Compute stopping boundaries and sample size for a group sequential SMART

Calculates the stopping boundaries and required sample size for a group sequential design with multiple treatment regimes embedded in a SMART. The boundaries are found first to control the type I error rate, then the sample size is determined to achieve the desired power. This function wraps get_bounds and get_sample_size.

Usage

smart_design(
  test_type = "one-sided",
  comp_type = "fixed.control",
  alpha = 0.05,
  beta = 0.1,
  delta = NULL,
  n_init = 400,
  inf_frac = 1,
  spend_fn = "OF",
  corr = NULL,
  variances = NULL,
  lambdaB = 0.1,
  lambdaC = 20,
  tol = 1e-06,
  max_iterB = 1000,
  max_iterC = 100,
  seed = 1,
  Bb = 100001,
  Bc = 10001,
  mu = NULL
)

Arguments

test_type: A character string specifying the type of hypothesis test. A test type of either one-sided or two-sided. Two-sided testing must be symmetric. This input is ignored for a global Chi-squared test.
comp_type: A character string specifying what comparison will be tested. Character string for either "fixed.control" or "global.chi.sq".
alpha: A numeric value between 0 and 1 specifying the overall familywise type I error rate. Default is 0.05.
beta: A numeric value between 0 and 1 specifying the type II error rate. Power is 1 - beta. Default is 0.1 for power of 0.9.
delta: A numeric vector of length equal to the number of treatment regimes specifying the alternative differences between each regime's value and the null (or control) value.
n_init: A positive integer specifying the initial total sample size to begin the iterative sample size search.
inf_frac: A numeric vector of information fractions indicating when analyses are conducted. Values should be between 0 and 1, with the last element equal to 1. Default is 1 (single analysis). For example, c(0.5, 1) specifies an interim analysis at 50\% information and a final analysis.
spend_fn: A character string specifying the alpha spending function. Either "OF" (O'Brien-Fleming, default) or "Pocock".
corr: A correlation matrix of Z-statistics across all regimes and analyses. The dimension should be \(L \times k\) by \(L \times k\), where \(L\) is the number of treatment regimes. This matrix accounts for both within-analysis correlations between regimes and across-analysis correlations due to shared participants.
variances: A numeric vector of length equal to the number of treatment regimes giving the variance of each value estimator scaled by sample size, i.e., \(N \times \mathrm{Var}(\hat{V}_d)\).
lambdaB: A numeric value for the initial step size used in the iterative boundary search. Default is 0.1.
lambdaC: A numeric value for the initial step size used in the iterative sample size search. Default is 20.
tol: A numeric value specifying the convergence tolerance. Default is 1e-6.
max_iterB: A positive integer specifying the maximum number of iterations for the boundary search. Default is 1000.
max_iterC: A positive integer specifying the maximum number of iterations for the sample size search. Default is 100.
seed: An integer seed for reproducibility of the Monte Carlo simulation. Default is 1.
Bb: A positive integer specifying the number of Monte Carlo samples for the boundary computation. Default is 100001.
Bc: A positive integer specifying the number of Monte Carlo samples for the sample size computation. Default is 10001.
mu: A parameter vector for the multivariate normal distribution of the treatment effect mean, used only for the chi-square distribution in the case of a non-centrality assumption, though unlikely to be needed.

Value

A list with the following components:

boundaries: The output from get_bounds (when comp_type = "fixed.control") or get_bounds_chi (when comp_type = "global.chi.sq"), containing the stopping boundaries and associated metadata. See those functions for details.
sample.size: The output from get_sample_size or get_sample_size_chi, containing the required sample sizes, achieved power, cumulative rejection probabilities, and echoed input parameters. If delta is NULL (no alternative specified), the sample size is not computed and this element is NULL.
inputs: A list echoing all input parameters passed to smart_design.