Bioequivalence and Bioavailability Forum

❝ My gut feeling is that they want nonparametrics for the Tmax comparability part (yes I am aware of the sentence).

❝ should we submit a dataset to EMA and suggest them to publish it along with a description (numerical example) of how exactly they wish to derive the decision?

❝ When FDA indicated that they were going in the direction of in vitro popBE for inhalanda and nasal sprays they published a dataset and showed exactly how to process the data to figure out the pass / fail criterion that satisfies the regulator.

❝ If EMA would do the same here we'd have all doubt eliminated.

• Rounded regulatory constant k = 0.760 and upper cap at CV_wR = 50% in reference-scaling,
  
• sequence(stage) term in TSDs,
  
• ‘substantial’ accumulation if AUC_0–τ > 90% of AUC_0–∞,
  
• for partial AUCs default cut-off time τ/2,
  
• comparison of C_ss,min for originators but of C_ss,τ for generics,
  
• …

❝ I think we need to know exactly:

❝ 1. Do we use nonparametrics or not?

❝ 2. Do we use logs or not?

❝ 3. Is the decision of 20% comparability based on a confidence interval or on something else?

❝ 3a. If there is a CI involved, is it a 90% or 95% CI or something else?

❝ 4. Are we primarily working on ratio or on a difference?

❝ 5. Is the bootstrap involved?

❝ 6. How should we treat datasets from parallel trials, and how should we treat data from XO (i.e. how to handle considerations of paired and non-paired options)?

❝ My gut feeling is that they want nonparametrics for the Tmax comparability part (yes I am aware of the sentence).

❝

Actually, perhaps they just want the decision taken on basis of the estimates of medians and ranges from min to max?

❝ If we submit a dataset, let us make sure we submit one with ties (the one I pasted above had none).

     median        re-sampled    med. diff (%)      pass.pct     
 Min.   :1.000   Min.   :1.000   Min.   :-50.000   Mode :logical 
 1st Qu.:1.375   1st Qu.:1.375   1st Qu.:-15.385   FALSE:34887   
 Median :1.500   Median :1.500   Median :  0.000   TRUE :65113   
 3rd Qu.:1.750   3rd Qu.:1.750   3rd Qu.: 18.182                 
 Max.   :2.500   Max.   :2.500   Max.   :100.000


Dashed lines 2.5 and 97.5 percentiles

R <- c(1.25, 2.00, 1.00, 1.25, 2.50, 1.25, 1.50, 2.25,
       1.00, 1.25, 1.50, 1.25, 2.25, 1.75, 2.50, 2.25)

❝ 2. Do we use logs or not?

The concentrations rise more steeply before the peak than they decline following the true maximum response. Consequently, it is more likely that large observed concentrations occur after than before the true peak time (\(\small{T_\textrm{max}^\circ}\)).

Sample size based on conventional PK metric
  BE limits    : 80.00% to 125.00%
  theta0       : 95% (assumed T/R ratio)
  CV           : 20% (assumed)
  Power        : 90% (target)
  n            : 26  (estimated)
  Power        : 92% (achieved)
  Sampling     : every 15 minutes
  mu.tmax (R)  : 1.50 h    (assumed for R)
  CV of tmax   : 50%       (assumed)
  shift        : -15.0 min (assumed for T)
  spread       : ±30.0 min
Not equivalent if medians differ by more than 20%
{-18 min, +18 min}
  Empiric power: 76.00%

  n            : 78  (specified)
  Power        : 100%
Not equivalent if medians differ by more than 20%
{-18 min, +18 min}
  Empiric power: 90.71%

• Tóthfálusi L, Endrényi L. Estimation of C_max and T_max in Populations After Single and Multiple Drug Ad­mi­ni­stra­tion. J Pharma­co­kin Pharma­codyn. 2003; 30(5): 363–85. doi:10.1023/b:jopa.0000008159.97748.09.

❝ 2. Do we use logs or not?

roundClosest <- function(x, y) {
  res           <- y * round(x / y)
  res[res <= 0] <- y # Force negatives | 0 to the 1st interval
  return(res)
}
HL <- function(x, na.action = na.omit) {
  x   <- na.action(x)
  y   <- outer(x, x, "+")
  res <- median(y[row(y) >= col(y)]) / 2
  return(res)
}
n       <- 500
mu.tmax <- 1.5 # hours
CV.tmax <- 0.5
shift   <- -15 # minutes
spread  <- 30  # --"--
smpl    <- 10  # --"--
# Sample tmax of R from lognormal distribution
# parameterized for the median
R       <- rlnorm(n = n, meanlog = log(mu.tmax),
                         sdlog = sqrt(log(CV.tmax^2 + 1)))
# Introduce shift in location of T
shifts  <- runif(n = n, min = shift / 60 - spread / 60, # can be negative!
                        max = shift / 60 + spread / 60)
T       <- R + shifts
# Discretization by the sampling interval 'smpl'
R       <- roundClosest(R, smpl / 60)
T       <- roundClosest(T, smpl / 60)
res     <- data.frame(min    = rep(NA_real_, 3),
                      median = NA_real_,
                      HL     = NA_real_,
                      max    = NA_real_)
row.names(res)    <- c("R", "T", "T-R")
res[1, c(1:2, 4)] <- quantile(R, probs = c(0, 0.5, 1))
res[1, 3]         <- HL(R)
res[2, c(1:2, 4)] <- quantile(T, probs = c(0, 0.5, 1))
res[2, 3]         <- HL(T)
res[3, 2:3]       <- res[1, 2:3] - res[2, 2:3]
print(round(res, 5))

        min  median      HL     max
R   0.33333 1.50000 1.58333 7.00000
T   0.16667 1.33333 1.33333 6.66667
T-R      NA 0.16667 0.25000      NA