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

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 Cmax. It is not a good idea rely on a mean Cmax (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 Cmax 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 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes Ing. Helmut Schütz
{"ft_lang_label":"__label__en","ft_lang_prob":0.7934248,"math_prob":0.9952437,"size":2952,"snap":"2022-27-2022-33","text_gpt3_token_len":992,"char_repetition_ratio":0.11261872,"word_repetition_ratio":0.07236842,"special_character_ratio":0.36246613,"punctuation_ratio":0.16940789,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9969431,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-13T12:30:13Z\",\"WARC-Record-ID\":\"<urn:uuid:3f9a82d8-55f4-4be9-8fb8-a0a2b21cc0b2>\",\"Content-Length\":\"15395\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:04d80d11-caef-40cd-8898-277405b24ea1>\",\"WARC-Concurrent-To\":\"<urn:uuid:2260a2d8-d129-4583-88d0-2d7f279f060f>\",\"WARC-IP-Address\":\"104.21.27.134\",\"WARC-Target-URI\":\"https://forum.bebac.at/forum_entry.php?id=22707\",\"WARC-Payload-Digest\":\"sha1:LP6THHCGWZOAEV6JN54RBGTF5W4NCQKC\",\"WARC-Block-Digest\":\"sha1:MWZ2SXGSYGHSXNJYD7NZGXOOD5GZB5YK\",\"WARC-Identified-Payload-Type\":\"text/x-php\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571950.76_warc_CC-MAIN-20220813111851-20220813141851-00175.warc.gz\"}"}