## Exclusion for the FDA? [Regulatives / Guidelines]

Hi Sereng,

❝ […] if […] one or more subjects contributes a large extrapolated AUC (>20%) in a BE study, how should we deal with it?

Since you posted in the -category: Contrary to the EMA* (and most other jurisdictions), in none of the FDA’s guidances a ‘rule’ like AUC0–t ≥ 80% of AUC0– is mentioned. Only that

[…] sampling should continue for at least three or more terminal elimination half-lives of the drug.
(e.g., ANDA draft, August 2021)

If you decide to follow the ‘80% rule’, state in the protocol that the respective subject(s) will be excluded from the comparison of AUCs but kept for the comparison of Cmax. Since Cmax is in general more variable than the AUCs, likely you based your sample size on it. Hence, excluding subjects from the comparison of AUCs is expected to have a limited effect on power.

An example for a 2×2×2 design, target power 80%, different CVs (Cmax > AUC0– > AUC0–t) and T/R-ratios in :

library(PowerTOST) metrics <- c("Cmax", "AUCt", "AUCinf") CV      <- c(0.25, 0.19, 0.20) theta0  <- c(0.95, 1.04, 1.06) x       <- data.frame(metric = metrics, CV = CV, theta0 = theta0,                       n = NA_integer_, power = NA_real_) # estimate sample size for all metrics for (j in seq_along(metrics)) {   x[j, 4:5] <- sampleN.TOST(CV = CV[j], theta0 = theta0[j], print = FALSE)[7:8] } # the nasty one txt     <- paste0("Sample size based on ", x$metric[x$n == max(x$n)], ".") # the easy ones (not leading the sample size) easy <- data.frame(metric = x$metric[!x$n == max(x$n)],                       CV = x$CV[!x$n == max(x$n)], theta0 = x$theta0[!x$n == max(x$n)]) # power for the required sample size for (j in 1:nrow(easy)) {   easy$power[j] <- power.TOST(CV = easy$CV[j], theta0 = easy$theta0[j], n = max(x$n)) } txt <- paste0(txt,               sprintf("\nPower for %6s with n = %.0f: %.7f",                       easy$metric[1], max(x$n), easy$power[1]), sprintf("\nPower for %6s with n = %.0f: %.7f", easy$metric[2], max(x$n), easy$power[2]),               "\n\n") # assess the impact on power if subjects are excluded y       <- data.frame(metric = easy$metric[1], n = max(x$n):min(x$n)) for (j in 1:nrow(y)) { y$power[j] <- suppressMessages(                   power.TOST(CV = easy$CV[1], theta0 = easy$theta0[1], n = y$n[j])) } z <- data.frame(metric =easy$metric[2], n = max(x$n):min(x$n)) for (j in 1:nrow(z)) {   z$power[j] <- suppressMessages( power.TOST(CV = easy$CV[2], theta0 = easy$theta0[2], n = y$n[j])) } res     <- merge(y, z, by = "n", all = TRUE) res     <- res[with(res, order(-n)), ] names(res)[2:5] <- c(rep(c("metric", "power"), 2)) # the EMA’s 20% limit triggering a ‘discussion’ res$EMA.warning <- 1 - res$n / max(res\$n) > 0.2 print(x, row.names = FALSE); cat(txt); print(res, row.names = FALSE)  metric   CV theta0  n     power    Cmax 0.25   0.95 28 0.8074395    AUCt 0.19   1.04 16 0.8184951  AUCinf 0.20   1.06 20 0.8086483 Sample size based on Cmax. Power for   AUCt with n = 28: 0.9717571 Power for AUCinf with n = 28: 0.9171503   n metric     power metric     power EMA.warning  28   AUCt 0.9717571 AUCinf 0.9171503       FALSE  27   AUCt 0.9667985 AUCinf 0.9075365       FALSE  26   AUCt 0.9614130 AUCinf 0.8976208       FALSE  25   AUCt 0.9546702 AUCinf 0.8858332       FALSE  24   AUCt 0.9473859 AUCinf 0.8737402       FALSE  23   AUCt 0.9382131 AUCinf 0.8592798       FALSE  22   AUCt 0.9283563 AUCinf 0.8445203        TRUE  21   AUCt 0.9158496 AUCinf 0.8267281        TRUE  20   AUCt 0.9024811 AUCinf 0.8086483        TRUE  19   AUCt 0.8853501 AUCinf 0.7866063        TRUE  18   AUCt 0.8671347 AUCinf 0.7642807        TRUE  17   AUCt 0.8434943 AUCinf 0.7366346        TRUE  16   AUCt 0.8184951 AUCinf 0.7086779        TRUE

That means, you can exclude up to twelve subjects from the comparison of AUC0–t and up to eight from the comparison of AUC0– and still have > 80% power.

• BE Guideline (2010): AUC(0–t) should cover at least 80% of AUC(0–∞). Subjects should not be excluded from the statistical analysis if AUC(0–t) covers less than 80% of AUC(0–∞), but if the percentage is less than 80% in more than 20% of the observations then the validity of the study may need to be discussed.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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