Determine sample size for a group sequential SMART design

For specified operating characteristics, iteratively increases the sample size until the desired power is achieved. Assumes the information fraction remains unchanged as the sample size increases, which is reasonable for small changes or at the design stage.

Usage

get_sample_size(
  variances,
  beta,
  delta,
  bounds,
  n_init = 100,
  corr = bounds$corr,
  inf_frac = bounds$inf_frac,
  n_split = NULL
)

Arguments

variances: A numeric vector of length \(L\) of variances of the value estimators, i.e., \(\sqrt{N} \times \mathrm{Cov}(\hat{\theta})\). These should reflect the population variances rather than sample variance or standard errors.
beta: A numeric value between 0 and 1 specifying the type II error rate. Power is 1 - beta.
delta: A numeric vector of length \(L\) of differences between regime values and the null value (or control arm).
bounds: A numeric vector of length \(S\) with the stopping boundaries for analyses \(1, \ldots, S\), or the boundaries from get_bounds function
n_init: A positive integer specifying the initial total trial sample size \(N\) to begin the search.
corr: A correlation matrix of dimension \(L \times L\) between regime value estimators across all analyses.
inf_frac: A numeric vector of information fractions indicating when analyses are conducted.
n_split: A numeric vector indicating the proportion of the sample size at the analysis times s=1,...,S. If no argument is given, assumes the split is proportional to the information available.

Value

A list with the following components:

N: A numeric vector of sample sizes at each analysis.
power: The achieved power at the final sample size.
prop_rej: A numeric vector of cumulative rejection probabilities at each analysis.
variances: The input variances.
beta: The input type II error rate.
delta: The input alternative differences.
bounds: The input stopping boundaries.
n_init: The input initial sample size.
corr: The input correlation matrix.
inf_frac: The input information fractions.
n_split: The input sample size split proportions.