What to consider when calculating sample size for non-inferiority (NI) study?

The Wise son:

In the previous post, we discussed non-inferiority (NI) study design. The first thing you need for establishing sample size for NI study, is to establish the NI-Margin (margin). It may be necessary to evaluate the sample-size (N) sensitivity to a range of margins.  Small margin may require unrealistic large sample size, while larger margin may not be clinically accepted as a non-inferiority.

The Simple son:

The sample size for a non-inferiority trial with a custom power of 85%  is calculated to satisfy the following Chow, 2017 equation:

Where:

In words, the sample size must be large enough so that the probability is sufficiently high that the lower bound of the 95% CI for the estimated means difference between the treatment and the control (or reference) products, (M_t-M_c) is greater than the NI margin (Δ).

The Wicked son:

Let’s see who understands formulas, shall we? OK then,

Which of the following cases requires the largest N?

1. Large margin (Δ), large standard deviation (SD).
2. Large margin (Δ), small standard deviation (SD).
3. Small margin (Δ), large standard deviation (SD).

The Simple son:

Wicked, you’re not scaring anyone. We can use R to perform a simulation to test that, for a trial with 2 equal-sized groups:

library(SampleSize4ClinicalTrials)

margins <- c(-0.5, -0.75, -1, -1.5, -2, -2.5)

powers <- c(0.8, 0.85, 0.9, 0.95)

SDs <- c(3.7, 3, 2.5, 2)

tab1 <- data.frame(Margin = c(), SD = c(), N = c())

list_tab <- list()

for (P in 1:length(powers)) {

  for (j in 1:length(SDs)) {

   for (i in 1:length(margins)) {

 N <-  as.numeric(ssc_meancomp(design = 3L, ratio = 1, alpha = 0.05, power = powers[P], sd = SDs[j], theta = 0, delta = margins[i])[1])

 tab1 <- rbind(tab1,

               data.frame(Margin = c(margins[i]), SD = c(SDs[j]), N = N) )

   }

  }

  list_tab[[P]] <- tab1

  tab1 <- data.frame(Margin = c(), SD = c(), N = c())

}

tab_final <- cbind(list_tab[[1]], list_tab[[2]][,3], list_tab[[3]][,3], list_tab[[4]][,3])

names(tab_final) <- c("Margin", "SD", "N.80%", "N.85%","N.90%","N.95%")

So, the answer to your question, Wicked, is the third case; small margin and big standard deviation yields the largest sample size.

He who couldn’t ask:

It took me a few hours to understand that “SampleSize4ClinicalTrials” means “sample size for clinical trials”. Nobody teaches you those things, they all just expect you to understand everything.