| Type: | Package |
| Title: | Bayesian Optimal Phase II Design with Futility and Efficacy Stopping Boundaries |
| Version: | 1.0.3 |
| Description: | Bayesian optimal design with futility and efficacy stopping boundaries (BOP2-FE) is a novel statistical framework for single-arm Phase II clinical trials. It enables early termination for efficacy when interim data are promising, while explicitly controlling Type I and Type II error rates. The design supports a variety of endpoint structures, including single binary endpoints, nested endpoints, co-primary endpoints, and joint monitoring of efficacy and toxicity. The package provides tools for enumerating stopping boundaries prior to trial initiation and for conducting simulation studies to evaluate the design’s operating characteristics. Users can flexibly specify design parameters to suit their specific applications. For methodological details, refer to Xu et al. (2025) <doi:10.1080/10543406.2025.2558142>. |
| BugReports: | https://github.com/belayb/BOP2FE/issues |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | gridExtra, patchwork, ggplot2, stats, utils |
| Suggests: | spelling |
| Language: | en-US |
| URL: | https://github.com/belayb/BOP2FE |
| NeedsCompilation: | no |
| Packaged: | 2025-09-22 09:45:47 UTC; A4044038 |
| Author: | Belay Birlie Yimer [aut, cre], Xinling Xu [aut], Atsuki Hashimoto [aut], Gosuke Homma [aut], Kentaro Takeda [aut] |
| Maintainer: | Belay Birlie Yimer <belayabyimer@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-09-29 16:40:07 UTC |
BOP2-FE design for binary endpoint
Description
Computes stopping boundaries and operating characteristics of Bayesian optimal phase II design with efficacy and futility stopping for a binary endpoint
Usage
BOP2FE_binary(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric value for the response rate under the null hypothesis. |
H1 |
A numeric value for the response rate under the alternative hypothesis. |
n |
A numeric vector representing the additional patients enrolled at each interim analysis. The value at index 'i' indicates the number of new patients added at interim analysis 'i'. The total sample size at interim 'i' is the cumulative sum of the values in 'n' up to that index. For example, for four interim analyses with total sample sizes of 10, 15, 20, and 30, the vector would be represented as 'n = c(10, 5, 5, 10)', where: - 10 is the number of patients enrolled at interim 1, - 5 (15 - 10) is the additional number of patients enrolled at interim 2, - 5 (20 - 15) is the additional number of patients enrolled at interim 3, - 10 (30 - 20) is the additional number of patients enrolled at interim 4. |
nsim |
number of simulation. A value at least 1000 for better result. |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search. |
lambda2 |
ending value for 'lambda' values to search. |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2. A fine grid by 0.01 is recommended. |
gamma1 |
starting value for 'gamma' values to search. |
gamma2 |
ending value for 'gamma' values to search. |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2. A fine grid by 0.01 is recommended. |
eta1 |
starting value for 'eta' values to search. |
eta2 |
ending value for 'eta' values to search. |
grid3 |
number of eta values to consider between eta1 and eta2. A fine grid by 0.01 is recommended. |
seed |
for reproducibility |
Value
An S3 object of class 'bop2fe'
References
Xu, X., Hashimoto, A., Yimer, B., & Takeda, K. (2025). BOP2-FE: Bayesian optimal phase II design with futility and efficacy stopping boundaries. Journal of Biopharmaceutical Statistics doi:10.1080/10543406.2025.2558142.
Examples
test_binary <- BOP2FE_binary(
H0=0.2, H1= 0.4,
n = c(10, 5, 5),
nsim = 1000, t1e = 0.1, method = "power",
lambda1 = 0, lambda2 = 1, grid1 = 11,
gamma1 = 0, gamma2 = 1, grid2 = 11,
eta1 = 0, eta2 = 3, grid3 = 31,seed = 123)
summary(test_binary)
#plot(test_binary)
BOP2-FE design for co-primary endpoint
Description
Computes stopping boundaries and operating characteristics of Bayesian optimal phase II design with efficacy and futility stopping for a co-primary endpoint.
