one_stage_multiarm {PlatformDesign}

Calculate the sample sizes and other design parameters for an one-stage K-experimental arm trial using the root-K rule for the allocation ratio, controlling for FWER or PWER

Description

This function can be used to design a K-experimental arm trial (with K experimental arm plus a common control arm) given a pre-planned family-wise error rate (or pair-wise error rate) and with a user-specified marginal power. It calculates required sample sizes for each of the experimental arm (n1), the control arm (n0_1), the total sample size (N1), and the critical value (z_alpha1) for each experimental arm-control comparison in the trial.

Usage

one_stage_multiarm(
  K,
  fwer = NULL,
  pwer = NULL,
  marginal.power,
  delta,
  seed = 123
)

Arguments

K

the number of experimental arms

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 choosing fwer

pwer

the pair-wise type I error rate, default to be null, users need to input a value for this argument if controlling for pwer

marginal.power

the marginal power for each experimental-control comparison

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

Given the number of experimental arms (K), the family-wise type I error rate (or the pair-wise type-I error-rate), the marginal power for each experimental-control comparison and the standardized effect size, to calculate the sample sizes and other design parameters for the K-experimental arm trial (with K-experimental arm in addition to one control arm).

Value

K the number of experimental arms in the K-experimental arm trial (with K experimental arm plus a common control arm), e.g., for a 3-arm trial with 3 experimental arm and 1 control arm, K=3.

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 arm and its corresponding control

FWER1 the family-wise type-I error rate

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

Power1 the disjunctive power of the K-experimental arm trial defined as the probability of rejecting at least one of the K experimental arms under the alternative hypothesis

corMat1 the correlation matrix of the Z-test statistics

delta the standardized effect size expected to be detected in the K-experimental arm trial

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

# controlling for FWER
one_stage_multiarm(K = 2, fwer = 0.025, marginal.power = 0.8, delta = 0.4)
#$K
#[1] 2
#
#$n1
#[1] 101
#
#$n0_1
#[1] 143
#
#$N1
#[1] 345
#
#$z_alpha1
#[1] 2.220604
#
#$FWER1
#[1] 0.025
#
#$z_beta1
#[1] 0.8416212
#
#$Power1
#[1] 0.9222971
#
#$corMat1
#[,1]      [,2]
#[1,] 1.0000000 0.4142136
#[2,] 0.4142136 1.0000000
#
#$delta
#[1] 0.4
#
# controlling for pwer
one_stage_multiarm(K = 2, pwer = 0.025, marginal.power = 0.8, delta = 0.4)
#$K
#[1] 2
#
#$n1
#[1] 84
#
#$n0_1
#[1] 119
#
#$N1
#[1] 287
#
#$z_alpha1
#[1] 1.959964
#
#$FWER1
#[1] 0.04647892
#
#$z_beta1
#[1] 0.8416212
#
#$Power1
#[1] 0.9222971
#
#$corMat1
#[,1]      [,2]
#[1,] 1.0000000 0.4142136
#[2,] 0.4142136 1.0000000
#
#$delta
#[1] 0.4