Guesstimates [Design Issues]
❝ ❝ Observed Pilot study ISCV% - 12.29%
❝ We […] considered the 13 subjects for final statistical analysis.
❝ ❝ […] is it possible to expect the 15% ISCV or not for pivotal study design?
Let’s consider the CV first. Calculate the upper confidence limit of the CV you observed in the pilot. Then you could calculate the probability of a CV which is ≥15%. R-code:
library(PowerTOST)
CV <- 0.1229 # observed
n <- 13 # sample size (crossover)
alpha <- 0.05 # default
target <- 0.15 # to explore
# 1. Upper 1-alpha CL of the CV
# -----------------------------
ucl <- CVCL(CV, df=n-2, alpha=alpha)[["upper CL"]]
# 2. Find the alpha which gives an upper CL = target CV
# -----------------------------------------------------
f <- function(x) CVCL(CV, df=n-2, alpha=x)[["upper CL"]]-target
p <- uniroot(f, interval=c(1e-8, 0.5), tol=1e-6)$root
cat(paste0("Sample size: ", n, ", observed CV: ", 100*CV, "%",
"\nUpper confidence limit of CV: ", round(100*ucl, 2),
"% (\u03b1 ", alpha, ")", "\nProbability to expect a CV of \u2265",
round(100*target, 2), "%: ~", signif(p, 2), "\n"))
Sample size: 13, observed CV: 12.29%
Upper confidence limit of CV: 19.16% (α 0.05)
Probability to expect a CV of ≥15%: ~0.24
CVCL()
. Let’s say you want to have a 90% chance (α 0.1):cat(sprintf("%.2f%%%s", 100*CVCL(CV, df=n-2, alpha=0.1)[["upper CL"]], "\n"))
17.32%
cat(sprintf("%.2f%%%s", 100*CVCL(CV, df=n-2, alpha=0.2)[["upper CL"]], "\n"))
15.45%
❝ Why we need to expect the Null (true) ratio = 0.95 only?
I never said that. The θ0 is unforgiving. Power curves are relatively flat close to 1, but become increasingly steep further away than ±5%. Had you any chance to look at my presentations as Detlew suggested? What does the 90% CI of a BE-study tell us? That the true ratio lies with a probability of 0.9 somewhere within its CI. Let’s assume the best (you observed a GMR of 1 in the pilot):
round(100*CI.BE(alpha=0.05, pe=1, CV=0.1229, n=13, design="2x2"), 2)
lower upper
91.74 109.01
Yet another story is the measured content. The EMA allows a dose-correction only if you provide a sound justification that it was impossible to find a batch of the reference which differs ≤5% from the test. Otherwise, any measured difference is ignored (i.e., DT ≡ DR has to be assumed). No analytical method is “perfect”. Let’s presume an amazing method (accuracy 100% and imprecision ±2.5%):
alpha <- 0.05
mean <- c(97.5, 100, 102.5)
CV <- rep(2.5, 3)
sd <- 100*CV/mean
lower <- qnorm(p=alpha/2, mean=mean, sd=sd)
upper <- qnorm(p=1-alpha/2, mean=mean, sd=sd)
cat("Measured contents (%) :", sprintf("%6.2f ", mean),
"\nCV of the method (%) : ", unique(CV),
"\nSD of means :", sprintf("%6.2f ", sd),
paste0("\n\u03b1 level : ", alpha, " (", 100*(1-alpha), "% CI)"),
"\nLower CL of contents (%):", sprintf("%6.2f ", lower),
"\nUpper CL of contents (%):", sprintf("%6.2f ", upper), "\n")
Measured contents (%) : 97.50 100.00 102.50
CV of the method (%) : 2.5
SD of means : 2.56 2.50 2.44
α level : 0.05 (95% CI)
Lower CL of contents (%): 92.47 95.10 97.72
Upper CL of contents (%): 102.53 104.90 107.28
Rule of thumb for a ~95% CI: x±2(100CV%/x). Talk to your analyst(s) about what to expect…
I think it is much more interesting to live with uncertainty
than to live with answers that might be wrong. Richard Feynman
- Fuglsang A. Pilot and Repeat Trials as Development Tools Associated with Demonstration of Bioequivalence. AAPS J. 2015;17(3):678–83. doi 10.1208/s12248-015-9744-6
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Science Quotes
Complete thread:
- Sample size justification bkrao 2015-08-06 09:12 [Design Issues]
- Sample size justification BE-proff 2015-08-06 14:19
- PASS simulator? d_labes 2015-08-06 15:25
- PASS simulator? BE-proff 2015-08-07 20:08
- Owen’s Q | noncentral t | shifted central t Helmut 2015-08-08 02:32
- Owen’s Q | noncentral t | shifted central t BE-proff 2015-08-09 15:36
- PowerTOST crash-course Helmut 2015-08-09 16:40
- Owen’s Q | noncentral t | shifted central t - PASS? d_labes 2015-08-10 11:30
- Owen’s Q | noncentral t | shifted central t BE-proff 2015-08-09 15:36
- Owen’s Q | noncentral t | shifted central t Helmut 2015-08-08 02:32
- PASS simulator? BE-proff 2015-08-07 20:08
- PASS simulator? d_labes 2015-08-06 15:25
- Sample size justification Helmut 2015-08-07 01:21
- Sample size justification bkrao 2015-08-07 06:06
- GuesstimatesHelmut 2015-08-07 13:53
- Guesstimates bkrao 2015-08-08 06:03
- Guesstimates jag009 2015-08-10 20:08
- Guesstimates bkrao 2015-08-10 20:44
- Guesstimates jag009 2015-08-10 20:08
- Guesstimates bkrao 2015-08-08 06:03
- GuesstimatesHelmut 2015-08-07 13:53
- Sample size justification bkrao 2015-08-07 06:06
- Sample size justification BE-proff 2015-08-06 14:19