## Fed (IBD) → fasting [General Statistics]

Hi ElMaestro & Sveta,

» Should read:

»

» 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

@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

Note that the EMA’s BE-GL states:

» 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.*, T_{1}*vs*R and T_{2}*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)- One would have to formalize the decision process in the selection of T
_{1}or T_{2}: 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…

- 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

- 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.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- higher order crossover methodology sweiner 2020-06-30 01:07 [General Statistics]
- All dosed subjects have to be analyzed Helmut 2020-06-30 12:19
- All dosed subjects have to be analyzed sweiner 2020-06-30 17:08
- All dosed subjects have to be analyzed sedhosen 2021-03-16 08:30
- All dosed subjects have to be analyzed Helmut 2021-03-16 16:00

- higher order crossover methodology Relaxation 2020-06-30 14:10
- higher order crossover methodology sweiner 2020-06-30 17:10
- higher order crossover methodology ElMaestro 2020-06-30 18:17
- Fed (IBD) → fastingHelmut 2020-07-01 11:14
- Fed (IBD) → fasting sweiner 2020-07-07 03:00

- Fed (IBD) → fastingHelmut 2020-07-01 11:14

- higher order crossover methodology ElMaestro 2020-06-30 18:17

- higher order crossover methodology sweiner 2020-06-30 17:10

- All dosed subjects have to be analyzed Helmut 2020-06-30 12:19