platform_design: Design an optimal two-period multiarm platform trial with new experimental arms added during the trial, controlling for FWER or PWER

Description

Find optimal design(s) for a two-period K+M experimental arm platform trial given a user-specified family-wise error rate (or pair-wise error rate) and marginal power. The K+M-experimental arm trial has K experimental arms and one control arm during the first period, and later M experimental arms are added on the start of the second period. The one common control arm is shared among all experimental arms across the trial. The function calculates required sample sizes for each of the experimental arm (n2), the concurrent control (n0_2), the total sample size (N2), the allocation ratios (A1 & A2), and the critical value (z_alpha1) for each experimental arm-control comparison in the trial. The number of patients saved in a K+M-experimental arm trial compared to conducting one K-experimental arm and one M-experimental arm trial separately is also provided. Users can choose to control for either FWER or PWER in the trial.

Usage

platform_design(
  nt,
  K,
  M,
  fwer = NULL,
  pwer = NULL,
  marginal.power,
  min.marginal.power = marginal.power,
  delta,
  seed = 123
)

Value

The function returns a list, including design_Karm, designs, flag.dp, flag.mp, and flag.dpmp.

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

K, the number of experimental arms

n1, the sample size for each of the K experimental arms

n0_1, the sample size of the common control arm

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

FWER1, the family-wise error rate

z_beta1, the quantile of the marginal power, i.e., qnorm(marginal power)

Power1, the disjunctive power

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 K-experimental arm 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 arms and its corresponding concurrent control, respectively

nt and n0t, the number of patients already enrolled on each of the K initial experimental arms and the 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 trial, i.e. , the sum of the 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 (control to experimental arm) 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 initial experimental arms (or between any two of the M new 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 arm and the concurrent 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 type-I error rate for the K+M-experimental arm trial

delta, the standardized effect size expected to be detected in the K+M-experimental arm 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.

flag.dp, flag.mp, and flag.dpmp indicate if the lower limit of disjunctive power, marginal power, or both of them has(have) met, respectively

Arguments

nt: the number of patients already enrolled on each of the K initial experimental arms at the time the M new arms are added.
K: the number of experimental arms in the first period in a two-period K+M-experimental arm trial
M: the number of new experimental arms added at the start of the second period
fwer: the family-wise type I error rate, default to be null, users need to choose between controlling for fwer or pwer and input a value for this argument if fwer is chosen
pwer: the pair-wise type I error rate, default to be null, users need to choose between controlling for fwer or pwer and input a value for this argument if pwer is chosen
marginal.power: the marginal power for each experimental-control comparison in the K-experimental arm trial. This is also the marginal power the algorithm aims to achieve in the K+M-experimental arm when min.marginal.power=marginal.power (default option).
min.marginal.power: the marginal power the function aims to achieve in the K+M-experimental arm trial, default to be the same as the marginal power of the K-experimental arm trial. It will be the marginal power of the K+M-experimental arm if optimal design exists. Don't change the default unless you need to achieve a marginal power level different than that of the K-experimental arm trial.
delta: the standardized effect size expected to be detected in the trial
seed: an integer used in random number generation for numerically evaluating integration, default = 123

Author

Xiaomeng Yuan, Haitao Pan

Details

Providing an optimized design in terms of minimizing the total sample size for adding M additional experimental arms in the middle of a clinical trial which originally have K experimental arms and 1 control arm, given user-defined FWER (or PWER) and marginal power. The optimal design for the K+M-experimental arm trial exists only if flag.dpmp = 0. It means that the optimal design can be found to keep both marginal and disjunctive power levels no less than those in the corresponding K-experimental arm trial. If flag.dpmp = 1 and flag.mp = 1, it means the optimal design to maintain both mariginal and disjunctive power levels can not be found, but the a design with the disjunctive power no less than its counterpart in the K-experimental arm trial is returned in designs.

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

platform_design(nt = 30, K = 2, M = 2, fwer = 0.025, marginal.power = 0.8,
 delta = 0.4)
#flag.dpmp == 0, lower limits of marginal and disjunctive power are both met
#
#$design_Karm
#   K  n1 n0_1  N1  z_alpha1 FWER1   z_beta1      Power1      cor0   delta
# 1 2 101  143 345  2.220604 0.025 0.8416212   0.9222971 0.4142136   0.4
#
#$designs
#       n2 n0_2 nt n0t  nc  N2
#15669 107  198 30  43 241 669
#15994 106  202 30  43 245 669
#16315 105  206 30  43 249 669
#16632 104  210 30  43 253 669
#
#        A1       A2       cor1      cor2          critical_value2
#15669 1.414214 2.012987 0.3508197 0.2746316       2.475233
#15994 1.414214 2.092105 0.3441558 0.2708949       2.475790
#16315 1.414214 2.173333 0.3376206 0.2671464       2.476330
#16632 1.414214 2.256757 0.3312102 0.2633910       2.476854
#
#      marginal.power2 disjunctive.power2
#15669  0.8001100      0.9853799
#15994  0.8003363      0.9857541
#16315  0.8003878      0.9860900
#16632  0.8002699      0.9863903
#
#         FWER2    delta     save
#15669    0.025      0.4       21
#15994    0.025      0.4       21
#16315    0.025      0.4       21
#16632    0.025      0.4       21
#
#$flag.dp
#[1] 0
#
#$flag.mp
#[1] 0
#
#$flag.dpmp
#[1] 0

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