Bioequivalence and Bioavailability Forum

Hi BRB,

❝ How would one show that there is, "Comparable median and range for tlag" between the test and reference?

By a combination of and box plots?

❝ Non-parametric test?

Unlikely… Let’s actuate our time machine and have a look what was / is suggested for t_max and t_lag.

1. Note for Guidance (1992) III/54/89-EN
   Statistical evaluation of t_max only makes sense if there is a clinically relevant claim for rapid release or action or signs for a relation to adverse effects. The non-parametric 90% confidence interval for this measure of relative bioavailability should lie within a clinically determined range.
   
2. Note for Guidance (2001) CPMP/EWP/QWP/1401/98
   Statistical evaluation of t_max only makes sense if there is a clinically relevant claim for rapid release or action […]. The non-parametric 90% confidence interval for this mea­sure of relative bioavail­ability should lie within a clinically determined range.
   
3. IR BE-GL (2010) CPMP/EWP/QWP/1401/98 Rev. 1/ Corr **
   A statistical evaluation of t_max is not required. However, if rapid release is claimed to be clinically relevant and of importance for onset of action or is related to adverse events, there should be no apparent difference in median t_max and its variability between test and reference product.
   
4. MR BE-GL (2014) EMA/CPMP/EWP/280/96 Corr1
   For delayed and multiphasic release formulations differences in t_max is also recommended to be assessed, especially for products where a fast onset of action is important. A formal statistical evaluation of t_max is not required. However, there should be no apparent difference in median t_max and its range between test and reference product.
   
5. Dimethyl fumarate gastro-resistant capsules 120 mg and 240 mg product-specific BE guidance (draft 2017) EMA/CHMP/421315/2017
   Comparable median and range for t_lag and t_max.

The EMA is allergic to non-parametrics. In #3 (though in the section about log-transformation and ANOVA) we find: A non-parametric analysis is not acceptable. t_lag is not mentioned in #1–#4.
For my current practice see this post and why assessing the range is crazy, this one. When it comes to t_lag I hope that this PK metric will be dropped in the final version of the dimethyl fumarate guidance.

Try this R-code to see how strangely the difference in ranges (of T and R) might behave:

t <- c(0.5,   0.6667, 0.8333, 1,    1.3333, 1.6667, 2)
p <- c(0.025, 0.1,    0.15,   0.45, 0.15,   0.1,    0.025)
n <- 24
nsims <- 1e4 # Number of bootstrap samples
set.seed(1234567)
res <- data.frame(sim=1:nsims, med.T=NA, med.R=NA, delta.med=NA,
                  rng.T=NA, rng.R=NA, delta.rng=NA,
                  iqr.T=NA, iqr.R=NA, delta.iqr=NA)
for (j in 1:nsims) {
  T <- sample(t, size=n, replace=TRUE, prob=p)
  R <- sample(t, size=n, replace=TRUE, prob=p)
  res$med.T[j] <- median(T)
  res$med.R[j] <- median(R)
  res$rng.T[j] <- diff(range(T)) # span
  res$rng.R[j] <- diff(range(R)) # span
  res$iqr.T[j] <- IQR(T)
  res$iqr.R[j] <- IQR(R)
}
res$delta.med <- res$med.T - res$med.R
res$delta.rng <- res$rng.T - res$rng.R
res$delta.iqr <- res$iqr.T - res$iqr.R
dev.new(record=TRUE)
op <- par(ask=TRUE)
# common axes for all histograms
xlim <- c(-1,1)*max(abs(range(res$delta.med, res$delta.rng, res$delta.iqr)))
ylim <- c(0, max(hist(res$delta.med, plot=FALSE)$density))
hist(res$delta.med, col="bisque", freq=FALSE, xlim=xlim, ylim=ylim,
     xlab="\u2206 of medians", main="", las=1)
box()
hist(res$delta.iqr, col="bisque", freq=FALSE, xlim=xlim, ylim=ylim,
     xlab="\u2206 of IQRs", main="", las=1)
box()
hist(res$delta.rng, col="bisque", freq=FALSE, xlim=xlim, ylim=ylim,
     xlab="\u2206 of ranges", main="", las=1)
box()
par(op)