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,
  timing_type = 2,
  recruit_type = 1,
  delta = 1,
  sigma_vec = c(1, 1),
  p_vec = c(0.5, 0.5),
  rho = 0,
  alpha = 0.05,
  beta = 0.1,
  m = 2,
  m_alloc = c(0.5, 0.5),
  n = 1,
  n_cv = c(0, 0),
  info_timing = 1,
  m_timing = c(1, 1),
  n_timing = c(1, 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
timing_type: 1= maximum and expected sample sizes based on specified information fractions in info_timing; recruit according to design specified in recruit_type
2= maximum sample size based on specified information fractions in info_timing and expected sample sizes based on specified sample size fractions in m_timing and n_timing
3= maximum and expected sample sizes based on specified sample size fractions in m_timing and n_timing @param recruit_type 1=recruit clusters with fixed sizes
2=recruit individuals into fixed number of clusters
3=recruit at both cluster and individual levels
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: Number of clusters for finding maximum mean cluster size. If m is a scalar, it is treated as the total number of clusters across arms. If m is a vector of length 2, it is treated as the number of clusters per arm.
m_alloc: Allocation ratio of clusters per arm. Default is c(0.5, 0.5).
n: Mean cluster size for finding maximum number of clusters. If n is a scalar, it is treated as the average cluster size for both arms. If n is a vector of length 2, it is treated as the average cluster size per arm.
n_cv: Coefficient of variation for cluster size. If n_cv is a scalar, it is treated as the coefficient of variation for both arms. If n_cv is a vector of length 2, it is treated as the coefficient of variation per arm.
info_timing: Sets timing of interim analyses based on information fractions. 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.
m_timing: Sets timing of interim analyses based on fractions of the number of clusters.
n_timing: Sets timing of interim analyses based on cluster size
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.
m_timing: As input.
n_timing: As input.
info_schedule: Fraction of maximum information at each planned interim analysis based on timing_type and info_timing.
m_schedule: Fraction of maximum number of clusters per arm at each planned interim analysis based on timing_type and m_timing.
n_schedule: Fraction of maximum cluster size at each planned interim analysis based on timing_type and n_timing.
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: Mean cluster size at each planned interim analysis.
max_n: Maximum mean cluster size.
e_n: A vector of length 2 with expected mean 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 total 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.

Anderson K (2025). gsDesign: Group Sequential Design. R package version 3.8.0, https://keaven.github.io/gsDesign/.

Author

Lee Ding lee_ding@g.harvard.edu