Bioequivalence and Bioavailability Forum

Dear all,

I stumbled across this old post. History (about exclusion of low profiles of gastric-resistant formulations):

1. Q&A-document Rev. 12 (25 June 2015); removed in Rev. 13.
   • […] concentration profiles (either non-existing or extremely delayed) can be obtained. […] only under the conditions that sampling times are designed to identify very delayed absorption and that the incidence of this outlier behaviour is observed with a comparable frequency in both, test and reference products, these incomplete profiles can be excluded from statistical analysis provided that it has been considered in the study protocol.
2. MR-GL, Draft (21 February 2013)
   • Gastric emptying of single unit dosage forms that do not disintegrate in the stomach (e.g. enteric coated tablets) may be prolonged and highly erratic. The consequences of this effect on the enteric coating of delayed release formulations are largely unpredictable. If the active substance release occurs prior to stomach emptying degradation of the active substance can result and non-existing concentration profiles can be obtained. If the incidence of this outlier behaviour is observed with a comparable frequency in both, test and reference product, data of a period with non-existing profile can be excluded from statistical analysis provided that it has been pre-specified in the study protocol.
3. MR-GL, Final (20 November 2014)
   • Gastric emptying of modified release dosage forms that do not disintegrate in the stomach (e.g. enteric coated tablets) may be prolonged and highly erratic. The consequences of this effect on the enteric coating of delayed release formulations are largely unpredictable and can result in non-existing or aberrant concentration profiles. If the incidence of this outlier behaviour is observed with a comparable frequency (e.g. the number of cases is not numerically higher in the test product) in both, test and reference product, data of a period with non-existing or aberrant profile can be excluded from statistical analysis provided that it has been pre-specified in the study protocol.

At the meeting in Bonn (June 2013; between #2 and #3) I presented the example in the post linked above, which the PKWP did not like at all. Am I guilty for the red text? I don’t believe that the comments on the draft will ever be published (though promised “within the next week” on 30 April 2015…).

Try this one (64 subjects, 5% outliers after R and exactly one more after T):

n        <- 64        # sample size
pct      <- 5         # percent of outliers of R
alpha    <- 0.05      # significance level
alt      <- "greater" # any of: "greater", "two.sided", "less"
##############################################################
R        <- as.integer(n*pct/100)
T        <- R + 1     # exactly one more
TR       <- T/R       # ratio of T/R
Ha       <- alt
comp     <- "than 1"
outliers <- matrix(c(T, n-T, R, n-R), nrow=2,
                   dimnames=list(Guess=c("Test", "Reference"),
                                 Truth=c("Test", "Reference")))
FT       <- fisher.test(outliers, alternative=alt, conf.level=1-alpha)
txt      <- ";\nalternative hypothesis: true odds ratio is"
txt      <- paste(txt, Ha, comp)
if (alt == "greater") {
  test <- "\np (T > R)"
  conf <- sprintf("(%s %.5g%% %s %.5g)", "lower", 100*(1-alpha), "CI:",
                                         FT$conf.int[1])
}
if (alt == "two.sided") {
  test <- "\np (T = R)"
  Ha   <- "not equal"
  comp <- "equal to 1"
  CI   <- c(FT$conf.int[1], FT$conf.int[2])
  conf <- sprintf("(%g%% %s %.5g, %.5g)", 100*(1-alpha), "CI:",
                                          FT$conf.int[1], FT$conf.int[2])
}
if (alt == "less") {
  test="\np (T < R)"
  conf <- sprintf("(%s %g%% %s %.5g)", "upper", 100*(1-alpha), "CI:",
                                       FT$conf.int[2])
}
txt      <- paste(txt, "\nOdds ratio   :", sprintf("%.5g", FT$estimate), conf)
sig      <- "significantly different"
if (FT$p.value >= alpha) sig <- paste("not", sig)
cat(sprintf("%s %i %s %s %i (%.2f%%), %s %i (%.2f%%)%s%.4f",
            "\nSample size  :", n,
            "\nOutliers     :",
            "T =", T, 100*T/n,
            "R =", R, 100*R/n,
            "\nOutlier-ratio: ", TR),
    sprintf("%s%s%s%s%s %.4g (%s)%s",
            "\n", FT$method, txt, test, "    :",
            FT$p.value, sig, "\n\n"))

# Sample size  : 64
# Outliers     : T = 4 (6.25%), R = 3 (4.69%)
# Outlier-ratio: 1.3333
# Fisher's Exact Test for Count Data;
# alternative hypothesis: true odds ratio is greater than 1
# Odds ratio   : 1.3523 (lower 95% CI: 0.28317)
# p (T > R)    : 0.5 (not significantly different)

Splendid. A p-value of 0.5. Try to increase the sample size and/or lower the percentage of outliers. I love n <- 120 and pct <- 0.2. Zero outliers after R and one after T in a study with 120 subjects. Is this pure chance? Guess. Are we allowed to exclude the single outlier? According to the EMA’s eternal wisdom: No.
Before the final MR-GL I would have thought that „comparable frequency” calls for a two-sided test.

# Sample size  : 64
# Outliers     : T = 4 (6.25%), R = 3 (4.69%)
# Outlier-ratio: 1.3333
# Fisher's Exact Test for Count Data;
# alternative hypothesis: true odds ratio is not equal equal to 1
# Odds ratio   : 1.3523 (95% CI: 0.2187, 9.623)
# p (T = R)    : 1 (not significantly different)

Oh no!

I can’t follow the argument that the reference has a documented efficacy/safety record whereas the test has not. Essentially T and R should be dealt with equally. The BE-GL:

The data from all treated subjects should be treated equally.

The FDA states somewhere nicely (can’t find it – changed the structure of the website again) that bioequivalence is bijective, i.e., the test of T vs. R gives exactly the same result as the test of R vs. T. If we follow the EMA’s logic above, this is no more the case.

OK, we lost our virginity already to reference-scaling. Only if CV_wT = CV_wR we would arrive at the same conclusion. I know, I know, the reference is safe and efficacious, . But does that represent reality? Sometimes a patient starts with a generic (prescribed by a general practitioner) and when hospitalized is switched to the originator. Common practice. What if CV_wR > CV_wT?