Usage
BOP2FE_coprimary(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': Response - PFS6, - 'H0[2]': Response - no PFS6, - 'H0[3]': No Response - PFS6, - 'H0[4]': No Response - no PFS6 |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': Response - PFS6, - 'H1[2]': Response - no PFS6, - 'H1[3]': No Response - PFS6, - 'H1[4]': No Response - no PFS6 |
n |
A numeric vector representing the additional patients enrolled at each interim analysis. The value at index 'i' indicates the number of new patients added at interim analysis 'i'. The total sample size at interim 'i' is the cumulative sum of the values in 'n' up to that index. For example, for four interim analyses with total sample sizes of 10, 15, 20, and 30, the vector would be represented as 'n = c(10, 5, 5, 10)', where: - 10 is the number of patients enrolled at interim 1, - 5 (15 - 10) is the additional number of patients enrolled at interim 2, - 5 (20 - 15) is the additional number of patients enrolled at interim 3, - 10 (30 - 20) is the additional number of patients enrolled at interim 4. |
nsim |
number of simulation. A value at least 1000 for better result. |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search. |
lambda2 |
ending value for 'lambda' values to search. |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2. A fine grid by 0.01 is recommended. |
gamma1 |
starting value for 'gamma' values to search. |
gamma2 |
ending value for 'gamma' values to search. |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2. A fine grid by 0.01 is recommended. |
eta1 |
starting value for 'eta' values to search. |
eta2 |
ending value for 'eta' values to search. |
grid3 |
number of eta values to consider between eta1 and eta2. A fine grid by 0.01 is recommended. |
seed |
for reproducibility |
Value
An S3 object of class 'bop2fe'
References
Xu, X., Hashimoto, A., Yimer, B., & Takeda, K. (2025). BOP2-FE: Bayesian optimal phase II design with futility and efficacy stopping boundaries. Journal of Biopharmaceutical Statistics doi:10.1080/10543406.2025.2558142.
Examples
test_coprimary <- BOP2FE_coprimary(
H0=c(0.05,0.05, 0.15, 0.75),
H1= c(0.15,0.15, 0.20, 0.50),
n = c(10, 5, 5),
nsim = 1000, t1e = 0.1, method = "power",
lambda1 = 0, lambda2 = 1, grid1 = 11,
gamma1 = 0, gamma2 = 1, grid2 = 11,
eta1 = 0, eta2 = 3, grid3 = 31,
seed = 123)
summary(test_coprimary)
#plot(test_coprimary)
BOP2-FE design for joint efficacy and toxicity endpoint
Description
Computes stopping boundaries and operating characteristics of Bayesian optimal phase II design with efficacy and futility stopping for a joint efficacy and toxicity endpoint.
Usage
BOP2FE_jointefftox(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': Response - toxicity, - 'H0[2]': Response - no toxicity, - 'H0[3]': No Response - toxicity, - 'H0[4]': No Response - no toxicity |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': Response - toxicity, - 'H1[2]': Response - no toxicity, - 'H1[3]': No Response - toxicity, - 'H1[4]': No Response - no toxicity. |
n |
A numeric vector representing the additional patients enrolled at each interim analysis. The value at index 'i' indicates the number of new patients added at interim analysis 'i'. The total sample size at interim 'i' is the cumulative sum of the values in 'n' up to that index. For example, for four interim analyses with total sample sizes of 10, 15, 20, and 30, the vector would be represented as 'n = c(10, 5, 5, 10)', where: - 10 is the number of patients enrolled at interim 1, - 5 (15 - 10) is the additional number of patients enrolled at interim 2, - 5 (20 - 15) is the additional number of patients enrolled at interim 3, - 10 (30 - 20) is the additional number of patients enrolled at interim 4. |
nsim |
number of simulation. A value at least 1000 for better result. |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search. |
lambda2 |
ending value for 'lambda' values to search. |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2. A fine grid by 0.01 is recommended. |
gamma1 |
starting value for 'gamma' values to search. |
gamma2 |
ending value for 'gamma' values to search. |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2. A fine grid by 0.01 is recommended. |
eta1 |
starting value for 'eta' values to search. |
eta2 |
ending value for 'eta' values to search. |
grid3 |
number of eta values to consider between eta1 and eta2. A fine grid by 0.01 is recommended. |
seed |
for reproducibility |
Value
An S3 object of class 'bop2fe'
References
Xu, X., Hashimoto, A., Yimer, B., & Takeda, K. (2025). BOP2-FE: Bayesian optimal phase II design with futility and efficacy stopping boundaries. Journal of Biopharmaceutical Statistics doi:10.1080/10543406.2025.2558142 .
