Bioequivalence and Bioavailability Forum

Dear Srinetram
Because of the complicated regulatory expectations, the features of the required sample sizes are also complicated. When the true GMR = 1.0 then, without additional constraints, the sample size is independent of the intrasubject variation. When the true GMR is increased or decreased from 1.0 then the required sample sizes rise at above but close to 30% variation. An additional regulatory constraint on the point estimate of GMR and a cap on the use of expanding limits further increase the required sample size at high variations. Fewer subjects are required by the FDA than by the EMA procedures. For further Information please refer to the article of the two Laszlos

L Tóthfalusi and L Endrenyi
Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs
J Pharm Pharmaceut Sci 15(1), 73 – 84 (2011)
http://ejournals.library.ualberta.ca/index.php/JPPS/article/download/11612/9489

I hope this helps.
Kind regards
Dr_Dan

Dear Srinetram,

in addition to Dan I recommend you the R-package PowerTOST which contains the functions sampleN.scABEL() and sampleN.RSABE() which allows you the sample size estimation for the EMA or FDA recommended methods with arbitrary anticipated CV's and point estimators, aka GMR's.

You will find that your expectation "EMA method requires higher sample size than FDA method" is fulfilled.

But your explanation " ... one have to meet the 95% Upper confidence interval ..." is at least somewhat vague or false if you mean "as compared to the usual 90% confidence intervals".
The reason behind is that the EMA method is more stringent then the FDA. This is best explained by the "implied BE limits". Read Helmut's excellent lectures about sample size planning to get further insight.

Hi Srinetram,

❝ Study meant for EMEA will need higher number of volunteers…

Since 2005 EMEA is called EMA. You are right about the sample sizes. However, your reasons are wrong (see Detlew’s post). Example: T/R 0.90 (suggested by the two Lászlós), 80% power; designs (1) RTRT|TRTR, (2) RTR|TRT, (3) TRR|RRT|RTR. R-code at the end.

CV%  design  FDA  EMA
40     (1)   24   30
       (2)   38   46
       (3)   33   42
50     (1)   22   28
       (2)   34   42
       (3)   30   39
60     (1)   24   32
       (2)   36   48
       (3)   33   48

• Sample sizes for the EMA are always higher than the ones for the FDA.
  
• Sample sizes show a minimum at ~50% CV_wR. At higher CVs the restriction on the PE cuts in.
  
• The increase is more pronounced for the EMA because you are not allowed to scale the acceptance range to more than to 69.84–143.19% if CV_wR >50%.

---

library(PowerTOST)
theta0 <- 0.90
target <- 0.80
CVwR   <- c(30, 40, 50, 60, 100)
design <- c("2x2x4", "2x2x3", "2x3x3")
expl   <- c("2-seq. 4-per. (full)",
            "2-seq. 3-per. (full)",
            "3-seq. 3-per. (partial)")
rows   <- length(CVwR)*length(design)
res    <- data.frame(CV=rep(CVwR, each=length(design)),
                     design=rep(design, length(CVwR)),
                     explanation=rep(expl, length(CVwR)),
                     n.FDA=integer(rows), pwr.FDA=numeric(rows),
                     n.EMA=integer(rows), pwr.EMA=numeric(rows),
                     stringsAsFactors=FALSE)
i      <- 0
pb     <- txtProgressBar(min=0, max=1, char="\u2588", style=3)
for (j in seq_along(CVwR)) {
  for (k in seq_along(design)) {
    i <- i + 1
    tmp <- sampleN.RSABE(CV=res[i, "CV"]/100, theta0=theta0,
                         targetpower=target, design=res[i, "design"],
                         details=FALSE, print=FALSE)
    res[i, "n.FDA"]   <- tmp[["Sample size"]]
    res[i, "pwr.FDA"] <- round(tmp[["Achieved power"]], 4)
    tmp <-  sampleN.scABEL(CV=res[i, "CV"]/100, theta0=theta0,
                           targetpower=target, design=res[i, "design"],
                           details=FALSE, print=FALSE)
    res[i, "n.EMA"]   <- tmp[["Sample size"]]
    res[i, "pwr.EMA"] <- round(tmp[["Achieved power"]], 4)
    setTxtProgressBar(pb, i/nrow(res))
  }
} # simulating 100,000 studies in each scenario
close(pb)
names(res)[1] <- "CV(%)"
res$design[which(res$design == "2x2x4")] <- "RTRT|TRTR"
res$design[which(res$design == "2x2x3")] <- "RTR|TRT"
res$design[which(res$design == "2x3x3")] <- "TRR|RRT|RTR"
names(res)[3] <- "type of replice design"
names(res)[4] <- "FDA (n)"
names(res)[5] <- "FDA (pwr)"
names(res)[6] <- "EMA (n)"
names(res)[7] <- "EMA (pwr)"
print(res, row.names=FALSE)

Gives:

 CV(%)      design  type of replice design FDA (n) FDA (pwr) EMA (n) EMA (pwr)
    30   RTRT|TRTR    2-seq. 4-per. (full)      32    0.8167      34    0.8028
    30     RTR|TRT    2-seq. 3-per. (full)      46    0.8064      50    0.8016
    30 TRR|RRT|RTR 3-seq. 3-per. (partial)      45    0.8034      54    0.8159
    40   RTRT|TRTR    2-seq. 4-per. (full)      24    0.8052      30    0.8066
    40     RTR|TRT    2-seq. 3-per. (full)      38    0.8124      46    0.8073
    40 TRR|RRT|RTR 3-seq. 3-per. (partial)      33    0.8084      42    0.8006
    50   RTRT|TRTR    2-seq. 4-per. (full)      22    0.8027      28    0.8143
    50     RTR|TRT    2-seq. 3-per. (full)      34    0.8020      42    0.8035
    50 TRR|RRT|RTR 3-seq. 3-per. (partial)      30    0.8023      39    0.8076
    60   RTRT|TRTR    2-seq. 4-per. (full)      24    0.8195      32    0.8101
    60     RTR|TRT    2-seq. 3-per. (full)      36    0.8111      48    0.8044
    60 TRR|RRT|RTR 3-seq. 3-per. (partial)      33    0.8171      48    0.8176
   100   RTRT|TRTR    2-seq. 4-per. (full)      40    0.8073      68    0.8032
   100     RTR|TRT    2-seq. 3-per. (full)      58    0.8023     102    0.8033
   100 TRR|RRT|RTR 3-seq. 3-per. (partial)      60    0.8073     102    0.8028

Note the extreme increase in sample sizes for the EMA’s method if CV_wR gets large.