Sereng
☆    

USA,
2022-05-12 17:17
(14 d 03:18 ago)

Posting: # 22975
Views: 240
 

 Handling large Extrapolated AUC Values [Regulatives / Guidelines]

Dear Colleagues, despite best efforts (adequate sampling duration), if you should determine that one or more subjects contributes a large extrapolated AUC (>20%) in a BE study, how should we deal with it? Regards,

Biostatistically Challenged CEO
mittyri
★★  

Russia,
2022-05-14 22:06
(11 d 22:29 ago)

@ Sereng
Posting: # 22986
Views: 204
 

 residual area < 20% for more than 80% subjects

Hi Sereng,

» despite best efforts (adequate sampling duration), if you should determine that one or more subjects contributes a large extrapolated AUC (>20%) in a BE study, how should we deal with it?

that's OK if the number of subjects with large residual area is less than 20%
Otherwise the sampling duration is not adequate or there are other issues with formulation/analyte/product

PS: above is true for EMA guide and bound jurisdictions

Kind regards,
Mittyri
Sereng
☆    

USA,
2022-05-18 05:59
(8 d 14:36 ago)

@ mittyri
Posting: # 22999
Views: 159
 

 residual area < 20% for more than 80% subjects

Many thanks!

Biostatistically Challenged CEO
Helmut
★★★
avatar
Homepage
Vienna, Austria,
2022-05-23 11:43
(3 d 08:52 ago)

@ Sereng
Posting: # 23011
Views: 115
 

 Exclusion for the FDA?

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 Regulatives / Guidelines-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 [image]:

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.

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