## LLOQ based on ‘worst case’ Cmax [Bioanalytics]

❝ 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.

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

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

Science Quotes

### Complete thread:

- Analytical range LOQ Farmacevt 2021-12-20 20:54 [Bioanalytics]
- Analytical range LOQ ElMaestro 2021-12-20 22:46
- Analytical range LOQ Farmacevt 2021-12-22 22:02

- Analytical range LOQ dshah 2021-12-21 12:03
- LLOQ based on ‘worst case’ CmaxHelmut 2021-12-21 13:31
- LLOQ based on ‘worst case’ Cmax ElMaestro 2021-12-21 15:48
- LLOQ based on ‘worst case’ Cmax Helmut 2021-12-22 23:16

- LLOQ based on ‘worst case’ Cmax ElMaestro 2021-12-21 15:48

- Analytical range LOQ ElMaestro 2021-12-20 22:46