Package {DACT}

Three-stage design

Description

Three-stage design

Usage

EXP_3_stg_sz(alpha, beta, p_0, p_low, p_1, d_23_cut)

Arguments

Value

n1: Number of patients at first look. n1 for the three-stage design is the from Simon’s design with p=p_1.

n_2: Number of patients at second look. n_2 for the three-stage design is the n1 from Simon’s design with p=p_low.

r1: If no more than r1 responses are observed at the first look, then the trial would be stopped for futility.

r_2: The null hypothesis will be rejected if at least r_2 responses are observed at the end of the trial.

EN(p0) is the expected sample size under the null hypothesis.

PET(p0) is the probability of early termination under the null hypothesis.

PET_p is the probability of early termination under p=p_1.

PET_p_low is the probability of early termination under p=p_low.

power_p_1 is the power under p=p_1.

power_p_low is the power under p=p_low.

Type I error is the probability of rejecting the null hypothesis under p<=p_0.

The minimax design has the smallest n_2 among all possible choices of (n1,r1,n_2,r_2).

The optimal design has the smallest EN(p0) among all possible choices of (n1,r1,n_2,r_2).

The n1 and n_2 for the average design is the average of n1's and n_2's from the minimax and the optimal designs.

References

R. Simon. Optimal Two-Stage Designs for Phase II Clinical Trials. Controlled Clinical Trials 10:1-10 (1989).

P. Gao & W. Zhang (15 Apr 2024): Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon’s design, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2341673. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2341673.

Examples

EXP_3_stg_sz(alpha=c(0.001,0.024),beta=0.1,p_0=0.2,p_low=0.33,p_1=0.4,d_23_cut=5)

Multiple comparisons Group sequential design: Binary distribution, Sample size calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Binary distribution, Sample size calculation, O'Brien-Fleming boundary

Usage

MSD_Sample_size_OF_boundary_binary_diff(
  p_t,
  p_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_OF_boundary_binary_diff(p_t = 0.4, p_c = 0.3, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1,
rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Negative binomial distribution, Sample size calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Negative binomial distribution, Sample size calculation, O'Brien-Fleming boundary

Usage

MSD_Sample_size_OF_boundary_neg_binomial(
  r_t,
  r_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  nu_t,
  kappa,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control', 'Reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_OF_boundary_neg_binomial(r_t = c(1.1, 1.1, 1.1), r_c = 1.1, margin = 0.1,
direction = 0, s = c(1/3, 2/3, 1),
alpha = 0.025, beta = 0.1, rand_ratio = 1, nu_t = 6, kappa = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Normal distribution, Sample size calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Normal distribution, Sample size calculation, O'Brien-Fleming boundary

Usage

MSD_Sample_size_OF_boundary_normal(
  mu_t,
  mu_c,
  std_t,
  std_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_OF_boundary_normal(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86,
margin = 0.1, direction = 0, s = c(1/3, 2/3, 1),
alpha = 0.025, beta = 0.1, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Poisson distribution, Sample size calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Poisson distribution, Sample size calculation, O'Brien-Fleming boundary

Usage

MSD_Sample_size_OF_boundary_poisson(
  lambda_t,
  lambda_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_OF_boundary_poisson(lambda_t = 1.1, lambda_c = 1.0, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025,
beta = 0.1, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Survival analysis, Sample size calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Survival analysis, Sample size calculation, O'Brien-Fleming boundary

Usage

MSD_Sample_size_OF_boundary_survival_Schoenfeld(
  HR,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'Combined number of events between a dose and control', 'total number of events from all doses and control', 'combined number of events in each dose and control in a two arm study with same critical boudary', 'Type I error control', 'reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_OF_boundary_survival_Schoenfeld(HR = 0.7, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Binary distribution, Sample size calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Binary distribution, Sample size calculation, Alpha-spending boundary

Usage

MSD_Sample_size_alsp_boundary_binary_diff(
  p_t,
  p_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_alsp_boundary_binary_diff(p_t = 0.4, p_c = 0.3, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Negative binomial distribution, Sample size calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Negative binomial distribution, Sample size calculation, Alpha-spending boundary

Usage

MSD_Sample_size_alsp_boundary_neg_binomial(
  r_t,
  r_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  nu_t,
  kappa,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control', 'Reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_alsp_boundary_neg_binomial(r_t = c(0.2,0.3,0.4), r_c = 0.6, margin = 0.1,
direction = 1, s = c(1/3,2/3,1), alpha = c(0.001,0.001,0.023), beta = 0.1, rand_ratio = 1,
nu_t = 1, kappa = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Normal distribution, Sample size calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Normal distribution, Sample size calculation, Alpha-spending boundary

Usage

MSD_Sample_size_alsp_boundary_normal(
  mu_t,
  mu_c,
  std_t,
  std_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_alsp_boundary_normal(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86,
margin = 0.1, direction = 0, s = c(1/3, 2/3, 1),
alpha = 0.025, beta = 0.1, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Poisson distribution, Sample size calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Poisson distribution, Sample size calculation, Alpha-spending boundary

Usage

MSD_Sample_size_alsp_boundary_poisson(
  lambda_t,
  lambda_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'test arm sample size', 'control arm sample size', 'sample size for each dose in a two arm study with same critical boudary', 'sample size for control arm corresponding to each dose in a two arm study with same critical boudary', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_alsp_boundary_poisson(lambda_t = 1.1, lambda_c = 1.0, margin = 0.1,
direction = 0, s = c(1/3, 2/3, 1), alpha = 0.025,
beta = 0.1, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Survival analysis, Sample size calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Survival analysis, Sample size calculation, Alpha-spending boundary

Usage

MSD_Sample_size_alsp_boundary_survival_Schoenfeld(
  HR,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'Combined number of events between a dose and control', 'total number of events from all doses and control', 'combined number of events in each dose and control in a two arm study with same critical boudary', 'Type I error control', 'reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_Sample_size_alsp_boundary_survival_Schoenfeld(HR = 0.7, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1,
rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Binary distribution, Power calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Binary distribution, Power calculation, O'Brien-Fleming boundary

Usage

MSD_power_OF_boundary_binary_diff(
  p_t,
  p_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_OF_boundary_binary_diff(p_t = 0.4, p_c = 0.3, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, sampsz_control = 100,
rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Negative binomial distribution, Power calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Negative binomial distribution, Power calculation, O'Brien-Fleming boundary

Usage

MSD_power_OF_boundary_neg_binomial(
  r_t,
  r_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  nu_t,
  kappa,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control', 'Reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_OF_boundary_neg_binomial(r_t = c(1.1, 1.1, 1.1), r_c = 1.1, margin = 0.1,
direction = 0, s = c(1/3, 2/3, 1), alpha = 0.025, sampsz_control = 100, rand_ratio = 1,
nu_t = 6, kappa = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Normal distribution, Power calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Normal distribution, Power calculation, O'Brien-Fleming boundary

Usage

MSD_power_OF_boundary_normal(
  mu_t,
  mu_c,
  std_t,
  std_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_OF_boundary_normal(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86, margin = 0.1,
direction = 0, s = c(1/3, 2/3, 1),
alpha = 0.025, sampsz_control = 100, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Poisson distribution, Power calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Poisson distribution, Power calculation, O'Brien-Fleming boundary

Usage

MSD_power_OF_boundary_poisson(
  lambda_t,
  lambda_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_OF_boundary_poisson(lambda_t = 1.1, lambda_c = 1.0, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, sampsz_control = 100, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Survival analysis, Power calculation, O'Brien-Fleming boundary

Description

Multiple comparisons Group sequential design: Survival analysis, Power calculation, O'Brien-Fleming boundary

Usage

MSD_power_OF_boundary_survival_Schoenfeld(
  HR,
  margin,
  direction,
  s,
  alpha,
  events_tot,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control', 'reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_OF_boundary_survival_Schoenfeld(HR = 0.7, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, events_tot = 100,
rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Binary distribution, Power calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Binary distribution, Power calculation, Alpha-spending boundary

Usage

MSD_power_alsp_boundary_binary_diff(
  p_t,
  p_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_alsp_boundary_binary_diff(p_t = c(0.2,0.3,0.4), p_c = 0.5, margin = 0.1,
direction = 1, s = c(1/3,2/3,1), alpha = c(0.001,0.001,0.048), sampsz_control = 68,
rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Negative binomial distribution, Power calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Negative binomial distribution, Power calculation, Alpha-spending boundary

Usage

MSD_power_alsp_boundary_neg_binomial(
  r_t,
  r_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  nu_t,
  kappa,
  dist
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control', 'Reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_alsp_boundary_neg_binomial(r_t=c(0.2,0.3,0.4), r_c=0.6, margin=0.1, direction=1,
s=c(1/3,2/3,1), alpha = c(0.001,0.001,0.023), sampsz_control = 90, rand_ratio = 1,
nu_t = 1, kappa = 1, dist = 1)

