Compute stopping boundaries, maximum sample size, and expected sample sizes for a group sequential cluster randomized trial.

gsDesignCRT() is used to determine the maximum sample size needed for a specified parallel group sequential cluster randomized trial to detect a clinically meaningful effect size with some Type I error rate and power. Code adapted from gsDesign package.

Usage

gsDesignCRT(
  k = 3,
  outcome_type = 1,
  test_type = 1,
  test_sides = 1,
  size_type = 1,
  recruit_type = 1,
  timing_type = 2,
  delta = 1,
  sigma_vec = c(1, 1),
  p_vec = c(0.5, 0.5),
  rho = 0,
  alpha = 0.05,
  beta = 0.1,
  m_fix = 1,
  n_fix = 1,
  info_timing = 1,
  size_timing = 1,
  alpha_sf = sfLDOF,
  alpha_sfpar = -4,
  beta_sf = sfLDOF,
  beta_sfpar = -4,
  tol = 1e-06,
  r = 18
)

Arguments

k: Number of analyses planned, including interim and final.
outcome_type: 1=continuous difference of means
2=binary difference of proportions
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
size_type: 1=clusters per arm
2=cluster size
recruit_type: 1=recruit clusters with fixed sizes
2=recruit individuals into fixed number of clusters
3=recruit both clusters and individuals
timing_type: 1= maximum and expected sample sizes based on specified information levels in info_timing
2= maximum sample size based on specified information levels in info_timing and expected sample sizes based on specified sample size levels in size_timing
delta: Effect size for theta under alternative hypothesis. Must be > 0.
sigma_vec: Standard deviations for control and treatment groups (continuous case).
p_vec: Probabilities of event for control and treatment groups (binary case).
rho: Intraclass correlation coefficient. Default value is 0.
alpha: Type I error, default value is 0.05.
beta: Type II error, default value is 0.1 (90% power).
m_fix: Number of clusters; used to find maximum size of each cluster.
n_fix: Mean size of each cluster; used to find maximum number of clusters per arm.
info_timing: Sets timing of interim analyses based on information levels. Default of 1 produces analyses at equal-spaced increments. Otherwise, this is a vector of length k or k-1. The values should satisfy 0 < info_timing[1] < info_timing[2] < ... < info_timing[k-1] < info_timing[k]=1.
size_timing: Sets timing of interim analyses based on sample size levels if timing_type = 2. Default of 1 produces analyses at equal-spaced increments. Otherwise, this is a vector of length k or k-1. The values should satisfy 0 < size_timing[1] < size_timing[2] < ... < size_timing[k-1] < size_timing[k]=1.
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:

k: As input.
outcome_type: As input.
test_type: As input.
test_sides: As input.
size_type: As input.
recruit_type: As input.
timing_type: As input.
delta: As input.
sigma_vec: As input.
p_vec: As input.
rho: As input.
alpha: As input.
beta: As input.
info_timing: As input.
size_timing: As input.
i: Fisher information at each planned interim analysis based on timing_type.
max_i: Maximum information corresponding to design specifications.
m: Number of clusters per arm at each planned interim analysis.
max_m: Maximum number of clusters per arm.
e_m: A vector of length 2 with expected number of clusters per arm under the null and alternative hypotheses. For simplicity, the expected sizes with non-binding futility boundaries are calculated assuming the boundaries are binding futility.
n: Average cluster size at each planned interim analysis.
max_n: Maximum cluster size.
e_m: A vector of length 2 with expected cluster sizes under the null and alternative hypotheses. For simplicity, the expected sizes with non-binding futility boundaries are calculated assuming the futility boundaries are binding.
max_total: Maximum number of individuals in the trial.
e_total: A vector of length 2 with expected number of individuals in the trial under the null and alternative hypotheses. For simplicity, the expected sizes with non-binding futility boundaries are calculated assuming the futility boundaries are binding.
sufficient: Value denoting whether calculated sample size will be sufficient to achieve specified Type I error rate and power given the trial specifications.
lower_bound: Calculated lower futility boundaries under analysis schedule specified by timing_type
upper_bound: Calculated upper efficacy boundaries under analysis schedule specified by timing_types.
tol: As input.
r: As input.

References

Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.

Author

Lee Ding lee_ding@g.harvard.edu