Examples
test_joint <- BOP2FE_jointefftox(
H0=c(0.15,0.30, 0.15, 0.40),
H1= c(0.18,0.42, 0.02, 0.38),
n = c(10, 5, 5),
nsim = 1000, t1e = 0.1, method = "power",
lambda1 = 0, lambda2 = 1, grid1 = 11,
gamma1 = 0, gamma2 = 1, grid2 = 11,
eta1 = 0, eta2 = 3, grid3 = 31,
seed = 123
)
summary(test_joint)
#plot(test_joint)
BOP2-FE design for nested (ordinal) endpoint
Description
Computes stopping boundaries and operating characteristics of Bayesian optimal phase II design with efficacy and futility stopping for a nested (ordinal) endpoint
Usage
BOP2FE_nested(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': CR: Complete remission, - 'H0[2]': PR: Partial remission, - 'H0[3]': 1-(CR+PR) |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': CR: Complete remission, - 'H1[2]': PR: Partial remission, - 'H1[3]': 1-(CR+PR) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis. The value at index 'i' indicates the number of new patients added at interim analysis 'i'. The total sample size at interim 'i' is the cumulative sum of the values in 'n' up to that index. For example, for four interim analyses with total sample sizes of 10, 15, 20, and 30, the vector would be represented as 'n = c(10, 5, 5, 10)', where: - 10 is the number of patients enrolled at interim 1, - 5 (15 - 10) is the additional number of patients enrolled at interim 2, - 5 (20 - 15) is the additional number of patients enrolled at interim 3, - 10 (30 - 20) is the additional number of patients enrolled at interim 4. |
nsim |
number of simulation. A value at least 1000 for better result. |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search. |
lambda2 |
ending value for 'lambda' values to search. |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2. A fine grid by 0.01 is recommended. |
gamma1 |
starting value for 'gamma' values to search. |
gamma2 |
ending value for 'gamma' values to search. |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2. A fine grid by 0.01 is recommended. |
eta1 |
starting value for 'eta' values to search. |
eta2 |
ending value for 'eta' values to search. |
grid3 |
number of eta values to consider between eta1 and eta2. A fine grid by 0.01 is recommended. |
seed |
for reproducibility |
Value
An S3 object of class 'bop2fe'
References
Xu, X., Hashimoto, A., Yimer, B., & Takeda, K. (2025). BOP2-FE: Bayesian optimal phase II design with futility and efficacy stopping boundaries. Journal of Biopharmaceutical Statistics doi:10.1080/10543406.2025.2558142.
Examples
test_nested <- BOP2FE_nested(
H0=c(0.15,0.15, 0.70),
H1= c(0.25,0.25, 0.50),
n = c(10, 5, 5),
nsim = 1000, t1e = 0.1, method = "power",
lambda1 = 0, lambda2 = 1, grid1 = 11,
gamma1 = 0, gamma2 = 1, grid2 = 11,
eta1 = 0, eta2 = 3, grid3 = 31,
seed = 123)
summary(test_nested)
#plot(test_nested)
Boundary values for binary Endpoint
Description
Boundary values for binary Endpoint
Usage
get_boundary_binary(
H0,
a1,
b1,
n,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
Response rate under the null |
a1 |
alpha values for the beta prior (i.e. usually set to the null response rate) |
b1 |
beta values for the beta prior (i.e. usually set to 1 - the null response rate) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
type of function to be used for the cut off probability for superiority. The default is "power" type function. method=OF is an alternative for "O'Brien-Fleming" |
seed |
seed number |
Value
A list with the first element corresponding to futility and the second for efficacy boundaries
Examples
H0 <- 0.2
a1 <- H0
b1 <- 1- a1
seed <- 123
n <- c(10, 5, 5)
method <- "power"
boundary_binary<- get_boundary_binary(H0=H0, a1=a1, b1=b1, n =n,
lambda = seq(0, 1, l = 101),
gamma = seq(0, 1, l = 101),
eta = seq(0, 3, l = 301),
method = method,
seed = seed)
Boundary values for co-primary Endpoint
Description
Boundary values for co-primary Endpoint
Usage
get_boundary_coprimary(
H0,
a,
n,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
Response rate under the null (Response - PFS6, Response - no PFS6, No response - PFS6, No response - No PFS6) |
a |
alpha values for the beta prior (i.e. usually set to the null response rate) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
type of function to be used for the cut off probability for superiority. The default is "power" type function. method=OF is an alternative for "O'Brien-Fleming" |
seed |
seed number |
Value
