Bioequivalence and Bioavailability Forum

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.