Bioequivalence and Bioavailability Forum

Dear all,

maybe some of you remember this interesting scary discovery of Detlew. This week a paper was pub­lished by a German group* confirming his findings. Appetizers:

Surprisingly, when ‘scaled’ bioequivalence limits were set as bioequivalence limits, the highest re­jec­tion rate observed was at the lowest variability investigated. With CV_ANOVA of 30%, it was 7.05%, and it was still 5.39% with a variability of 40%. Therefore, taking into account a simulation error of roughly 0.5%, and the fact that our simulations are based on uncorrelated data and do not consider interindividual variabilities, one may doubt that an α-error of 5% is controlled even with the pre-set ‘scaled’ limits, at least for variabilities close to the cut-off point of CV_ANOVA of 30%.

• Table II Rejection Rate After 10000 Simulations […] and Empirical α-Error Rate at the ‘Scaled’ BE Limits […] According to EMA with Increasing Intraindividual Variability
CVANOVA [%]  N   GMR   Empirical α-error rate [%]
────────────────────────────────────────────────
    30     22  1.250         7.05 *
    35     25  1.295         5.58 *
    40     27  1.340         5.39 *
    45     27  1.386         4.25  
    50     28  1.432         3.51  
────────────────────────────────────────────────
  

(* significantly >0.05; my addition)

Try this code:

library(PowerTOST)
CV  <- seq(30, 50, 5)
res <- data.frame(CV = CV, N = c(22, 25, 27, 27, 28),
                  GMR = scABEL(CV/100)[, "upper"], pBE = NA, sig = "",
                  stringsAsFactors = FALSE)
for (j in seq_along(CV)) {
  res$pBE[j] <- round(100*power.scABEL(CV = CV[j]/100, theta0 = res$GMR[j],
                                       n = res$N[j], design = "2x3x3",
                                       nsims = 1e6), 2)
}
sig <- binom.test(0.05*1e6, 1e6, alternative = "less")$conf.int[[2]]
res$sig[res$pBE/100 > sig] <- "*"
names(res)[5] <- ""
print(res, row.names = FALSE)

Do these results look familiar?

 CV  N      GMR  pBE 
 30 22 1.250000 6.88 *
 35 25 1.294796 5.42 *
 40 27 1.340165 5.04 *
 45 27 1.385915 4.34 
 50 28 1.431910 3.32

If you are planning a study for evaluation with EMA’s ABEL-method think about it.

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• Wonnemann M, Frömke C, Koch A. Inflation of the Type I Error: Investigations on Regulatory Recommendations for Bioequivalence of Highly Variable Drugs. Pharm Res. 31 (preprint published 18 July 2014) doi:10.1007/s11095-014-1450-z.