Multiple comparisons Group sequential design: Normal distribution, Power calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Normal distribution, Power calculation, Alpha-spending boundary

Usage

MSD_power_alsp_boundary_normal(
  mu_t,
  mu_c,
  std_t,
  std_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_alsp_boundary_normal(mu_t = c(0.2,0.3,0.4), mu_c = 0, std_t = 1, std_c = 1,
margin = 0, direction = 1, s = c(1/3,2/3,1),
alpha = c(0.001,0.001,0.023), sampsz_control = 148, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Poisson distribution, Power calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Poisson distribution, Power calculation, Alpha-spending boundary

Usage

MSD_power_alsp_boundary_poisson(
  lambda_t,
  lambda_c,
  margin,
  direction,
  s,
  alpha,
  sampsz_control,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_alsp_boundary_poisson(lambda_t = c(0.2,0.3,0.4), lambda_c = 0.5, margin = 0.1,
direction = 2, s = c(1/3,2/3,1),
alpha = c(0.001,0.001,0.023), sampsz_control = 67, rand_ratio = 1, dist1 = 1, dist2 = 1)

Multiple comparisons Group sequential design: Survival analysis, Power calculation, Alpha-spending boundary

Description

Multiple comparisons Group sequential design: Survival analysis, Power calculation, Alpha-spending boundary

Usage

MSD_power_alsp_boundary_survival_Schoenfeld(
  HR,
  margin,
  direction,
  s,
  alpha,
  events_tot,
  rand_ratio,
  dist1,
  dist2
)

Arguments

Value

A named list containing the following elements: 'power', 'Type I error control', 'reference'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

MSD_power_alsp_boundary_survival_Schoenfeld(HR = c(0.2,0.3,0.4), margin = 1.1, direction = 2,
s = c(1/3,2/3,1), alpha = c(0.001,0.001,0.023),
events_tot = 17, rand_ratio = 1, dist1 = 1, dist2 = 1)

Group sequential designs / Adaptive sequential designs: Binary distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Binary distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_binary_diff(p_t, p_c, s, alpha_2, beta, rand_ratio)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_binary_diff(p_t = 0.4, p_c = 0.3, s = c(1/3, 2/3, 1),
alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Binary distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Binary distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_binary_diff_NI(
  p_t,
  p_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_binary_diff_NI(p_t = 0.4, p_c = 0.3, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_neg_binomial(
  r_t,
  r_c,
  s,
  alpha_2,
  beta,
  rand_ratio,
  nu_t,
  kappa
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_neg_binomial(r_t = 0.2, r_c = 0.4, s = c(1/3,2/3,1), alpha_2 = 0.05,
beta = 0.1, rand_ratio = 1, nu_t = 1, kappa = 1)

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_neg_binomial_NI(
  r_t,
  r_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  nu_t,
  kappa
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_neg_binomial_NI(r_t = 0.2, r_c = 0.4, margin = 0.1, direction = 1,
s = c(1/3,2/3,1), alpha = 0.025, beta = 0.1, rand_ratio = 1, nu_t = 1, kappa = 1)

Group sequential designs / Adaptive sequential designs: Normal distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Normal distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_normal(
  mu_t,
  mu_c,
  std_t,
  std_c,
  s,
  alpha_2,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_normal(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86,
s = c(1/3, 2/3, 1), alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Normal distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Normal distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_normal_NI(
  mu_t,
  mu_c,
  std_t,
  std_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_normal_NI(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86,
margin = 0.1, direction = 0, s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Poisson distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Poisson distribution, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_poisson(
  lambda_t,
  lambda_c,
  s,
  alpha_2,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_poisson(lambda_t = 1.1, lambda_c = 1.0, s = c(1/3, 2/3, 1),
alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Poisson distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Poisson distribution, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_poisson_NI(
  lambda_t,
  lambda_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_poisson_NI(lambda_t = 1.1, lambda_c = 1.0, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Survival analysis, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Survival analysis, Superiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_survival_Schoenfeld(HR, s, alpha_2, beta, rand_ratio)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_survival_Schoenfeld(HR = 0.7, s = c(1/3, 2/3, 1),
alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Survival analysis, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Description

Group sequential designs / Adaptive sequential designs: Survival analysis, Non-inferiority trial, Sample size calculation, O'Brien-Fleming boundary

Usage

Sample_size_OF_boundary_survival_Schoenfeld_NI(
  HR,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_OF_boundary_survival_Schoenfeld_NI(HR = 0.7, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Binary distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Binary distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_binary_diff(p_t, p_c, s, alpha_2, beta, rand_ratio)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_binary_diff(p_t = 0.2, p_c = 0.6, s = c(1/3,2/3,1),
alpha_2 = c(0.001,0.001,0.048), beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Binary distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Binary distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_binary_diff_NI(
  p_t,
  p_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_binary_diff_NI(p_t = 0.4, p_c = 0.3, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_neg_binomial(
  r_t,
  r_c,
  s,
  alpha_2,
  beta,
  rand_ratio,
  nu_t,
  kappa
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_neg_binomial(r_t = 0.2, r_c = 0.4, s = c(1/3,2/3,1),
alpha_2 = c(0.001,0.001,0.048), beta = 0.1, rand_ratio = 1, nu_t = 1, kappa = 1)

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_neg_binomial_NI(
  r_t,
  r_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  nu_t,
  kappa
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_neg_binomial_NI(r_t = 0.2, r_c = 0.4, margin = 0.1, direction = 1,
s = c(1/3,2/3,1), alpha = c(0.001,0.001,0.023), beta = 0.1, rand_ratio = 1, nu_t = 1, kappa = 1)

Group sequential designs / Adaptive sequential designs: Normal distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Normal distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_normal(
  mu_t,
  mu_c,
  std_t,
  std_c,
  s,
  alpha_2,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_normal(mu_t = 0.2, mu_c = 0, std_t = 1, std_c = 1, s = c(1/3,2/3,1),
alpha_2 = c(0.001,0.001,0.048), beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Normal distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Normal distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_normal_NI(
  mu_t,
  mu_c,
  std_t,
  std_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_normal_NI(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86,
margin = 0.1, direction = 0, s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Poisson distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Poisson distribution, Superiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_poisson(
  lambda_t,
  lambda_c,
  s,
  alpha_2,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_poisson(lambda_t = 0.2, lambda_c = 0.4, s = c(1/3,2/3,1),
alpha_2 = c(0.001,0.001,0.048), beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Poisson distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Poisson distribution, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_poisson_NI(
  lambda_t,
  lambda_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_poisson_NI(lambda_t = 1.1, lambda_c = 1.0, margin = 0.1,
direction = 0, s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Survival analysis, Superiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Survival analysis, Superiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_survival_Schoenfeld(HR, s, alpha_2, beta, rand_ratio)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_survival_Schoenfeld(HR = 0.59, s = c(0.596,1),
alpha_2 = c(0.001,0.0249), beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Survival analysis, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Description

Group sequential designs / Adaptive sequential designs: Survival analysis, Non-inferiority trial, Sample size calculation, Alpha-spending boundary

Usage

Sample_size_alsp_boundary_survival_Schoenfeld_NI(
  HR,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_alsp_boundary_survival_Schoenfeld_NI(HR = 0.7, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Binary distribution, Superiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Binary distribution, Superiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_binary_diff(p_t, p_c, s, alpha_2, beta, rand_ratio)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_binary_diff(p_t = 0.4, p_c = 0.3, s = c(1/3, 2/3, 1),
alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Binary distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Binary distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_binary_diff_NI(
  p_t,
  p_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_binary_diff_NI(p_t = 0.4, p_c = 0.3, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Superiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Superiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_neg_binomial(
  r_t,
  r_c,
  s,
  alpha_2,
  beta,
  rand_ratio,
  nu_t,
  kappa
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_neg_binomial(r_t = 0.2, r_c = 0.4, s = c(1/3,2/3,1),
alpha_2 = 0.05, beta = 0.1, rand_ratio = 1, nu_t = 1, kappa = 1)

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Negative binomial distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_neg_binomial_NI(
  r_t,
  r_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio,
  nu_t,
  kappa
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_neg_binomial_NI(r_t = 0.2, r_c = 0.4, margin = 0.1, direction = 1,
s = c(1/3,2/3,1), alpha = 0.025, beta = 0.1, rand_ratio = 1, nu_t = 1, kappa = 1)

