Bioequivalence and Bioavailability Forum

Hi Mikalai,

❝ […] what regulators say on this subject? I do not remember any reflection on this matter in official documents (EMA, FDA)?

Some slides of Terry Hyslop (Director, Division of Biostatistics) of his presentation “Bioequivalence (BE) for Highly Variable Drugs” at the AAPS Workshop (New Orleans, Nov 2010) – after the progesterone guidance was published…

Aka the ‘implied limits’ (see this post and slide 23 below).




Well roared, lion! Trouble starts because we use \(s_{WR}\) instead of the unknown \(\sigma_{WR}\).
Nasty but \(s_{WR}\) is all we have.
Typo, should read
… use scaled average BE if s_WR > cutoff.




Illegible text (white with grey shadowing):
  assuming no subject-by-formulation interaction, σWT = σWR,
  true GMR = max (1.25, implied scaled BE limit)

What‽
library(PowerTOST)
swR           <- sort(c(CV2se(0.3), 0.294, seq(0.2, 0.3, 0.01)))
CVwR          <- se2CV(swR)
reg           <- reg_const("FDA")
reg$CVswitch  <- se2CV(0.294)
reg$pe_constr <- FALSE # pure RSABE (without PE constraint)
GMRs          <- data.frame(GMR       = scABEL(CV = CVwR,
                                               regulator = reg)[, "upper"],
                            GMR.Terry = exp(reg$r_const * swR))
res           <- data.frame(swR = swR, CVwR = CVwR, GMR = GMRs$GMR,
                            TIE = NA_real_, GMR.max = NA_real_,
                            TIE.Terry = NA_real_)
for (j in seq_along(swR)) {
  # Cheating: That is not implemented in the guidance!
  res$GMR.max[j]   <- max(c(1.25, GMRs$GMR.Terry[j]))
  res$TIE.Terry[j] <- power.RSABE(CV = CVwR[j], theta0 = res$GMR.max[j],
                                  design = "2x3x3", n = 36, nsims = 1e6)
  # That is correct!
  res$TIE[j]       <- power.RSABE(CV = CVwR[j], theta0 = res$GMR[j],
                                  design = "2x3x3", n = 36, nsims = 1e6)

}
reg; print(res, digits = 4, row.names = FALSE)

FDA regulatory settings
- CVswitch            = 0.3004689
- no cap on scABEL
- regulatory constant = 0.8925742
- no pe constraint
    swR   CVwR   GMR     TIE GMR.max TIE.Terry
 0.2000 0.2020 1.250 0.04988   1.250   0.04988
 0.2100 0.2123 1.250 0.04997   1.250   0.04997
 0.2200 0.2227 1.250 0.05037   1.250   0.05037
 0.2300 0.2331 1.250 0.05166   1.250   0.05166
 0.2400 0.2435 1.250 0.05460   1.250   0.05460
 0.2500 0.2540 1.250 0.06027   1.250   0.06027
 0.2600 0.2645 1.250 0.06985   1.261   0.05152
 0.2700 0.2750 1.250 0.08389   1.273   0.04749
 0.2800 0.2856 1.250 0.10211   1.284   0.04621
 0.2900 0.2962 1.250 0.12375   1.295   0.04612
 0.2936 0.3000 1.250 0.13233   1.300   0.04621
 0.2940 0.3005 1.250 0.13341   1.300   0.04621
 0.3000 0.3069 1.307 0.04628   1.307   0.04628

Check:

library(PowerTOST)
res        <- data.frame(method = c("ABE", "RSABE"), TIE = NA)
res$TIE[1] <- power.TOST(CV = 0.3, n = 36, theta0 = 1.25,
                         design ="2x3x3")
res$TIE[2] <- power.RSABE(CV = 0.3, n = 36, theta0 = 1.25,
                          design ="2x3x3", nsims = 1e6)
res$TIE    <- signif(res$TIE, 4)
print(res, row.names = FALSE)

# method    TIE
#    ABE 0.0500
#  RSABE 0.1323

Hence, the FDA was well aware of the inflated type I error and decided to ignore it.