Helmut
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2021-02-26 15:46
(153 d 17:46 ago)

Posting: # 22236
Views: 1,078
 

 Question raised by the PMDA [Design Issues]

Dear all,

I received a question from a member of the forum (he couldn’t post for some technical issues).

Parallel design, CV 36%, T/R-ratio 0.95, target power 90%, parallel design, anticipated dropout rate 10%, 20% of subjects (in each group) of Japanese origin. Easy so far.

library(PowerTOST)
balance <- function(n, groups) {
  # Round up to get balanced groups for potentially unbalanced case.
  return(as.integer(groups * (n %/% groups + as.logical(n %% groups))))
}
adjust.dropouts <- function(n, do.rate, groups = 2) {
  # To be dosed subjects which should result in n eligible subjects
  # based on the anticipated droput-rate.

  n <- as.integer(balance(n / (1 - do.rate), groups = groups))
  return(n)
}
##############
# data below #
##############

design  <- "parallel"
CV      <- 0.36 # total (pooled) for parallel design, intra-subject for Xovers
target  <- 0.90 # target (desired) power
theta0  <- 0.95 # assumed T/R-ratio
theta1  <- 0.80 # lower BE limit
theta2  <- 1.25 # upper BE limit
do.rate <- 0.10 # anticipated dropout-rate 10%
# estimate sample size & power

estim   <- sampleN.TOST(CV = CV, theta0 = theta0, theta1 = theta1,
                        theta2 = theta2, targetpower = target,
                        design = design, details = FALSE, print = FALSE)
# calculate to be dosed subjects based on the anticipated dropout-rate
n.adj   <- adjust.dropouts(estim[["Sample size"]], do.rate, 2)
# eligible subjects
n.elig  <- n.adj:estim[["Sample size"]]
info    <- paste0("\nDesign                  : ", design,
                  "\nAssumed CV              : ", sprintf("%.2g%%", 100*CV),
                  "\nAssumed T/R ratio       : ", sprintf("%.2g%%", 100*theta0),
                  "\nBE limits               : ", sprintf("%.2f\u2013%.2f%%",
                                                  100*theta1, 100*theta2),
                  "\nTarget (desired) power  : ", sprintf("%.2g%%", 100*target),
                  "\nAnticipated dropout-rate: ", sprintf("%.2g%%", 100*do.rate),
                  "\nEstimated sample size   : ", estim[["Sample size"]],
                  " (", estim[["Sample size"]]/2, "/group)",
                  "\nAchieved power          : ", sprintf("%.2f%%",
                                                  100*estim[["Achieved power"]]),
                  "\nAdjusted sample size    : ", n.adj,
                  " (",  n.adj/2, "/group)", "\n\n")
# explore possible outcome for increasing number of dropouts
results <- data.frame(dosed = n.adj, eligible = n.elig,
                      dropouts = n.adj - n.elig,
                      do.pct = sprintf("%.3f%%", 100*(n.adj - n.elig)/n.adj),
                      power.pct = NA, stringsAsFactors = FALSE)
for (j in 1:nrow(results)) {
  results$power.pct[j] <- sprintf("%.2f%%", 100*(
                            suppressMessages(
                              power.TOST(CV = CV, theta0 = theta0,
                                         theta1 = theta1, theta2 = theta2,
                                         design = design,
                                         n = results$eligible[j]))))
}
cat(info); print(results, row.names = FALSE)

Gives:

Design                  : parallel
Assumed CV              : 36%
Assumed T/R ratio       : 95%
BE limits               : 80.00–125.00%
Target (desired) power  : 90%
Anticipated dropout-rate: 10%
Estimated sample size   : 144 (72/group)
Achieved power          : 90.11%
Adjusted sample size    : 160 (80/group)

 dosed eligible dropouts  do.pct power.pct
   160      160        0  0.000%    92.67%
   160      159        1  0.625%    92.53%
   160      158        2  1.250%    92.39%
   160      157        3  1.875%    92.25%
   160      156        4  2.500%    92.10%
   160      155        5  3.125%    91.95%
   160      154        6  3.750%    91.80%
   160      153        7  4.375%    91.64%
   160      152        8  5.000%    91.49%
   160      151        9  5.625%    91.32%
   160      150       10  6.250%    91.16%
   160      149       11  6.875%    90.99%
   160      148       12  7.500%    90.82%
   160      147       13  8.125%    90.65%
   160      146       14  8.750%    90.48%
   160      145       15  9.375%    90.30%
   160      144       16 10.000%    90.11%


As usual in parallel designs – if the drug is subjected to polymorphic metabolism – the study should be performed in fast/extensive metabolizers.
When the proposal was submitted to the PMDA, this question was raised:

What is probability of getting point estimate for the ratio of GeoMean in this Bioequivalence Limit for Japanese population?