Group sequential designs / Adaptive sequential designs: Normal distribution, Superiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Normal distribution, Superiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_normal(
  mu_t,
  mu_c,
  std_t,
  std_c,
  s,
  alpha_2,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_normal(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86,
s = c(1/3, 2/3, 1), alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Normal distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Normal distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_normal_NI(
  mu_t,
  mu_c,
  std_t,
  std_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_normal_NI(mu_t = 2.6, mu_c = 0.6, std_t = 9.43, std_c = 9.86,
margin = 0.1, direction = 0, s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Poisson distribution, Superiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Poisson distribution, Superiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_poisson(
  lambda_t,
  lambda_c,
  s,
  alpha_2,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_poisson(lambda_t = 0.2, lambda_c = 0.4, s = c(1/3,2/3,1),
alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Poisson distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Poisson distribution, Non-inferiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_poisson_NI(
  lambda_t,
  lambda_c,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_poisson_NI(lambda_t = 1.1, lambda_c = 1.0, margin = 0.1,
direction = 0, s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Survival analysis, Superiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Survival analysis, Superiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_survival_Schoenfeld(
  HR,
  s,
  alpha_2,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_survival_Schoenfeld(HR = 0.7, s = c(1/3, 2/3, 1),
alpha_2 = 0.05, beta = 0.1, rand_ratio = 1)

Group sequential designs / Adaptive sequential designs: Survival analysis, Non-inferiority trial, Sample size calculation, Pocock boundary

Description

Group sequential designs / Adaptive sequential designs: Survival analysis, Non-inferiority trial, Sample size calculation, Pocock boundary

Usage

Sample_size_pocock_boundary_survival_Schoenfeld_NI(
  HR,
  margin,
  direction,
  s,
  alpha,
  beta,
  rand_ratio
)

Arguments

Value

The output will show the sample size for the control arm and the test arm

Examples

Sample_size_pocock_boundary_survival_Schoenfeld_NI(HR = 0.7, margin = 0.1, direction = 0,
s = c(1/3, 2/3, 1), alpha = 0.025, beta = 0.1, rand_ratio = 1)

Phase 2/3 seamless combination Group sequential design: Simulations, Binary distribution, Optimizing adaptive sequential design

Description

Phase 2/3 seamless combination Group sequential design: Simulations, Binary distribution, Optimizing adaptive sequential design

Usage

Two_stage_asd_simu_OC_binary(
  groups,
  p_c,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

P. Gao, Y. Li (05 May 2024): Adaptive two-stage seamless sequential design for clinical trials, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2342518. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2342518

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

Two_stage_asd_simu_OC_binary(
groups = rbind(c(0.3,0.4,0.5),c(0.1,0.2,0.3),c(0.1,0.2,0.3),c(0.1,0.2,0.3)), p_c = 0,
direction = 1, s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05,
alpha_2_alps_s1 = c(0.001,0.001,0.048), alpha_2_alps_s2 = c(0.001,0.049),
theta_cut = 0.01, samsz_1 = 100, samsz_2 = 150, N_max_1 = 200, N_max_2 = 300,
beta = 0.1, sim_num = 2)

Phase 2/3 seamless combination Group sequential design: Simulations, Negative binomial distribution, Optimizing adaptive sequential design

Description

Phase 2/3 seamless combination Group sequential design: Simulations, Negative binomial distribution, Optimizing adaptive sequential design

Usage

Two_stage_asd_simu_OC_neg_binomial(
  groups,
  r_c,
  kappa,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

P. Gao, Y. Li (05 May 2024): Adaptive two-stage seamless sequential design for clinical trials, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2342518. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2342518

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

Two_stage_asd_simu_OC_neg_binomial(
groups = rbind(c(0.3,0.4,0.5),c(0.2,0.2,0.5),c(0.2,0.2,0.3),c(0.2,0.3,0.4)), r_c = 0.2,
kappa = 1, direction = 1, s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05,
alpha_2_alps_s1 = c(0.001,0.001,0.048), alpha_2_alps_s2 = c(0.001,0.049), theta_cut = 0.01,
samsz_1 = 100, samsz_2 = 150, N_max_1 = 200, N_max_2 = 300, beta = 0.1, sim_num = 2)

Phase 2/3 seamless combination Group sequential design: Simulations, Normal distribution, Optimizing adaptive sequential design

Description

Phase 2/3 seamless combination Group sequential design: Simulations, Normal distribution, Optimizing adaptive sequential design

Usage

Two_stage_asd_simu_OC_normal(
  groups,
  mu_c,
  sigma_t,
  sigma_c,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

P. Gao, Y. Li (05 May 2024): Adaptive two-stage seamless sequential design for clinical trials, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2342518. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2342518

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

Two_stage_asd_simu_OC_normal(groups = rbind(c(0.2, 0.3, 0.4), c(0.3, 0.4, 0.5)), mu_c = 0,
sigma_t = 1, sigma_c = 1, direction = 1, s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05,
alpha_2_alps_s1 = c(0.001,0.001,0.048), alpha_2_alps_s2 = c(0.001,0.049), theta_cut = 0.01,
samsz_1 = 100, samsz_2 = 150, N_max_1 = 200, N_max_2 = 300, beta = 0.1, sim_num = 2)

Phase 2/3 seamless combination Group sequential design: Simulations, Poisson distribution, Optimizing adaptive sequential design

Description

Phase 2/3 seamless combination Group sequential design: Simulations, Poisson distribution, Optimizing adaptive sequential design

Usage

Two_stage_asd_simu_OC_poisson(
  groups,
  lambda_c,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

P. Gao, Y. Li (05 May 2024): Adaptive two-stage seamless sequential design for clinical trials, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2342518. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2342518

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

Two_stage_asd_simu_OC_poisson(
groups = rbind(c(0.3,0.4,0.5),c(0.2,0.2,0.5),c(0.2,0.2,0.3),c(0.2,0.3,0.4)), lambda_c = 0.2,
direction = 1, s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05,
alpha_2_alps_s1 = c(0.001,0.001,0.048), alpha_2_alps_s2 = c(0.001,0.049), theta_cut = 0.01,
samsz_1 = 100, samsz_2 = 150, N_max_1 = 200, N_max_2 = 300, beta = 0.1, sim_num = 2)

Phase 2/3 seamless combination Group sequential design: Simulations, Survival analysis, Optimizing adaptive sequential design

Description

Phase 2/3 seamless combination Group sequential design: Simulations, Survival analysis, Optimizing adaptive sequential design

Usage

Two_stage_asd_simu_OC_survival(
  groups,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  surv_rate,
  evt_num_1,
  evt_num_2,
  evt_max_1,
  evt_max_2,
  HR_cut,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

P. Gao, Y. Li (05 May 2024): Adaptive two-stage seamless sequential design for clinical trials, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2342518. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2342518

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

Two_stage_asd_simu_OC_survival(groups = rbind(c(0.75,0.8,0.85),c(0.7,0.75,0.8),c(0.65,0.7,0.75)),
s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05, alpha_2_alps_s1 = c(0.001,0.001,0.048),
alpha_2_alps_s2 = c(0.01,0.04), surv_rate = 0.5, evt_num_1 = 200, evt_num_2 = 300,
evt_max_1 = 500, evt_max_2 = 600, HR_cut = 0.95, beta = 0.1, sim_num = 2)

Group sequential designs / Adaptive sequential designs: Final analysis, With one sample size change

Description

Group sequential designs / Adaptive sequential designs: Final analysis, With one sample size change

Usage

asd_ci_est_back(
  s,
  c_bry,
  snew,
  c_bry_new,
  theta_hat_inter,
  theta_hat_inter_sd,
  inter_vt,
  theta_hat_last_ad,
  theta_hat_last_ad_sd,
  last_vt_ad,
  alpha_2
)

Arguments

Value

A named list containing the following elements: 'p-value', 'confidence interval'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_ci_est_back(s = c(0.3,0.7,1), c_bry = c(4.347011, 2.845787, 2.380956), snew = c(0.5,1),
c_bry_new = c(3.310743, 2.781890), theta_hat_inter = 1.2, theta_hat_inter_sd = 1, inter_vt = 1,
theta_hat_last_ad = 2.2, theta_hat_last_ad_sd = 1, last_vt_ad = 2, alpha_2 = 0.05)

Final analysis: two stage design, with sample size change

Description

Final analysis: two stage design, with sample size change

Usage

asd_ci_est_one_arm_2_stage(p_0, n_1, n_2, r_1_e, r_2, n_new, x_1, x_new, alpha)

Arguments

Value

UL: upper limit of confidence interval.

LL: lower limit of confidence interval.

The results with continuity correction are not necessarily different from those with continuity correction.

