## Probability of Success in BE studies [Design Issues]

Hi Achievwin,

❝ Recently I was asked to give Probability of success for a proposed BE study, My thinking is Target study power (usually 80%) is POS with additional correction factor due to the variability during study conduct applied to this target power, is my understanding correct?

Not sure whether I understand you correctly. POS is a Bayesian concept, where you need some prior information. Let’s start with a conventional sample size estimation based purely on assumptions.

library(PowerTOST) CV     <- 0.25 theta0 <- 0.95 target <- 0.80 sampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target, details = FALSE) +++++++++++ Equivalence test - TOST +++++++++++             Sample size estimation ----------------------------------------------- Study design: 2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 True ratio = 0.95,  CV = 0.25 Sample size (total)  n     power 28   0.807439

Say, you obtained the CV and T/R-ratio in another study with 24 subjects. Based on that, you can take the uncertainty of the CV (#1), of the T/R-ratio (#2), or both (#3) into account.

m <- 24 # sample size of prior study

1. expsampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target,                 prior.parm = list(m = m, design = "2x2"), prior.type = "CV", details = FALSE) ++++++++++++ Equivalence test - TOST ++++++++++++        Sample size est. with uncertain CV ------------------------------------------------- Study design:  2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 Ratio = 0.95 CV = 0.25 with 22 df Sample size (ntotal)  n   exp. power 32   0.822645
2. expsampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target,                 prior.parm = list(m = m, design = "2x2"), prior.type = "theta0", details = FALSE) ++++++++++++ Equivalence test - TOST ++++++++++++      Sample size est. with uncertain theta0 ------------------------------------------------- Study design:  2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 Ratio = 0.95 CV = 0.25 Sample size (ntotal)  n   exp. power 44   0.810063
3. expsampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target,                 prior.parm = list(m = m, design = "2x2"), prior.type = "both", details = FALSE) ++++++++++++ Equivalence test - TOST ++++++++++++   Sample size est. with uncertain CV and theta0 ------------------------------------------------- Study design:  2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 Ratio = 0.95 with 22 df CV = 0.25 with 22 df Sample size (ntotal)  n   exp. power 48   0.801190
As usual, the T/R-ratio is the killer.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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