## n iteratively from power [Power / Sample Size]

Hi Imph,

❝ Thank you so much. Your response has been of great help.

Welcome.

❝ – By consulting Dileti's paper, I noticed that there is no formula for the calculation of the number of subjects. Is there a way or a reference to get the formula please.

You can only calculate power for a given sample size, i.e., you start with an assumption and then increase (or decrease) n to obtain at least the target power. See there for the details.

Step by step:

library(PowerTOST) CV     <- 0.25 theta0 <- 0.95 target <- 0.80 n      <- 12                    # minimum acc. to the GLs power  <- power.TOST(CV = CV, theta0 = theta0, n = n) iter   <- 1 res    <- data.frame(iter = iter, n = n, power = power) if (res\$power[iter] < target) { # upwards   repeat {     power <- power.TOST(CV = CV, theta0 = theta0, n = n)     res[iter, ] <- c(iter, n, power)     if (power >= target) {       break     } else {       iter <- iter + 1       n    <- n + 2     }   } } else {                        # downwards   repeat {     power <- power.TOST(CV = CV, theta0 = theta0, n = n)     res[iter, ] <- c(iter, n, power)     if (power < target) {       res <- res[-nrow(res), ]       break     } else {       iter <- iter + 1       n    <- n - 2     }   } } print(res, row.names = FALSE)  iter  n     power     1 12 0.3137351     2 14 0.4141013     3 16 0.5041795     4 18 0.5801284     5 20 0.6430574     6 22 0.6953401     7 24 0.7391155     8 26 0.7760553     9 28 0.8074395

In PowerTOST’s sample size functions you can show the iterations by setting the argument details to TRUE (by default only the final result is shown):

sampleN.TOST(CV = 0.25, theta0 = 0.95, targetpower = 0.80, details = TRUE) +++++++++++ Equivalence test - TOST +++++++++++             Sample size estimation ----------------------------------------------- Study design: 2x2 crossover Design characteristics: df = n-2, design const. = 2, step = 2 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 search (ntotal)  n     power 26   0.776055 28   0.807439 Exact power calculation with Owen's Q functions.

❝ – […] in the calculation of the degrees of freedom, for example (2n-2), where "n" has to be estimated. I would like to know on what basis this "n" is estimated.

See above.

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