The need for continuity correction can be determined through simulations on type I error (see Gao, Zhang, 2004).

References

P. Gao & W. Zhang (15 Apr 2024): Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon’s design, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2341673. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2341673.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_ci_est_one_arm_2_stage( p_0=0.2,n_1=100,n_2=105,r_1_e=33,r_2=29,n_new=115,
x_1=28,x_new=34,alpha=0.025)

Final analysis: three stage design, with sample size change

Description

Final analysis: three stage design, with sample size change

Usage

asd_ci_est_one_arm_3_stage(
  p_0,
  n_2,
  n_3,
  r_2_e,
  r_2,
  r_3,
  n_new,
  x_2,
  x_new,
  alpha
)

Arguments

Value

UL: upper limit of confidence interval.

LL: lower limit of confidence interval.

The results with continuity correction are not necessarily different from those with continuity correction.

The need for continuity correction can be determined through simulations on type I error (see Gao, Zhang, 2004).

References

P. Gao & W. Zhang (15 Apr 2024): Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon’s design, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2341673. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2341673.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_ci_est_one_arm_3_stage( p_0=0.2,n_2=105,n_3=110,r_2_e=33,r_3=29,n_new=115,
x_2=28,x_new=34,alpha=0.025)

Group sequential designs / Adaptive sequential designs: Interim analysis, Non-survival analysis, Use theta_interim

Description

Group sequential designs / Adaptive sequential designs: Interim analysis, Non-survival analysis, Use theta_interim

Usage

asd_new_design(
  s,
  c_bry,
  inter_vt,
  snew,
  theta_hat_inter,
  theta_hat_inter_sd,
  n_control_inter,
  beta
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Estimated effect size: theta', 'c_alpha', 'c_power_theta', 'N_control_new', 'new information fraction', 'New critical boundary'.

Examples

asd_new_design(s = c(1/3, 2/3, 1), c_bry = c(3.984298, 3.961146, 2.349682), inter_vt = 1,
snew = c(0.5, 1), theta_hat_inter = 0.3, theta_hat_inter_sd = 0.5,
n_control_inter = 100, beta = 0.1)

Group sequential designs / Adaptive sequential designs: Interim analysis, Survival analysis, Use theta_interim

Description

Group sequential designs / Adaptive sequential designs: Interim analysis, Survival analysis, Use theta_interim

Usage

asd_new_design_survival(
  s,
  c_bry,
  inter_vt,
  snew,
  theta_hat_inter,
  theta_hat_inter_sd,
  events_inter,
  beta
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Estimated effect size: theta', 'c_alpha', 'c_power_theta', ' events_new', 'New information fraction', 'New critical boundary'.

Examples

asd_new_design_survival(s = c(1/3, 2/3, 1), c_bry = c(3.984298, 3.961146, 2.349682),
inter_vt = 1, snew = c(0.5, 1), theta_hat_inter = 0.3, theta_hat_inter_sd = 0.5,
events_inter = 100, beta = 0.1)

Group sequential designs / Adaptive sequential designs: Interim analysis, Non-survival analysis, Input theta

Description

Group sequential designs / Adaptive sequential designs: Interim analysis, Non-survival analysis, Input theta

Usage

asd_new_design_theta(
  theta,
  s,
  c_bry,
  inter_vt,
  snew,
  theta_hat_inter,
  theta_hat_inter_sd,
  n_control_inter,
  beta
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Assumed effect size: theta', 'c_alpha', 'c_power_theta', 'N_control_new', 'new information fraction', 'New critical boundary'.

Examples

asd_new_design_theta(theta = 0.2, s = c(1/3, 2/3, 1), c_bry = c(3.984298, 3.961146, 2.349682),
inter_vt = 1, snew = c(0.5, 1), theta_hat_inter = 0.3, theta_hat_inter_sd = 0.5,
n_control_inter = 100, beta = 0.1)

Group sequential designs / Adaptive sequential designs: Interim analysis, Survival analysis, Input theta

Description

Group sequential designs / Adaptive sequential designs: Interim analysis, Survival analysis, Input theta

Usage

asd_new_design_theta_survival(
  theta,
  s,
  c_bry,
  inter_vt,
  snew,
  theta_hat_inter,
  theta_hat_inter_sd,
  events_inter,
  beta
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Assumed effect size: theta', 'c_alpha', 'c_power_theta', ' events_new', 'New information fraction', 'New critical boundary'.

Examples

asd_new_design_theta_survival(theta = 0.2, s = c(1/3, 2/3, 1),
c_bry = c(3.984298, 3.961146, 2.349682), inter_vt = 1, snew = c(0.5, 1), theta_hat_inter = 0.3,
theta_hat_inter_sd = 0.5, events_inter = 100, beta = 0.1)

Group sequential designs / Adaptive sequential designs: Simulations, Binary distribution, Operating characteristics

Description

Group sequential designs / Adaptive sequential designs: Simulations, Binary distribution, Operating characteristics

Usage

asd_power_simu_binary(
  p_t,
  p_c,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  N_max,
  theta_cut,
  beta,
  sim_num
)

Arguments

Value

A matrix in which each row corresponds to one simulation replicate and the columns hold the simulated operating characteristics (e.g. rejection indicators, sample sizes and stopping stages).

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_power_simu_binary(p_t = 0.4, p_c = 0.2, direction = 1, s = c(1/3,2/3,1), bry_type = 1,
alpha_2 = 0.05, samsz = 107, N_max = 500, theta_cut = 0.05, beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Negative binomial distribution, Operating characteristics

Description

Group sequential designs / Adaptive sequential designs: Simulations, Negative binomial distribution, Operating characteristics

Usage

asd_power_simu_neg_binomial(
  r_t,
  r_c,
  kappa,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  N_max,
  theta_cut,
  beta,
  sim_num
)

Arguments

Value

A matrix in which each row corresponds to one simulation replicate and the columns hold the simulated operating characteristics (e.g. rejection indicators, sample sizes and stopping stages).

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_power_simu_neg_binomial(r_t = 1.1, r_c = 1.1, kappa = 1, direction = 1, s = c(1/3,2/3,1),
bry_type = 1, alpha_2 = 0.05, samsz = 100, N_max = 200, theta_cut = 0.01,
beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Normal distribution, Operating characteristics

Description

Group sequential designs / Adaptive sequential designs: Simulations, Normal distribution, Operating characteristics

Usage

asd_power_simu_normal(
  mu_t,
  mu_c,
  sigma_t,
  sigma_c,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  N_max,
  theta_cut,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Power at planned sample size', 'names(unlist(simu_out[[2]]'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_power_simu_normal(mu_t = 0, mu_c = 0, sigma_t = 1, sigma_c = 1, direction = 1,
s = c(1/3,2/3,1), bry_type = 1, alpha_2 = 0.05, samsz = 100, N_max = 500, theta_cut = 0.05,
beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Poisson distribution, Operating characteristics

Description

Group sequential designs / Adaptive sequential designs: Simulations, Poisson distribution, Operating characteristics

Usage

asd_power_simu_poisson(
  lambda_t,
  lambda_c,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  N_max,
  theta_cut,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Sequential design', 'Simulation results'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_power_simu_poisson(lambda_t = 1.1, lambda_c = 0.8, direction = 1, s = c(1/3,2/3,1),
bry_type = 1, alpha_2 = 0.05, samsz = 100, N_max = 200, theta_cut = 0.01,
beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Survival analysis, Operating characteristics

Description

Group sequential designs / Adaptive sequential designs: Simulations, Survival analysis, Operating characteristics

Usage

asd_power_simu_survival(
  HR,
  s,
  bry_type,
  alpha_2,
  evt_num,
  evt_max,
  HR_cut,
  surv_rate,
  beta,
  sim_num
)

Arguments

Value

A matrix in which each row corresponds to one simulation replicate and the columns hold the simulated operating characteristics (e.g. rejection indicators, sample sizes and stopping stages).

