| platform_design2 {PlatformDesign} | R Documentation |
A faster version of platform_design()
Description
The function platform_design2() is a faster version of platform_design(). It adopts a more efficient algorithm to 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_design2(
nt,
K,
M,
fwer = NULL,
pwer = NULL,
marginal.power,
min.marginal.power = marginal.power,
delta,
seed = 123
)
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 |
Details
This function is basically a faster version of platform_design(). Just like the latter, It provides 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 algorithm searches for the optimal design starting from the maximum N2 until it reaches a design meets the requirements for both marginal and disjunctive power levels for the K+M-experimental arm trial. If the function returns NULL for $design, the optimal design for the K+M-experimental arm trial does not exists because the lower limits of marginal and disjunctive power cannot be met at the same time given the inputs. Unlike the platform_design(), the suboptimal design (i.e., the design only meets the requirement for the disjunctive power) is not provided.
Value
The function returns a list, including design_Karm and designs.
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.
Author(s)
Xiaomeng Yuan, Haitao Pan
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
platform_design2(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
#39 107 198 30 43 241 669
#40 106 202 30 43 245 669
#41 105 206 30 43 249 669
#42 104 210 30 43 253 669
#
# A1 A2 cor1 cor2 critical_value2
#39 1.414214 2.012987 0.3508197 0.2746316 2.475233
#40 1.414214 2.092105 0.3441558 0.2708949 2.475790
#41 1.414214 2.173333 0.3376206 0.2671464 2.476330
#42 1.414214 2.256757 0.3312102 0.2633910 2.476854
#
# marginal.power2 disjunctive.power2
#39 0.8001100 0.9853799
#40 0.8003363 0.9857541
#41 0.8003878 0.9860900
#42 0.8002699 0.9863903
#
# FWER2 delta save
#39 0.025 0.4 21
#40 0.025 0.4 21
#41 0.025 0.4 21
#42 0.025 0.4 21