N.APPLE.plus: APPLE+ sample size computation

Description

Perform the sample size calculation given the power and post-delay hazard ratio using the close-form APPLE+ method based on the generalized piecewise weighted log-rank test when the treatment time-lag effect is present and the lag duration varies heterogeneously from individual to individual or from study to study, within a certain domain and following a specific pattern.

Usage

N.APPLE.plus(lambda1, tl, tu, HR, tao, A, beta, ap=0.5, alpha=0.05)

Value

The sample size

Arguments

lambda1: Baseline hazard
tl: Lower bound of delayed duration domain
tu: Upper bound of delayed duration domain
HR: Post-delay hazard ratio after tu, defined as the post-delay hazard rate of the treatment group compared to that of the control group
tao: Total study duration
A: Total enrollment duration
beta: Type II error rate; Power=1-beta
ap: Experimental-control allocation ratio. The default is 0.5.
alpha: Type I error rate (two-sided). The default is 0.05.

Author

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

Details

APPLE+ is an acronym for:
Analytic Power calculation method based on generalized Piecewise weighted Log-rank tEst with random treatment time-lag effect. See the reference for details of this method.

References

Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random treatment time-lag effect. Biometrika. Under review.

Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with delayed treatment effect. Statistics in medicine, 36(4), 592-605.

Examples

Run this code

  lambda1 <- 0.001982
  tl      <- 30
  tu      <- 30*11
  HR      <- 1.3
  tao     <- 365*3
  A       <- 365
  beta    <- 0.2
  N.APPLE.plus(lambda1, tl, tu, HR, tao, A, beta)

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