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_power_simu_survival(HR = 0.8, s = c(1/3,2/3,1), bry_type = 1, alpha_2 = 0.05, evt_num = 845,
evt_max = 1500, HR_cut = 0.95, surv_rate = 0.5, beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Binary distribution, Optimizing adaptive sequential design

Description

Group sequential designs / Adaptive sequential designs: Simulations, Binary distribution, Optimizing adaptive sequential design

Usage

asd_simu_OC_binary(
  p_t,
  p_c,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_simu_OC_binary(p_t = c(0.3,0.4,0.5), p_c = 0.2, direction = 1, s1 = c(1/3,2/3,1),
s2 = c(0.5,1), alpha_2 = 0.05, alpha_2_alps_s1 = c(0.001,0.001,0.048),
alpha_2_alps_s2 = c(0.001,0.049), theta_cut = 0.01, samsz_1 = 100, samsz_2 = 150,
N_max_1 = 200, N_max_2 = 300, beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Negative binomial distribution, Optimizing adaptive sequential design

Description

Group sequential designs / Adaptive sequential designs: Simulations, Negative binomial distribution, Optimizing adaptive sequential design

Usage

asd_simu_OC_neg_binomial(
  r_t,
  r_c,
  kappa,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_simu_OC_neg_binomial(r_t = c(0.3,0.4,0.5), r_c = 0.2, kappa = 1, direction = 1,
s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05, alpha_2_alps_s1 = c(0.001,0.001,0.048),
alpha_2_alps_s2 = c(0.001,0.049), theta_cut = 0.01, samsz_1 = 100,
samsz_2 = 150, N_max_1 = 200, N_max_2 = 300, beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Normal distribution, Optimizing adaptive sequential design

Description

Group sequential designs / Adaptive sequential designs: Simulations, Normal distribution, Optimizing adaptive sequential design

Usage

asd_simu_OC_normal(
  mu_t,
  mu_c,
  sigma_t,
  sigma_c,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_simu_OC_normal(mu_t = c(0.3,0.4,0.5), mu_c = 0, sigma_t = 1, sigma_c = 1, direction = 1,
s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05, alpha_2_alps_s1 = c(0.001,0.001,0.048),
alpha_2_alps_s2 = c(0.001,0.049), theta_cut = 0.01, samsz_1 = 100,
samsz_2 = 150, N_max_1 = 200, N_max_2 = 300, beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Poisson distribution, Optimizing adaptive sequential design

Description

Group sequential designs / Adaptive sequential designs: Simulations, Poisson distribution, Optimizing adaptive sequential design

Usage

asd_simu_OC_poisson(
  lambda_t,
  lambda_c,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_simu_OC_poisson(lambda_t = c(0.3,0.4,0.5), lambda_c = 0.2, direction = 1, s1 = c(1/3,2/3,1),
s2 = c(0.5,1), alpha_2 = 0.05, alpha_2_alps_s1 = c(0.001,0.001,0.048),
alpha_2_alps_s2 = c(0.001,0.049), theta_cut = 0.01, samsz_1 = 50, samsz_2 = 80,
N_max_1 = 120, N_max_2 = 150, beta = 0.1, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Survival analysis, Optimizing adaptive sequential design

Description

Group sequential designs / Adaptive sequential designs: Simulations, Survival analysis, Optimizing adaptive sequential design

Usage

asd_simu_OC_survival(
  HR,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  surv_rate,
  evt_num_1,
  evt_num_2,
  evt_max_1,
  evt_max_2,
  HR_cut,
  beta,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Looks', 'Information fractions', 'O'Brien-Fleming boundaries'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

asd_simu_OC_survival(HR = c(0.7,0.78,0.8), s1 = c(1/3,2/3,1), s2 = c(0.5,1), alpha_2 = 0.05,
alpha_2_alps_s1 = c(0.001,0.001,0.048), alpha_2_alps_s2 = c(0.001,0.049), surv_rate = 0.5,
evt_num_1 = 600, evt_num_2 = 800, evt_max_1 = 1000, evt_max_2 = 1500,
HR_cut = 0.95, beta = 0.1, sim_num = 20)

Fixed sample designs: Negative binomial distribution, Simulations

Description

Fixed sample designs: Negative binomial distribution, Simulations

Usage

fixed_rej_nbglm_simu(alpha_2, r_c, r_t, rand_ratio, kappa, samsz, sim_num)

Arguments

Value

The output is the simulated power, which can be used to verify if the calculated sample size provided intended power

Examples

fixed_rej_nbglm_simu(alpha_2 = 0.05, r_c = 1, r_t = 1*0.6, rand_ratio = 1, kappa = 1,
samsz = 188, sim_num = 20)

Fixed sample designs: Binary distribution, Simulations

Description

Fixed sample designs: Binary distribution, Simulations

Usage

fixed_rej_rate_binary(p_t, p_c, rand_ratio, alpha_2, samsz, sim_num)

Arguments

Value

The output is the simulated power, which can be used to verify if the calculated sample size provided intended power

Examples

fixed_rej_rate_binary(p_t = 0.4, p_c = 0.2, rand_ratio = 1, alpha_2 = 0.05,
samsz = 106, sim_num = 20)

Fixed sample designs: Normal distribution, Simulations

Description

Fixed sample designs: Normal distribution, Simulations

Usage

fixed_rej_rate_normal(
  mu_t,
  mu_c,
  sigma_t,
  sigma_c,
  alpha_2,
  rand_ratio,
  samsz,
  sim_num
)

Arguments

Value

The output is the simulated power, which can be used to verify if the calculated sample size provided intended power

Examples

fixed_rej_rate_normal(mu_t = 0, mu_c = 0, sigma_t = 1, sigma_c = 1, alpha_2 = 0.05,
rand_ratio = 1, samsz = 82, sim_num = 20)

Fixed sample designs: Poisson distribution, Simulations

Description

Fixed sample designs: Poisson distribution, Simulations

Usage

fixed_rej_rate_poisson(lambda_t, lambda_c, rand_ratio, alpha_2, samsz, sim_num)

Arguments

Value

The output is the simulated power, which can be used to verify if the calculated sample size provided intended power

Examples

fixed_rej_rate_poisson(lambda_t = 11, lambda_c = 10, rand_ratio = 2, alpha_2 = 0.05,
samsz = 163, sim_num = 20)

Fixed sample designs: Survival analysis, Simulations

Description

Fixed sample designs: Survival analysis, Simulations

Usage

fixed_rej_rate_surv_cox(HR, evt_num, alpha_2, sim_num)

Arguments

Value

The output is the simulated power, which can be used to verify if the calculated sample size provided intended power

Examples

fixed_rej_rate_surv_cox(HR = 0.8, evt_num = 845, alpha_2 = 0.05, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Final analysis, Without sample size change

Description

Group sequential designs / Adaptive sequential designs: Final analysis, Without sample size change

Usage

gsd_ci_est(s, c_bry, theta_hat_last, theta_hat_last_sd, last_vt, alpha_2)

Arguments

Value

A named list containing the following elements: 'p-value', 'confidence interval'.

Examples

gsd_ci_est(s = c(1/3,2/3,1), c_bry = c(3.471095, 2.454434,2.004037), theta_hat_last = 2.004,
theta_hat_last_sd = 1, last_vt = 3, alpha_2 = 0.05)

Final analysis: two stage design, no sample size change

Description

Final analysis: two stage design, no sample size change

Usage

gsd_ci_est_2_stage(p_0, n_1, n_2, r_1_e, r_2, x_last, last_vt, alpha)

Arguments

Value

UL: upper limit of confidence interval.

LL: lower limit of confidence interval.

The results with continuity correction are not necessarily different from those with continuity correction.

The need for continuity correction can be determined through simulations on type I error (see Gao, Zhang, 2004).

References

P. Gao & W. Zhang (15 Apr 2024): Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon’s design, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2341673. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2341673.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

gsd_ci_est_2_stage(p_0=0.2,n_1=100,n_2=105,r_1_e=NA,r_2=29,x_last=31,last_vt=1,alpha=0.025)

Final analysis: three stage design, no sample size change

Description

Final analysis: three stage design, no sample size change

Usage

gsd_ci_est_3_stage(p_0, n_2, n_3, r_2_e, r_3, x_last, last_vt, alpha)

Arguments

Value

UL: upper limit of confidence interval.

LL: lower limit of confidence interval.

The results with continuity correction are not necessarily different from those with continuity correction.

The need for continuity correction can be determined through simulations on type I error (see Gao, Zhang, 2004).

