Bioequivalence Tests for 2x2 Cross-Over Trial Designs with Log-Normal Data

In the examples below, we illustrate the use of SimTOST for 2x2 cross-over trials. As a first step, we load the package.

library(SimTOST)

Bioequivalence Tests for AUC and Cmax

In the first example, we consider Example 1 from the PASS Sample Size Software Chapter 351. We aim to estimate the sample size required to demonstrate bioequivalence between a test and reference product for two pharmacokinetic parameters: the area under the curve (AUC) and the maximum concentration (Cmax). We assume a 2x2 cross-over design. The true ratio of the test to the reference product is assumed to be 1.02 for AUC and 1.03 for Cmax. Based on previous experiments, it is assumed that the standard deviation for $\log(AUC)$ = 0.25 and the standard deviation for $\log(Cmax = 0.3)$ . The equivalence limits for the means ratio are set at 0.80 and 1.25.

The significance level is set to 5%, and the sample size is calculated to achieve 80% power. Additionally, the correlation between AUC and Cmax is assumed to be 0.25. A difference-of-means test on the log scale is employed to determine bioequivalence. In the PASS software, this scenario yielded a total sample size of $n=37$ patients. In SimTOST, we can estimate the sample size using the sampleSize() function.

mu_r <- c(AUC = log(1.00), Cmax = log(1.00))
mu_t <- c(AUC = log(1.02), Cmax = log(1.03))
sigma <- c(AUC = 0.25, Cmax = 0.3)
lequi_lower <- c(AUC = log(0.80), Cmax = log(0.80))
lequi_upper <- c(AUC = log(1.25), Cmax = log(1.25))

ss <- sampleSize(power = 0.8, alpha = 0.05,
                 mu_list = list("R" = mu_r, "T" = mu_t),
                 sigma_list = list("R" = sigma, "T" = sigma),
                 list_comparator = list("T_vs_R" = c("R", "T")),
                 rho = 0.25,
                 list_lequi.tol = list("T_vs_R" = lequi_lower),
                 list_uequi.tol = list("T_vs_R" = lequi_upper),
                 dtype = "2x2", ctype = "DOM", lognorm = FALSE, 
                 adjust = "no", ncores = 1, nsim = 10000, seed = 1234)
ss
#> Given a 80%  target power with 100(1-2*0.05)% confidence level.
#> 
#> The total required sample size to achieve 80.9% power is 37 sample units.
#> 
#>  n_drop n_seq0_RvsT n_seq1_RvsT n_total  power power_LCI power_UCI
#>   <num>       <num>       <num>   <num>  <num>     <num>     <num>
#>       0          19          18      37 0.8089 0.8010253  0.816536

The total sample size is 37 subjects.

Thomas Debray

November 18, 2024

Bioequivalence Tests for AUC and Cmax

References