Bioequivalence and Bioavailability Forum

Hi Ohlbe,

successful cheating is not for lay persons… -script at the end.
The CVs calculated from the confidence intervals in both ‘parts’ are much lower than the ones in the ‘full’ study. Or the other way ’round: If we pool the CVs of the ‘parts’ we could expect values which are lower than the ‘observed’ (tee-hee!) ones.

       CRO  study  n metric     PE  lower  upper   BE    CV CV.pooled
 Panexcell part 1 12   Cmax  71.26  64.78  78.38 fail 12.93         
 Panexcell part 2 12   Cmax 141.80 124.27 161.82 fail 17.98         
 Panexcell   full 24   Cmax 100.52  86.88 116.31 pass 30.08     15.25
 Panexcell part 1 12 AUC0-t  85.41  78.45  93.00 fail 11.53         
 Panexcell part 2 12 AUC0-t 126.89 115.81 139.04 fail 12.40         
 Panexcell   full 24 AUC0-t 104.11  94.97 114.12 pass 18.69     11.96
  Synchron part 1 41   Cmax 135.55 115.53 159.04 fail 44.99         
  Synchron part 2 31   Cmax  73.54  60.53  89.36 fail 47.50         
  Synchron   full 72   Cmax 103.50  90.30 118.62 pass 52.21     46.04
  Synchron part 1 41 AUC0-t 122.98 110.07 137.41 fail 30.47         
  Synchron part 2 31 AUC0-t  75.24  63.33  89.38 fail 41.54         
  Synchron   full 72 AUC0-t  99.01  88.86 110.32 pass 40.46     34.78

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# https://www.fda.gov/media/151569/download (page 4)
# https://www.fda.gov/media/151570/download (page 4)
library(PowerTOST)
CRO     <- c("Panexcell", "Synchron")
designs <- c("2x2x2", "2x2x2")
metric  <- c("Cmax", "AUC0-t")
# arbitrary identifiers, only the last one must be "full"
study   <- c("part 1", "part 2", "full")
ns1     <- c(12, 12, 24)
ns2     <- c(41, 31, 72)
PE1     <- c( 71.26, 141.80, 100.52,
              85.41, 126.89, 104.11)
PE2     <- c(135.55,  73.54, 103.5 ,
             122.98,  75.24,  99.01)
lower1  <- c( 64.78, 124.27,  86.88,
              78.45, 115.81,  94.97)
lower2  <- c(115.53,  60.53,  90.3 ,
             110.07,  63.33,  88.86)
upper1  <- c( 78.38, 161.82, 116.31,
              93.00, 139.04, 114.12)
upper2  <- c(159.04,  89.36, 118.62,
             137.41,  89.38, 110.32)
res     <- data.frame(CRO = rep(CRO, each = length(study) * length(metric)),
                      design = rep(designs, each = length(study) * length(metric)),
                      study = rep(study, length(CRO) * length(metric)),
                      n = c(rep(ns1, length(metric)),
                            rep(ns2, length(metric))), df = NA_integer_,
                      metric = rep(rep(metric, each = length(study)), length(CRO)),
                      PE = c(PE1, PE2), lower = c(lower1, lower2),
                      upper = c(upper1, upper2), BE = "fail",
                      CV = NA_real_, CV.pooled = "")
for (j in 1:nrow(res)) {
  if (res$lower[j] >= 80 & res$upper[j] <= 125) res$BE[j] <- "pass"
  # calculate the CV from the CI
  res$CV[j] <- signif(100 * suppressMessages(
                              CI2CV(pe = res$PE[j] / 100,
                                    lower = res$lower[j] / 100,
                                    upper = res$upper[j] / 100,
                                    n = res$n[j])), 4)
  # degrees of freedom as expression
  df <- PowerTOST:::.design.df(PowerTOST:::.design.props(
                               PowerTOST:::.design.no(res$design[j])),
                                                      robust = FALSE)
  n         <- res$n[j]
  res$df[j] <- eval(df) # calculate df from sample size
}
for (j in seq_along(CRO)) {
  for (k in seq_along(metric)) {
    # extract the ‘parts’ (design, df, and CV)
    CVs <- res[res$CRO == CRO[j] & res$study != "full" &
               res$metric == metric[k], c(2, 5, 11)]
    # CV pooled from the ‘parts’
    res$CV.pooled[res$CRO == CRO[j] & res$study == "full" &
                  res$metric == metric[k]] <- signif(CVpooled(CVs)$CV, 4)
  }
}
res <- res[, -which(names(res) %in% c("design", "df"))] # no more needed
print(res, row.names = FALSE)