References

P. Gao & W. Zhang (15 Apr 2024): Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon’s design, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2341673. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2341673.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

gsd_ci_est_3_stage(p_0=0.2,n_2=100,n_3=105,r_2_e=31,r_3=29,x_last=31,last_vt=3,alpha=0.025)

Group sequential designs / Adaptive sequential designs: Simulations, Binary distribution, Type I error and power

Description

Group sequential designs / Adaptive sequential designs: Simulations, Binary distribution, Type I error and power

Usage

gsd_power_simu_binary(
  p_t,
  p_c,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Planned sample size', 'rejection rate', 'Mean sample size'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

gsd_power_simu_binary(p_t = 0.4, p_c = 0.4, direction = 1, s = c(1/3,2/3,1), bry_type = 1,
alpha_2 = 0.05, samsz = 100, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Negative binomial distribution, Type I error and power

Description

Group sequential designs / Adaptive sequential designs: Simulations, Negative binomial distribution, Type I error and power

Usage

gsd_power_simu_negbinom(
  r_t,
  r_c,
  kappa,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Planned sample size', 'rejection rate', 'Mean sample size'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

gsd_power_simu_negbinom(r_t = 1.1, r_c = 1.1, kappa = 1, direction = 1, s = c(1/3,2/3,1),
bry_type = 1, alpha_2 = 0.05, samsz = 100, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Normal distribution, Type I error and power

Description

Group sequential designs / Adaptive sequential designs: Simulations, Normal distribution, Type I error and power

Usage

gsd_power_simu_normal(
  mu_t,
  mu_c,
  sigma_t,
  sigma_c,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Planned control sample size', 'rejection rate', 'Mean control sample size'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

gsd_power_simu_normal(mu_t = 0.4, mu_c = 0, sigma_t = 1, sigma_c = 1, direction = 1,
s = c(1/4,1/3,2/3,1), bry_type = 1, alpha_2 = 0.05, samsz = 100, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Poisson distribution, Type I error and power

Description

Group sequential designs / Adaptive sequential designs: Simulations, Poisson distribution, Type I error and power

Usage

gsd_power_simu_poisson(
  lambda_c,
  lambda_t,
  direction,
  s,
  bry_type,
  alpha_2,
  samsz,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'Planned sample size', 'rejection rate', 'Mean sample size'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

gsd_power_simu_poisson(lambda_c = 0.5, lambda_t = 0.8, direction = 1, s = c(1/3,2/3,1),
bry_type = 1, alpha_2 = 0.05, samsz = 100, sim_num = 20)

Group sequential designs / Adaptive sequential designs: Simulations, Survival analysis, Type I error and power

Description

Group sequential designs / Adaptive sequential designs: Simulations, Survival analysis, Type I error and power

Usage

gsd_power_simu_survival(HR, s, bry_type, alpha_2, surv_rate, evt_num, sim_num)

Arguments

Value

A named list containing the following elements: 'Planned sample size', 'Rejection rate', 'Mean sample size'.

References

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Gao, P., L. Liu, and C. Mehta. 2013 Oct 15. Exact inference for adaptive group sequential designs. Statistics in Medicine 32(23):3991–4005. doi:10.1002/sim.5847.

Examples

gsd_power_simu_survival(HR = 0.8, s = c(1/3,2/3,1), bry_type = 1, alpha_2 = 0.05,
surv_rate = 0.5, evt_num = 845, sim_num = 20)

Hybrid: Simulations, Binary distribution, Using given estimates of informative prior

Description

Hybrid: Simulations, Binary distribution, Using given estimates of informative prior

Usage

hybrid_fixed_prior_rej_binary_simu(
  t_prior,
  theta_prior,
  p_t,
  p_c,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_fixed_prior_rej_binary_simu(t_prior = 5, theta_prior = 0.2, p_t = 0.3, p_c = 0.3,
s = c(0.5,1), sampsz = 100, N_max = 150, theta_cut = 0.001, cp_min = 0.27, gamma = 0.5,
alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Negative binomial distribution, Using given estimates of informative prior

Description

Hybrid: Simulations, Negative binomial distribution, Using given estimates of informative prior

Usage

hybrid_fixed_prior_rej_negbinom_simu(
  t_prior,
  theta_prior,
  r_t,
  r_c,
  kappa,
  nu_t,
  rand_ratio,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior.

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_fixed_prior_rej_negbinom_simu(t_prior = 5, theta_prior = 0.2, r_t = 1, r_c = 1,
kappa = 1, nu_t = 1, rand_ratio = 1, s = c(0.5,1), sampsz = 100, N_max = 150,
theta_cut = 0.001, cp_min = 0.27, gamma = 0.5, alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Normal distribution, Using given estimates of informative prior

Description

Hybrid: Simulations, Normal distribution, Using given estimates of informative prior

Usage

hybrid_fixed_prior_rej_normal_simu(
  t_prior,
  theta_prior,
  mu,
  sigma,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_fixed_prior_rej_normal_simu(t_prior = 5, theta_prior = 0.2, mu = 0, sigma = 1,
s = c(0.5,1), sampsz = 100, N_max = 150, theta_cut = 0.001, cp_min = 0.27, gamma = 0.5,
alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Poisson distribution, Using given estimates of informative prior

Description

Hybrid: Simulations, Poisson distribution, Using given estimates of informative prior

Usage

hybrid_fixed_prior_rej_poisson_simu(
  t_prior,
  theta_prior,
  lambda_t,
  lambda_c,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_fixed_prior_rej_poisson_simu(t_prior = 5, theta_prior = 0.2, lambda_t = 0.5,
lambda_c = 0.5, s = c(0.5,1), sampsz = 100, N_max = 150, theta_cut = 0.001, cp_min = 0.27,
gamma = 0.5, alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Survival analysis, Using given estimates of informative prior

Description

Hybrid: Simulations, Survival analysis, Using given estimates of informative prior

Usage

hybrid_fixed_prior_rej_survival_simu(
  t_prior,
  theta_prior,
  HR,
  lambda,
  s,
  alpha_2,
  surv_rate,
  evt_num,
  evt_max,
  HR_cut,
  cp_min,
  gamma,
  samp_multip,
  sim_num,
  beta
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_fixed_prior_rej_survival_simu(t_prior = 10, theta_prior = 0.8, HR = 1, lambda = 1,
s = c(0.5,1), alpha_2 = 0.05, surv_rate = 0.5, evt_num = 88, evt_max = 331, HR_cut = 0.95,
cp_min = 0.27, gamma = 0.5, samp_multip = 5, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Binary distribution, Using random informative prior from previous trial

Description

Hybrid: Simulations, Binary distribution, Using random informative prior from previous trial

Usage

hybrid_random_prior_rej_binary_simu(
  p_t_0,
  p_c_0,
  sampsz_0,
  p_t,
  p_c,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_random_prior_rej_binary_simu(p_t_0 = 0.4, p_c_0 = 0.3, sampsz_0 = 60, p_t = 0.3,
p_c = 0.3, s = c(0.5,1), sampsz = 100, N_max = 150, theta_cut = 0.001, cp_min = 0.27,
gamma = 0.5, alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Negative binomial distribution, Using random informative prior from previous trial

Description

Hybrid: Simulations, Negative binomial distribution, Using random informative prior from previous trial

Usage

hybrid_random_prior_rej_negbinom_simu(
  r_t_0,
  r_c_0,
  sampsz_0,
  r_t,
  r_c,
  kappa,
  nu_t,
  rand_ratio,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_random_prior_rej_negbinom_simu(r_t_0 = 1.2, r_c_0 = 1, sampsz_0 = 50, r_t = 1, r_c = 1,
kappa = 1, nu_t = 1, rand_ratio = 1, s = c(0.5,1), sampsz = 100, N_max = 150,
theta_cut = 0.001, cp_min = 0.27, gamma = 0.5, alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Normal distribution, Using random informative prior from previous trial

Description

Hybrid: Simulations, Normal distribution, Using random informative prior from previous trial

Usage

hybrid_random_prior_rej_normal_simu(
  mu_0,
  sigma_0,
  sampsz_0,
  mu,
  sigma,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_random_prior_rej_normal_simu(mu_0 = 0.3, sigma_0 = 1, sampsz_0 = 60, mu = 0, sigma = 1,
s = c(0.5,1), sampsz = 100, N_max = 250, theta_cut = 0.01, cp_min = 0.27, gamma = 0.5,
alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Poisson distribution, Using random informative prior from previous trial

Description

Hybrid: Simulations, Poisson distribution, Using random informative prior from previous trial

Usage

hybrid_random_prior_rej_poisson_simu(
  lambda_t_0,
  lambda_c_0,
  sampsz_0,
  lambda_t,
  lambda_c,
  s,
  sampsz,
  N_max,
  theta_cut,
  cp_min,
  gamma,
  alpha_2,
  beta,
  sim_num
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_random_prior_rej_poisson_simu(lambda_t_0 = 0.5, lambda_c_0 = 0.3, sampsz_0 = 60,
lambda_t = 0.5, lambda_c = 0.5, s = c(0.5,1), sampsz = 100, N_max = 150, theta_cut = 0.001,
cp_min = 0.27, gamma = 0.5, alpha_2 = 0.05, beta = 0.1, sim_num = 20)

Hybrid: Simulations, Survival analysis, Using random informative prior from previous trial

Description

Hybrid: Simulations, Survival analysis, Using random informative prior from previous trial

Usage

hybrid_random_prior_rej_survival_simu(
  HR_0,
  evt_num_0,
  HR,
  lambda,
  s,
  alpha_2,
  surv_rate,
  evt_num,
  evt_max,
  HR_cut,
  cp_min,
  gamma,
  samp_multip,
  sim_num,
  beta
)

Arguments

Value

The simulations are conducted with both non-informative prior and informative prior

References

Gao, P. Improving the effectiveness of sample size re-estimation: an operating characteristic focused, hybrid frequentist-Bayesian approach, Statistics in Medicine, 2025; 44:e10310. To link to this article: https://onlinelibrary.wiley.com/doi/10.1002/sim.10310.