At least interesting. There are other examples in the Japanese guideline where the PE within 80.00–125.00% is sufficient to demonstrate BE if the CI fails (similar dissolution, sample size ≥24 in a crossover), Hence, such a question is not unexpected.
Problematic in the Japanese population is the (age-dependent) high percentage of achlorohydric subjects. IIRC, already at an age of 20 years it is about 10% and increases to more than 80% at 60+ years. Since in a parallel design the comparison of treatments is done between groups, one could only try to get the same age-distribution in both groups. Not so important for the other subjects but for the sub-group of Japanese subjects.
Is the PMDA asking for a prospective sub-group power estimation? If yes, my attempt:

sub.group <- unique(as.data.frame(cbind(dosed    = results[, 1]*0.2,
                                        eligible = floor(results[, 2]*0.2),
                                        p        = NA)))
# with alpha = 0.5 we assess the probability that the PE lies within the BE limits
for (j in 1:nrow(sub.group)) {
  sub.group$p[j] <- suppressMessages(
                      power.TOST(alpha = 0.5, CV = CV, theta0 = theta0,
                                 theta1 = theta1, theta2 = theta2,
                                 design = design, n = sub.group$eligible[j]))
}
print(signif(sub.group, 4), row.names = FALSE)

Gives:

 dosed eligible      p
    32       32 0.9050
    32       31 0.9003
    32       30 0.8955
    32       29 0.8902
    32       28 0.8849

Hence, I guess one has not worry if (if!) the age-distribution is similar, and hence, the distribution of achlorohydric subjects across groups. Tricky: What if we face – by change – say, 2 young dropouts in one group and 2 old dropouts in the other? Can get nasty (biased T/R-ratio) if the drug exhibits pH-dependent release/absorption characteristics…

Does this make sense?

Based on the agency’s question, what do they require in such a study?
  • 90% CI within 80.00–125.00% (all subjects) and
  • additionally the PE of the Japanese sub-group within 80.00–125.00%?
The PMDA doesn’t give a damn about multiplicity issues (still recommend Add-On designs with an unadjusted α and the approach of assessing the PE if the CI fails inflates the Type I Error as well). Therefore, I guess they don’t care.

Dif-tor heh smusma 🖖
Helmut Schütz
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The quality of responses received is directly proportional to the quality of the question asked. 🚮
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Ben
★    

2021-03-19 15:47
(132 d 17:45 ago)

@ Helmut
Posting: # 22275
Views: 573
 

 Question raised by the PMDA

Hi Helmut

» Based on the agency’s question, what do they require in such a study?
  • 90% CI within 80.00–125.00% (all subjects) and
    »
  • additionally the PE of the Japanese sub-group within 80.00–125.00%?

This is what came to my mind.

» Problematic in the Japanese population is the (age-dependent) high percentage of achlorohydric subjects. IIRC, already at an age of 20 years it is about 20% and increases to more than 80% at 60 years.

Oh, this is interesting. I was not aware of this phenomenon. Do you have a reference and/or an explanation why this is the case?


Best regards,
Ben.
Helmut
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Vienna, Austria,
2021-03-19 18:06
(132 d 15:26 ago)

@ Ben
Posting: # 22276
Views: 573
 

 Question raised by the PMDA

Hi Ben,

» » [:blahblah:]»
» This is what came to my mind.

THX for the second opinion.

» » Problematic in the Japanese population is the (age-dependent) high percentage of achlorohydric subjects. […]
» Oh, this is interesting. I was not aware of this phenomenon. Do you have a reference …

Mentioned at various conferences. Even by speakers of the Japanese agency. I’m a little bit stressed at the moment – maybe I can dig out some handouts. I’m sure you find sumfink im Zwischennetz.
This story is the reason why the Japanese agency does not accept BCS-based biowaivers. They think that the concept with three (sometimes four) pH-values is not suitable for them.
I was surprised when I heard for the first time that the ICH will come up with a guideline. Japan is a founding member of the ICH… In the meantime the GL is final.
Of course you find:

1.2. Scope
BCS-based biowaivers may be used to substantiate in vivo bioequivalence. Examples include comparison between products used during clinical development through commercialization, post-approval changes, and applications for generic drug products in accordance with regional regulations.

(my emphasis)

End of the story.

» … and/or an explanation why this is the case?

Genetics, Helicobacter pylori?

Morihara M, Aoyagi N, Kaniwa N, Kojima S, Ogata H. Assessment of Gastric Acidity of Japanese Subjects over the Last 15 Years. Biol. Pharm. Bull. 2001; 24(3): 313—5. doi:10.1248/bpb.24.313. [image] Open access.

»[…] bioavailability and bioequivalence studies should be performed taking into consideration the effects of gastric acidity on in vivo performance of drug products.«


Dif-tor heh smusma 🖖
Helmut Schütz
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The quality of responses received is directly proportional to the quality of the question asked. 🚮
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