Bioequivalence and Bioavailability Forum

Hi ElMaestro & Sveta,

❝ Should read: "In a 5-way BE crossover trial, is there a methodology available that allows one to analyze 3 out of 5 periods for BE in an interim fashion, and contingent upon results complete the remaining 2 periods and analyze all 5 periods at the conclusion?"

❝

❝ It is definitely doable as a single protocol. […] I think it may not require much operational adjustment or statistical fiddling, …

@ElMaestro: Operational – no. Statistical – likely yes.
The current regulatory thinking expressed at numerous conferences (nothing published) is that one still has to adjust α because in the first part one gets two chances to demonstrate BE (see this presentation, slide 23). I belonged to the first church (90% CI) for decades though now I’m a convert. I would not try to find an ‘optimal’ ¹ adjusted α.

I regolatori stanno bene con Signor Bonferroni.

@Sveta: For most drugs it is more difficult to demonstrate BE in fed state (true food-drug interaction, higher variability) than in fasted state. Consider to switch your approach (fed followed by fast­ed). I haven’t seen a single case where the fed study passed and the fasted one failed, but a lot of cases the other way ’round – which required reformulation. Unfortunately many companies start with the fasted study (hey, that’s standard) only to be hit in fed state.
I recommend also to evaluate the first part according to the “Two at a Time” principle (two separate ana­lyses ² as Incomplete Block Designs, i.e., T₁ vs R and T₂ vs R) and not “All at Once” (by one – pooled – ANOVA). ³ For details and references see the vignette of PowerTOST.
Note that the EMA’s BE-GL states:

In studies with more than two treatment arms (e.g. […] a four period study including test and reference in fed and fasted states), the analysis for each comparison should be conducted excluding the data from the treatments that are not relevant for the comparison in question.

(my emphasis)

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1. One would have to formalize the decision process in the selection of T₁ or T₂: GMR closer to one; if similar, the one with lower variability, etc. IMHO, not worth the efforts, since the average gain in sample sizes even for an optimistic α 0.0304 over Bonferroni’s 0.025 is just ~5%. Add the given reluctance of assessors towards simulation-based methods…
   
   
2. Since you will have only two treatments in each analysis, estimate the sample size for a 2×2×2 design and not for 3×3 Latin Squares. Requires sometimes slightly higher sample sizes.
   library(PowerTOST)
CV     <- seq(0.15, 0.3, 0.01) # Intra-subject CV
theta0 <- 0.95                  # Assumed T/R-ratio
target <- 0.80                  # Target (desired) power
alpha0 <- 0.05                  # Nominal level
k      <- 2                     # Number of tests
alpha  <- alpha0/k              # Bonferroni-adjustment
res    <- data.frame(CV = CV,
                     design.3 = "3x3",   n.3 = NA, power.3 = NA,
                     design.2 = "2x2x2", n.2 = NA, power.2 = NA)
for (j in 1:nrow(res)) {
  res[j, 3:4] <- signif(sampleN.TOST(alpha = alpha, CV = res$CV[j], theta0 = theta0,
                                     targetpower = target, design = res$design.3[j],
                                     details = FALSE,  print = FALSE)[7:8], 3)
  res[j, 6:7] <- signif(sampleN.TOST(alpha = alpha, CV = res$CV[j], theta0 = theta0,
                                     targetpower = target, design = res$design.2[j],
                                     details = FALSE,  print = FALSE)[7:8], 3)
}
res$change <- sprintf("%+4.2f", 100*(res[, 6] - res[, 3])/res[, 3])
res$change[res$change == "+0.00"] <- "±0.00"
names(res)[2:6] <- rep(c("design", "n", "power"), 2)
txt    <- paste0("Assumed \u03B8 ", theta0, ", target (desired) power ", target)
if (alpha != 0.05) {
  txt <- paste0(txt, ", adjusted \u03B1 ", alpha, " (", 100*(1-2*alpha), "% CI), ")
} else {
  txt <- paste0(txt, ", \u03B1 0.05 (conventional 90% CI), ")
}
txt    <- paste0(txt, "TIE \u2264", signif(1-(1-alpha)^k, 5), "\n")
cat(txt); print(res, row.names = FALSE)
   
   Peanuts:
   Assumed θ 0.95, target (desired) power 0.8, adjusted α 0.025 (95% CI), TIE ≤0.049375
   CV design  n power design  n power change
 0.15    3x3 15 0.857  2x2x2 16 0.855  +6.67
 0.16    3x3 15 0.808  2x2x2 16 0.806  +6.67
 0.17    3x3 18 0.839  2x2x2 18 0.813  ±0.00
 0.18    3x3 21 0.858  2x2x2 20 0.816  -4.76
 0.19    3x3 21 0.817  2x2x2 22 0.817  +4.76
 0.20    3x3 24 0.833  2x2x2 24 0.815  ±0.00
 0.21    3x3 27 0.844  2x2x2 26 0.812  -3.70
 0.22    3x3 27 0.808  2x2x2 28 0.808  +3.70
 0.23    3x3 30 0.817  2x2x2 30 0.802  ±0.00
 0.24    3x3 33 0.824  2x2x2 34 0.823  +3.03
 0.25    3x3 36 0.828  2x2x2 36 0.816  ±0.00
 0.26    3x3 39 0.830  2x2x2 38 0.808  -2.56
 0.27    3x3 39 0.801  2x2x2 40 0.801  +2.56
 0.28    3x3 42 0.803  2x2x2 44 0.813  +4.76
 0.29    3x3 45 0.805  2x2x2 46 0.805  +2.22
 0.30    3x3 48 0.805  2x2x2 50 0.814  +4.17
   
   
3. In the ANOVA you get only one – pooled – residual variance. Apart from problems with potentially biased estimates and inflated TIE, you could base your decision only on the T/R-ratios. If they are similar, which one will you select? Flip a coin? In the IBD-analyses you get two variance estimates, which in such a case would be helpful.