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796.

C. R. Mehta, S. J. Pocock. Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine. Volume30, Issue28, 10 December 2011, Pages 3267-3284

Examples

hybrid_random_prior_rej_survival_simu(HR_0 = 0.63, evt_num_0 = 40, HR = 1, lambda = 1,
s = c(0.5,1), alpha_2 = 0.05, surv_rate = 0.5, evt_num = 88, evt_max = 331, HR_cut = 0.95,
cp_min = 0.27, gamma = 0.5, samp_multip = 5, beta = 0.1, sim_num = 20)

Two-stage design: the hybrid design

Description

Two-stage design: the hybrid design

Usage

hybrid_sz(alpha, beta, p_0, p_low, p_1, d_12_cut)

Arguments

Value

n1: Number of patients at first look.

n_2: Number of patients at second look. n_2 is also the total sample size.

r1: If no more than r1 responses are observed at the first look, then the trial would be stopped for futility.

r_2: The null hypothesis will be rejected if at least r_2 responses are observed at the end of the trial.

EN(p0) is the expected sample size under the null hypothesis.

PET(p0) is the probability of early termination under the null hypothesis.

PET_p is the probability of early termination under p=p_1.

PET_p_low is the probability of early termination under p=p_low.

power_p is the power under p=p_1.

power_p_low is the power under p=p_low.

Type I error is the probability of rejecting the null hypothesis under p<=p_0.

The minimax design has the smallest n2 among all possible choices of (n1,r1,n_2,r_2).

The optimal design has the smallest EN(p0) ) among all possible choices of (n1,r1,n_2,r_2).

The n1 for the average design is the average of n1's from the minimax and the optimal designs.

References

R. Simon. Optimal Two-Stage Designs for Phase II Clinical Trials. Controlled Clinical Trials 10:1-10 (1989).

P. Gao & W. Zhang (15 Apr 2024): Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon’s design, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2341673. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2341673.

Examples

hybrid_sz(alpha=c(0.001,0.024),beta=0.1,p_0=0.2,p_low=0.4,p_1=0.55,d_12_cut=0)

The interim analysis can be conducted for both two-stage and three-stage designs

Description

The interim analysis can be conducted for both two-stage and three-stage designs

Usage

interim_analysis(p_0, r_final, n_inter, n_final, x_inter, beta, N_max)

Arguments

Value

n_new: is the new sample size.

r_new (without continuity correction) and r_new (with continuity correction) are thresholds such that the null hypothesis will be rejected at n_new if at least r_new responses are observed. Simulations on type I error will help to determine if continuity correction is needed.

References

R. Simon. Optimal Two-Stage Designs for Phase II Clinical Trials. Controlled Clinical Trials 10:1-10 (1989).

P. Gao & W. Zhang (15 Apr 2024): Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon’s design, Journal of Biopharmaceutical Statistics, DOI: 10.1080/10543406.2024.2341673. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2341673.

P. Gao, J.H. Ware, C. Mehta, (2008), Sample size re-estimation for adaptive sequential designs. Journal of Biopharmaceutical Statistics, 18: 1184–1196, 2008.

Examples

interim_analysis(p_0=0.2,r_final=17,n_inter=22,n_final=56,x_inter=7,beta=0.1,N_max=120)

Multiple comparisons Group sequential design: Final analysis, With one sample size change, orgin_comp==comp2

Description

Multiple comparisons Group sequential design: Final analysis, With one sample size change, orgin_comp==comp2

Usage

masd_est_back_no_drop(
  s,
  c_bry,
  snew,
  c_bry_new,
  theta_hat_inter_m1,
  theta_hat_inter_m1_sd,
  inter_vt,
  theta_hat_last_ad_m1,
  theta_hat_last_ad_m1_sd,
  last_vt_ad,
  alpha_2,
  dist
)

Arguments

Value

A named list containing the following elements: 'p-value', 'confidence interval'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_est_back_no_drop(s = c(0.3,0.7,1), c_bry = c(4.347011, 2.845787, 2.380956), snew = c(0.5,1),
c_bry_new = c(3.310743,2.781890), theta_hat_inter_m1 = c(1.2,1.3,1.5), theta_hat_inter_m1_sd = 1,
inter_vt = 1, theta_hat_last_ad_m1 = c(2.2,1.4,1.8), theta_hat_last_ad_m1_sd = 1,
last_vt_ad = 2, alpha_2 = 0.05, dist = 1)

Multiple comparisons Group sequential design: Final analysis, With one sample size change, orgin_comp>comp2

Description

Multiple comparisons Group sequential design: Final analysis, With one sample size change, orgin_comp>comp2

Usage

masd_est_back_with_drop(
  s,
  c_bry,
  snew,
  c_bry_new,
  theta_hat_inter_m1,
  theta_hat_inter_m1_sd,
  theta_hat_inter_m2,
  theta_hat_inter_m2_sd,
  inter_vt,
  theta_hat_last_ad_m2,
  theta_hat_last_ad_m2_sd,
  last_vt_ad,
  alpha_2,
  dist
)

Arguments

Value

A named list containing the following elements: 'p-value', 'confidence interval'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_est_back_with_drop(s = c(0.3,0.7,1), c_bry = c(4.347011,2.845787,2.380956), snew = c(0.5,1),
c_bry_new = c(3.310743,2.781890), theta_hat_inter_m1 = c(1.2,1.3,1.5), theta_hat_inter_m1_sd = 1,
theta_hat_inter_m2 = c(1.3,1.5), theta_hat_inter_m2_sd = 1, inter_vt = 1,
theta_hat_last_ad_m2 = c(2.2,1.4), theta_hat_last_ad_m2_sd = 1, last_vt_ad = 2,
alpha_2 = 0.05, dist = 1)

Multiple comparisons Group sequential design: Final analysis, Without sample size change

Description

Multiple comparisons Group sequential design: Final analysis, Without sample size change

Usage

masd_est_ci(
  s,
  c_bry,
  theta_hat_last_m1,
  theta_hat_last_m1_sd,
  last_vt,
  alpha_2,
  dist
)

Arguments

Value

A named list containing the following elements: 'p-value', 'confidence interval'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_est_ci(s = c(1/3, 2/3, 1), c_bry = c(3.984298, 3.961146, 2.349682),
theta_hat_last_m1 = 0.35, theta_hat_last_m1_sd = 0.6,
last_vt = 1, alpha_2 = 0.05, dist = 1)

Multiple comparisons Group sequential design: Interim analysis, Non-survival analysis, Use theta_interim

Description

Multiple comparisons Group sequential design: Interim analysis, Non-survival analysis, Use theta_interim

Usage

masd_new_samsz(
  s,
  c_bry,
  snew,
  inter_vt,
  theta_hat_inter_m1,
  theta_hat_inter_m1_sd,
  theta_hat_inter_m2,
  theta_hat_inter_m2_sd,
  beta,
  n_control_inter,
  dist
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Estimated effect size: theta', 'remaining effect size', 'c_alpha', 'c_power_m1', 'c_power_m2', 'N_control_new', 'new information fraction', 'New critical boundary'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_new_samsz(s=c(1/3,2/3,1), c_bry=c(3.984298, 3.961146, 2.349682), snew=1, inter_vt=2,
theta_hat_inter_m1=c(1.2,1.5,1.1), theta_hat_inter_m1_sd=0.2, theta_hat_inter_m2=c(1.2,1.5),
theta_hat_inter_m2_sd=0.2, beta=0.1, n_control_inter=65, dist=1)

Multiple comparisons Group sequential design: Interim analysis, Survival analysis, Use theta_interim

Description

Multiple comparisons Group sequential design: Interim analysis, Survival analysis, Use theta_interim

Usage

masd_new_samsz_survival(
  s,
  c_bry,
  snew,
  inter_vt,
  theta_hat_inter_m1,
  theta_hat_inter_m1_sd,
  theta_hat_inter_m2,
  theta_hat_inter_m2_sd,
  beta,
  tot_events_inter_m1,
  dist
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Assumed effect size: theta', 'remaining effect size', 'c_alpha', 'c_power_m1', 'c_power_m2', 'new events between a test arm and control', 'new total events', 'new information fraction', 'New critical boundary'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_new_samsz_survival(s = c(1/3,2/3,1), c_bry = c(3.984298, 3.961146, 2.349682), snew = 1,
inter_vt = 2, theta_hat_inter_m1 = c(1.2,1.5,1.1),
theta_hat_inter_m1_sd = 1.2, theta_hat_inter_m2 = c(1.2,1.5),
theta_hat_inter_m2_sd = 1.2, beta = 0.1, tot_events_inter_m1 = 65, dist = 1)

