one_design: Calculate other design parameters of a two-period K+M-experimental arm platform design given sample sizes

Description

Provide other design parameters for a two-period K+M-experimental arm trial, given n2 and n0_2, nt, K, M, fwer(or pwer) and marginal power (of the K-experimental arm trial). This function serves for the purpose of spot-testing for any pre-specified n, n0_2 pair. Please use platform_design() for finding optimal values of n and n0_2, controlling for FWER (or PWER).

Usage

one_design(
  n2,
  n0_2,
  nt,
  K,
  M,
  fwer = NULL,
  pwer = NULL,
  marginal.power,
  delta,
  seed = 123
)

Value

design_Karm contains the design parameters for the K-experimental arm trial including:

K, the number of experimental arms in the K-experimental arm trial

n1, the sample size for each of the K experimental arms in the k-experimental arm trial

n0_1, the sample size of the common control arm in the K-experimental arm trial

N1 the total sample size of a K-experimental arm trial

z_alpha1, the critical value for the comparison between any of the K experimental arms and the control in the K-experimental arm trial

FWER1, the family-wise error rate for the K-experimental arm trial

z_beta1, the quantile of the marginal power, i.e., qnorm(marginal power) for the K-experimental arm trial

Power1, the disjunctive power for the K-experimental arm trial

cor0, the correlation of Z-test statistics between any two of the K experimental arms

delta, the standardized effect size expected to be detected in the trial

designs contains the recommended optimal design parameters for the K+M-experimental arm trial including:

n2 and n0_2, the sample sizes of each of the K+M-experimental arm experimental arms and its corresponding concurrent control, respectively, in the K+M-experimental arm trial

nt and n0t, the number of patients already enrolled on each of the K initial experimental arms and the common control arm, respectively, at the time the M new arms are added

nc, the total sample size of the control arm for the K+M-experimental arm trial, i.e. , the sum of concurrent (n0_2) and nonconcurrent (n0t) controls

N2, the total sample size of the two-period K+M-experimental arm trial

A1, the allocation ratio (control to experimental arm) before the M new experimental arms are added and after the initial K experimental arms end

A2, the allocation ratio after the M new experimental arms are added and before the initial K experimental arms end

cor1, the correlation of Z-test statistics between any two of the K initially opened experimental arms (or between any two of the M newly added arms)

cor2, the correlation of Z-test statistics between any pair of one initially opened and one newly added experimental arm

critical_value2, the critical value for the comparison between each experimental arms and the corresponding control in the K+M-experimental arm trial

mariginal.power2, the marginal power for the K+M-experimental arm trial

disjunctive.power2, the disjunctive power for the K+M-experimental arm trial

FWER2, the family-wise error rate for the K+M-experimental arm trial.

delta, the standardized clinical effect size expected to be detected in the trial

save, the number of patients saved in the K+M-experimental arm trial compared to conducting one K-experimental arm and one M-experimental arm trial, separately.

Arguments

n2: a positive integer, which is the sample size in each experimental arm in the K+M-experimental arm trial
n0_2: a positive integer, which is the sample size of the concurrent control for each experimental arms in the K+M-experimental arm trial
nt: a positive integer, the number of patients already enrolled on each of the K initial experimental arms when the M new arms are added
K: a positive integer, the number of experimental arms in the first period in a two-period K+M-experimental arm trial
M: a positive integer, the number of delayed (newly added) experimental arms added in the beginning of the second period of the K+M-experimental arm trial
fwer: the family-wise error rate (FWER) to be controlled, default to be the same throughout the trial
pwer: the pair-wise error rate (PWER) to be controlled, default to be the same throughout the trial
marginal.power: the marginal power to achieve in the K-experimental arm (and K+M-experimental arm) trial
delta: the standardized clinical effect size expected to be detected in the trial
seed: an integer for random number generation for numerically evaluating integration, default = 123

Author

Xiaomeng Yuan, Haitao Pan

Details

Given n2 and n0_2, nt, K, M, fwer (or pwer) and marginal power (of the K-experimental arm trial), provide other design parameters for a two-period K+M-experimental arm trial.

References

Pan, H., Yuan, X. and Ye, J. (2022). An optimal two-period multiarm platform design with new experimental arms added during the trial. Manuscript submitted for publication.

Dunnett, C. W. (1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50(272), 1096-1121.

Examples

Run this code

# control fwer
one_design(n2 = 107, n0_2 = 198, nt = 30, K = 2, M = 2, fwer = 0.025,
           marginal.power = 0.8, delta = 0.4)
#$design_Karm
#  K  n1 n0_1  N1 z_alpha1 FWER1   z_beta1    Power1      cor0 delta
#1 2 101  143 345 2.220604 0.025 0.8416212 0.9222971 0.4142136   0.4
#
#$designs
#   n2 n0_2 nt n0t  nc  N2       A1       A2      cor1      cor2 critical_value2
#1 107  198 30  43 241 669 1.414214 2.012987 0.3508197 0.2746316        2.475233
#
#  marginal.power2  disjunctive.power2 FWER2 delta save
#1    0.80011                0.9853799 0.025   0.4   21
#
# control pwer
one_design(n2 = 76, n0_2 = 140, nt = 30, K = 2, M = 2, pwer = 0.025,
             marginal.power = 0.8, delta = 0.4)
#$design_Karm
#  K n1 n0_1  N1 z_alpha1      FWER1   z_beta1    Power1      cor0 delta
#1 2 84  119 287 1.959964 0.04647892 0.8416212 0.9222971 0.4142136   0.4
#
#$designs
#  n2 n0_2 nt n0t  nc  N2       A1       A2      cor1      cor2 critical_value2
#1 76  140 30  43 183 487 1.414214 2.108696 0.3518519 0.2437831        1.959964
#  marginal.power2  disjunctive.power2      FWER2 delta save
#1       0.8001424           0.9867451 0.08807302   0.4   87

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