## Back Calculating Sample Size [Power / Sample Size]

Hi ElMaestro & Sereng,

❝ ❝ Parallel Group Design

❝ ❝ Two Groups (n=70/group)

❝ ❝ Ratio (90% CI): 109.00 (87.00-135.00)

❝ I am getting around CV = 156% (pooled variance estimate).

Hhm…

library(PowerTOST) CV <- CI2CV(lower = 0.87, upper = 1.35, n = 140, design = "parallel") sampleN.TOST(CV = CV, theta0 = sqrt(0.87 * 1.35), design = "parallel") +++++++++++ Equivalence test - TOST +++++++++++             Sample size estimation ----------------------------------------------- Study design: 2 parallel groups log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 True ratio = 1.083744,  CV = 0.9227379 Sample size (total)  n     power 750   0.800246

❝ ❝ is it possible to calculate a new sample size that would likely meet the BE requirements …

See above.

❝ ❝ … (or declare futility)?

If this is not a blockbuster and/or you have a large budget, yes.
Furthermore, there is no guarantee that you will observe exactly the same T/R-ratio and CV in another study. Especially the T/R-ratio is nasty. In PowerTOST a Bayesian method is implemented, which takes the uncertainties of the estimated T/R-ratio and CV of the provious study into account.

library(PowerTOST) m      <- 140 CV     <- 0.9227379 theta0 <- 1.083744 design <- "parallel" res    <- data.frame(method = c("naïve",                                 "uncertain CV",                                 "uncertain T/R-ratio",                                 "both uncertain"),                      n = NA_integer_, power = NA_real_) res[1, 2:3] <- sampleN.TOST(CV = CV, theta0 = theta0, targetpower = 0.8,                             design = design, print = FALSE)[7:8] res[2, 2:3] <- expsampleN.TOST(CV = CV, theta0 = theta0,                                targetpower = 0.80,                                design = design,                                prior.parm = list(m = m, design = design),                                prior.type = "CV",                                details = FALSE, print = FALSE)[9:10] res[3, 2:3] <- expsampleN.TOST(CV = CV, theta0 = theta0,                                targetpower = 0.80,                                design = design,                                prior.parm = list(m = m, design = design),                                prior.type = "theta0",                                details = FALSE, print = FALSE)[9:10] res[4, 2:3] <- expsampleN.TOST(CV = CV, theta0 = theta0,                                targetpower = 0.80,                                design = design,                                prior.parm = list(m = m, design = design),                                prior.type = "both",                                details = FALSE, print = FALSE)[9:10] print(res, row.names = FALSE)               method     n     power                naïve   750 0.8002443         uncertain CV   760 0.8008385  uncertain T/R-ratio 13764 0.8000035       both uncertain 14858 0.8000001

Terrible.

Dif-tor heh smusma 🖖🏼 Довге життя Україна! Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes  Ing. Helmut Schütz 