations,", sprintf("mean of Cmax = %.2f (CV = %.2f%%).",
    mean(Cmax.sim), 100 * sd(Cmax.sim) / mean(Cmax.sim)),
    "\nProbability that pre-dose concentrations are > LLOQ =",
    sprintf("%.1f%%.", 100 * p.above),
    "\nIn a study with", n, "subjects expected for at least",
    sprintf("%i subjects.", floor(p.above * n)), "\n")

Assumed Cmax = 100 (CV = 20%), LLOQ set to 5% of Cmax.
1,000,000 simulations, mean of Cmax = 99.99 (CV = 20.00%).
Probability that pre-dose concentrations are > LLOQ = 46.0%.
In a study with 24 subjects expected for at least 11 subjects.