Multiple comparisons Group sequential design: Interim analysis, Non-survival analysis, Input theta

Description

Multiple comparisons Group sequential design: Interim analysis, Non-survival analysis, Input theta

Usage

masd_new_samsz_theta(
  theta,
  s,
  c_bry,
  snew,
  inter_vt,
  theta_hat_inter_m1,
  theta_hat_inter_m1_sd,
  theta_hat_inter_m2,
  theta_hat_inter_m2_sd,
  beta,
  n_control_inter,
  dist
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Assumed effect size: theta', 'remaining effect size', 'c_alpha', 'c_power_m1', 'c_power_m2', 'N_control_new', 'new information fraction', 'New critical boundary'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_new_samsz_theta(theta = c(0,0.2,0), s = c(1/3,2/3,1),
c_bry = c(3.984298, 3.961146, 2.349682), snew = 1, inter_vt = 2,
theta_hat_inter_m1 = c(1.2,1.5,1.1), theta_hat_inter_m1_sd = 0.2,
theta_hat_inter_m2 = c(1.2,1.5), theta_hat_inter_m2_sd = 0.2,
beta = 0.1, n_control_inter = 65, dist = 1)

Multiple comparisons Group sequential design: Interim analysis, Survival analysis, Input theta

Description

Multiple comparisons Group sequential design: Interim analysis, Survival analysis, Input theta

Usage

masd_new_samsz_theta_survival(
  theta,
  s,
  c_bry,
  snew,
  inter_vt,
  theta_hat_inter_m1,
  theta_hat_inter_m1_sd,
  theta_hat_inter_m2,
  theta_hat_inter_m2_sd,
  beta,
  tot_events_inter_m1,
  dist
)

Arguments

Value

A named list containing the following elements: 'Interim analysis hypothesis test', 'Wald statistics', 'Critical boundary', 'Assumed effect size: theta', 'remaining effect size', 'c_alpha', 'c_power_m1', 'c_power_m2', 'new events between a test arm and control', 'new total events', 'new information fraction', 'New critical boundary'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_new_samsz_theta_survival(theta=c(0,0.2,0), s=c(1/3,2/3,1),
c_bry=c(3.984298, 3.961146, 2.349682), snew=1, inter_vt=2,
theta_hat_inter_m1=c(1.2,1.5,1.1), theta_hat_inter_m1_sd=0.2, theta_hat_inter_m2=c(1.2,1.5),
theta_hat_inter_m2_sd=0.2, beta=0.1, tot_events_inter_m1=65, dist=1)

Multiple comparisons Group sequential design: Simulations, Binary distribution, Operating characteristics

Description

Multiple comparisons Group sequential design: Simulations, Binary distribution, Operating characteristics

Usage

masd_power_simu_adapt_binary(
  p_t,
  p_c,
  direction,
  s,
  bry_type,
  alpha_2,
  theta_cut,
  beta,
  samsz,
  N_max,
  sim_num
)

Arguments

Value

A matrix in which each row corresponds to one simulation replicate and the columns hold the simulated operating characteristics (e.g. rejection indicators, sample sizes and stopping stages).

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_power_simu_adapt_binary(p_t = c(0.4,0.4,0.4), p_c = 0.4, direction = 1, s = c(1/3,2/3,1),
bry_type = 1, alpha_2 = 0.05, theta_cut = 0.01, beta = 0.1, samsz = 100,
N_max = 200, sim_num = 20)

Multiple comparisons Group sequential design: Simulations, Negative binomial distribution, Operating characteristics

Description

Multiple comparisons Group sequential design: Simulations, Negative binomial distribution, Operating characteristics

Usage

masd_power_simu_adapt_neg_binomial(
  r_t,
  r_c,
  kappa,
  direction,
  s,
  bry_type,
  alpha_2,
  beta,
  theta_cut,
  samsz,
  N_max,
  sim_num
)

Arguments

Value

A matrix in which each row corresponds to one simulation replicate and the columns hold the simulated operating characteristics (e.g. rejection indicators, sample sizes and stopping stages).

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_power_simu_adapt_neg_binomial(r_t = c(1.1,1.1,1.1), r_c = 1.1, kappa = 1, direction = 1,
s = c(1/3,2/3,1), bry_type = 1, alpha_2 = 0.05, beta = 0.1, theta_cut = 0.01, samsz = 100,
N_max = 500, sim_num = 20)

Multiple comparisons Group sequential design: Simulations, Normal distribution, Operating characteristics

Description

Multiple comparisons Group sequential design: Simulations, Normal distribution, Operating characteristics

Usage

masd_power_simu_adapt_normal(
  mu_t,
  mu_c,
  sigma_t,
  sigma_c,
  direction,
  s,
  bry_type,
  alpha_2,
  beta,
  theta_cut,
  samsz,
  N_max,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'simulation summary', 'planned control', 'planned total'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_power_simu_adapt_normal(mu_t = c(0,0,0), mu_c = 0, sigma_t = 1, sigma_c = 1, direction = 1,
s = c(1/3,2/3,1), bry_type = 1, alpha_2 = 0.05, beta = 0.1, theta_cut = 0.01, samsz = 100,
N_max = 500, sim_num = 20)

Multiple comparisons Group sequential design: Simulations, Poisson distribution, Operating characteristics

Description

Multiple comparisons Group sequential design: Simulations, Poisson distribution, Operating characteristics

Usage

masd_power_simu_adapt_poisson(
  lambda_t,
  lambda_c,
  direction,
  s,
  bry_type,
  alpha_2,
  beta,
  theta_cut,
  samsz,
  N_max,
  sim_num
)

Arguments

Value

A named list containing the following elements: 'simulation summary', 'planned control', 'planned total'.

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_power_simu_adapt_poisson(lambda_t = c(1.1,1.1,1.1), lambda_c = 1.1, direction = 1,
s = c(1/3,2/3,1), bry_type = 1, alpha_2 = 0.05, beta = 0.1, theta_cut = 0.01, samsz = 100,
N_max = 500, sim_num = 20)

Multiple comparisons Group sequential design: Simulations, Survival analysis, Operating characteristics

Description

Multiple comparisons Group sequential design: Simulations, Survival analysis, Operating characteristics

Usage

masd_power_simu_adapt_survival(
  HR,
  s,
  bry_type,
  alpha_2,
  surv_rate,
  HR_cut,
  evt_num,
  evt_max,
  beta,
  sim_num
)

Arguments

Value

A matrix in which each row corresponds to one simulation replicate and the columns hold the simulated operating characteristics (e.g. rejection indicators, sample sizes and stopping stages).

References

P. Gao & Y. Li (2024) Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials, Journal of Biopharmaceutical Statistics, 34:3, 424-440, DOI:10.1080/10543406.2023.2233590. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2023.2233590

Gao, P., Zhang, W. (2024). A systematic approach to adaptive sequential design for clinical trials: using simulations to select a design with desired operating characteristics. Journal of Biopharmaceutical Statistics,2024 Aug;34(5):737-752. doi:10.1080/10543406.2024.2358796. Epub 2024 May 30. To link to this article: https://www.tandfonline.com/doi/full/10.1080/10543406.2024.2358796

H.H. Müller, H. Sch?fer. Adaptive Group Sequential Designs for Clinical Trials: Combining the Advantages of Adaptive and of Classical Group Sequential Approaches. BIOMETRICs 57, 886-891. September 2001.

P. Gao, J. H. Ware, C. Mehta. Sample size re-estimation for adaptive sequential design in clinical trials. J Biopharm Stat. 2008;18(6):1184-96.

Examples

masd_power_simu_adapt_survival(HR = c(0.8,0.8), s = c(1/3,2/3,1), bry_type = 1, alpha_2 = 0.05,
surv_rate = 0.5, HR_cut = 0.95, evt_num = 800, evt_max = 1200, beta = 0.1, sim_num = 2)

Multiple comparisons Group sequential design: Simulations, Binary distribution, Optimizing adaptive sequential design

Description

Multiple comparisons Group sequential design: Simulations, Binary distribution, Optimizing adaptive sequential design

Usage

masd_simu_OC_binary(
  groups,
  p_c,
  direction,
  s1,
  s2,
  alpha_2,
  alpha_2_alps_s1,
  alpha_2_alps_s2,
  theta_cut,
  samsz_1,
  samsz_2,
  N_max_1,
  N_max_2,
  beta,
  sim_num
)

Arguments