Simulate group sequential cluster-randomized trial with continuous outcomes.

Usage

gsSimContCRT(
  k,
  data,
  test_type,
  test_sides,
  recruit_type,
  stat_type,
  balance_size,
  precompute = FALSE,
  delta,
  sigma_vec = c(1, 1),
  rho,
  alpha = 0.05,
  beta = 0.1,
  lower_bound = NULL,
  upper_bound = NULL,
  m_max = 1,
  n_max = 1,
  schedule_m = NULL,
  schedule_n = NULL,
  alpha_sf,
  alpha_sfpar = -4,
  beta_sf,
  beta_sfpar = -4,
  tol = 1e-06,
  r = 18
)

Arguments

k: Number of analyses planned, including interim and final.
data: Simulated continuous outcomes. Should be an n x 4 matrix with the columns encoding the treatment arm, cluster, individual, and response.
test_type: 1= early stopping for efficacy only
2= early stopping for binding futility only
3= early stopping for non-binding futility only
4= early stopping for either efficacy or binding futility
5= early stopping for either efficacy or non-binding futility
test_sides: 1= one-sided test
2= two-sided test
recruit_type: 1=by clusters with all individuals recruited
2=by individuals in recruited cluster
3=by both clusters and individuals in clusters
stat_type: 1= Z-test with known variance and ICC
2= Z-test with re-estimated variance and ICC
3= t-test with re-estimated variance and ICC
balance_size: 1= exact sample increments according to the scheduled interim analyses.
2= randomized sample increments from multinomial distribution according to the scheduled interim analyses.
precompute: Use pre-computed stopping boundaries if true.
delta: Effect size for theta under alternative hypothesis.
sigma_vec: Standard deviations for control and treatment groups.
rho: Intraclass correlation coefficient. Default value is 0.
alpha: Desired Type I error, always one-sided. Default value is 0.05.
beta: Desired Type II error, default value is 0.1 (90% power).
lower_bound: Pre-computed lower futility boundaries at the specified interim analyses. Must be specified if precompute is TRUE. NULL otherwise.
upper_bound: Pre-computed upper efficacy boundaries at the specified interim analyses. Must be specified if precompute is TRUE. NULL otherwise.
m_max: Number of clusters.
n_max: Mean size of each cluster.
schedule_m: Number of clusters at each interim look. Interim analyses will be conducted according to the information levels in schedule_m and schedule_n if provided. Otherwise, interim analyses will be conducted at equal-sized sample increments according to recruit_type.
schedule_n: Average cluster size at each interim look. Interim analyses will be conducted according to the information levels in schedule_m and schedule_n if provided. Otherwise, interim analyses will be conducted at equal-sized sample increments according to recruit_type.
alpha_sf: A spending function or a character string indicating an upper boundary type (that is, “WT” for Wang-Tsiatis bounds, “OF” for O'Brien-Fleming bounds, and “Pocock” for Pocock bounds). The default value is sfLDOF which is a Lan-DeMets O'Brien-Fleming spending function. See details, vignette("SpendingFunctionOverview"), manual and examples.
alpha_sfpar: Real value, default is \(-4\) which is an O'Brien-Fleming-like conservative bound when used with a Hwang-Shih-DeCani spending function. This is a real-vector for many spending functions. The parameter alpha_sfpar specifies any parameters needed for the spending function specified by alpha_sf; this will be ignored for spending functions (sfLDOF, sfLDPocock) or bound types (“OF”, “Pocock”) that do not require parameters.
beta_sf: A spending function or a character string indicating an lower boundary type (that is, “WT” for Wang-Tsiatis bounds, “OF” for O'Brien-Fleming bounds, and “Pocock” for Pocock bounds). The default value is sfLDOF which is a Lan-DeMets O'Brien-Fleming spending function. See details, vignette("SpendingFunctionOverview"), manual and examples.
beta_sfpar: Real value, default is \(-4\) which is an O'Brien-Fleming-like conservative bound when used with a Hwang-Shih-DeCani spending function. This is a real-vector for many spending functions. The parameter beta_sfpar specifies any parameters needed for the spending function specified by beta_sf; this will be ignored for spending functions (sfLDOF, sfLDPocock) or bound types (“OF”, “Pocock”) that do not require parameters.
tol: Tolerance for error (default is 0.000001). Normally this will not be changed by the user. This does not translate directly to number of digits of accuracy, so use extra decimal places.
r: Integer value controlling grid for numerical integration as in Jennison and Turnbull (2000); default is 18, range is 1 to 80. Larger values provide larger number of grid points and greater accuracy. Normally r will not be changed by the user.

Value

Object containing the following elements:

reject: Whether the null hypothesis was rejected in the simulated trial.
k_i: Interim analysis at which simulated trial was stopped.
m_i: Number of clusters per arm when the simulated trial was stopped.
n_i: Average number of individuals per cluster when the simulated trial was stopped.
total_i: Total number of individuals per arm when the simulated trial was stopped.
i_frac: Information fraction when the simulated trial was stopped.

Author

Lee Ding lee_ding@g.harvard.edu