Now I got it! [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2022-01-31 23:53 (115 d 16:31 ago) – Posting: # 22766
Views: 649

Hi Sereng,

» Many thanks for your response.

Welcome – though I missed the target. ;-)

» I am not even sure if I need to reply before or after your text.

See there.

» Is it possible you misunderstood my question?

Given what you posted in the following, yes, indeed.

» What I meant to ask is if I do replicate crossover, i.e., 50 subjects on Test x 2 periods and 50 subjects on Reference x 2 periods (replicate crossover, 2X2X4) as opposed to 100 subjects on test x 1 period and 100 subjects on Reference x 1 period (2X2X2), do I gain any sample size (or power) efficiency using FDA 3-tests (per PSG) for Levothyroxine?

That’s hypothetical cause the FDA will not accept a 2×2×2 crossover. Study cost hinges mainly on the number of treatments (which drives the number of samples and hence, costs of bioanalytics). Peanuts: In a replicate (less subjects) you safe some costs of pre-/post study lab exams which might be outweighed by a higher chance of dropouts.
See Fig.1.
Anyway: Let’s compare the FDA’s RSABE and the EMA’s fixed limits of 90.00–111.11% (in 2×2×2 and 2×2×4 crossovers) to conventional ABE with fixed limits of 80.00–125.00% (2×2×2 crossover)* based on data assessed by the FDA in 2011.

library(PowerTOST)
# Yu (2011) https://www.fda.gov/media/82940/Download
# 9 ANDAs of Levothyroxine: Cmax

CV     <- c(0.052, 0.096, 0.186) # min, mean, max)
theta0 <- 0.975                  # assumed T/R-ratio
target <- 0.80                   # target power ≥80%
x      <- data.frame(CV = CV, n.FDA = NA_integer_, cost.FDA = NA_real_,
                     n.EMA2 = NA_integer_, cost.EMA2 = NA_real_,
                     n.EMA4 = NA_integer_, cost.EMA4 = NA_real_,
                     n.ABE = NA_integer_, cost.ABE = 1)
for (j in seq_along(CV)) {
  # RSABE for NTIDs, 2x2x4 design mandatory acc. to the guidance
  x$n.FDA[j] <- sampleN.NTIDFDA(CV = CV[j], theta0 = theta0,
                                targetpower = target, details = FALSE,
                                print = FALSE)[["Sample size"]]
  # EMA for NTIDs, fixed limits 90.00-111.11%
  # 2x2x2 design (in product-specific guidance for NTIDs)

  x$n.EMA2[j] <- sampleN.TOST(CV = CV[j], theta0 = theta0, theta1 = 0.90,
                              targetpower = target, design = "2x2x2",
                              print = FALSE)[["Sample size"]]
  # 2x2x4 design (optional)
  x$n.EMA4[j] <- sampleN.TOST(CV = CV[j], theta0 = theta0, theta1 = 0.90,
                              targetpower = target, design = "2x2x4",
                              print = FALSE)[["Sample size"]]
  # conventional ABE, 2x2x2 design, fixed limits 80.00-125.00%
  x$n.ABE[j] <- sampleN.TOST(CV = CV[j], theta0 = theta0, theta1 = 0.80,
                          targetpower = target, design = "2x2x2",
                          print = FALSE)[["Sample size"]]
  # minimum sample size acc. to the guideline
  if (x$n.EMA2[j] < 12) x$n.EMA2[j] <- 12
  if (x$n.EMA4[j] < 12) x$n.EMA4[j] <- 12
  if (x$n.ABE[j] < 12) x$n.ABE[j] <- 12
}
# cost relative to ABE 2×2×2 design with fixed limits 80.00-125.00%
x$cost.FDA  <- x$n.FDA * 2 / x$n.ABE
x$cost.EMA2 <- x$n.EMA2 / x$n.ABE
x$cost.EMA4 <- x$n.EMA4 * 2 / x$n.ABE
names(x)[c(3, 5, 7, 9)] <- rep("cost", 4)
print(signif(x, 4), row.names = FALSE)

    CV n.FDA  cost n.EMA2  cost n.EMA4  cost n.ABE cost
 0.052    30 5.000     12 1.000     12 2.000    12    1
 0.096    18 3.000     20 1.667     12 2.000    12    1
 0.186    16 2.286     70 5.000     34 4.857    14    1


In short: For low variability RSABE is more costly than the EMA’s fixed limits. If the CV is larger than ~12% it is the other way ’round.
Don’t forget the comparisons of variabilities. Whereas for the EMA’s approaches we assume homoscedasticity \(\small{(s_\textrm{wT}^2\equiv s_\textrm{wR}^2)}\), in RSABE a test for unequual variances is part of the procedure (see Fig.3). Hence, I recommend a pilot study to avoid surprises.



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