A list with the first element corresponding to futility and the second for efficacy boundaries
Examples
H0=c(0.05,0.05, 0.15, 0.75)
a <- H0
seed <- 123
n <- c(10, 5, 5)
method <- "power"
test1<- get_boundary_coprimary(H0=H0, a=a, n =n,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power")
Boundary values for joint Endpoint
Description
Boundary values for joint Endpoint
Usage
get_boundary_jointefftox(
H0,
a,
n,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
Response rate under the null (toxicity - OR, no toxicity - OR, toxicity - no OR, no toxicity - No OR) |
a |
alpha values for the beta prior (i.e. usually set to the null response rate) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
type of function to be used for the cut off probability for superiority. The default is "power" type function. method=OF is an alternative for "O'Brien-Fleming" |
seed |
seed number |
Value
A list with the first element corresponding to futility and the second for efficacy boundaries
Examples
H0=c(0.15,0.30, 0.15, 0.40)
a <- H0
seed <- 123
n <- c(10, 5, 5)
method <- "power"
test1<- get_boundary_jointefftox(H0=H0, a=a, n =n,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power")
Boundary values for Nested Endpoint
Description
Boundary values for Nested Endpoint
Usage
get_boundary_nested(
H0,
a,
n,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
Response rate under the null , specified in the following order: - 'H0[1]': Complete Remission (CR) rate, - 'H0[2]': Partial Remission (PR) rate, - 'H0[3]': No Complete Remission or Partial Remission rate, calculated as '1 - (CR + PR)'. |
a |
alpha values for the beta prior (i.e. usually set to the null response rate) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
type of function to be used for the cut off probability for superiority. The default is "power" type function. method=OF is an alternative for "O'Brien-Fleming" |
seed |
seed number |
Value
A list with the first element corresponding to futility and the second for efficacy boundaries
Examples
H0 <- c(0.15, 0.15, 0.70)
a <- H0
seed <- 123
n <- c(10, 5, 5)
method <- "power"
boundary_nested<- get_boundary_nested(H0=H0, a=a, n =n,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = method,
seed = seed)
Computes both the boundary and corresponding operating characteristics for binary endpoints
Description
Computes both the boundary and corresponding operating characteristics for binary endpoints
Usage
get_boundary_oc_binary(
H0,
H1,
n,
nsim,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
Null response rates |
H1 |
Alternative response rates |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_i:
Futility boundary at the ith analysis
- sup_boundary_i:
Superiority boundary at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
Examples
oc_binary<-get_boundary_oc_binary(
H0=0.2,
H1= 0.4,
n = c(10, 5, 5),
nsim = 1000,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power",
seed = 1
)
Computes both the boundary and corresponding operating characteristics for co primary endpoints
Description
Computes both the boundary and corresponding operating characteristics for co primary endpoints
Usage
get_boundary_oc_coprimary(
H0,
H1,
n,
nsim,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': Response - PFS6, - 'H0[2]': Response - no PFS6, - 'H0[3]': No Response - PFS6, - 'H0[4]': No Response - no PFS6 |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': Response - PFS6, - 'H1[2]': Response - no PFS6, - 'H1[3]': No Response - PFS6, - 'H1[4]': No Response - no PFS6 |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_resp_i:
Futility boundary for response at the ith analysis
- fut_boundary_tox_i:
Futility boundary for toxicity at the ith analysis
- sup_boundary_resp_i:
Superiority boundary for response at the ith analysis
- sup_boundary_tox_i:
Superiority boundary for toxicity at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
Examples
oc_coprimary<-get_boundary_oc_coprimary(
H0=c(0.15,0.30, 0.15, 0.40),
H1= c(0.18,0.42, 0.02, 0.38),
n = c(10, 5, 5),
nsim = 1000,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power",
seed = 1
)
Computes both the boundary and corresponding operating characteristics for joint efficacy and toxicity endpoints
Description
Computes both the boundary and corresponding operating characteristics for joint efficacy and toxicity endpoints
Usage
get_boundary_oc_efftox(
H0,
H1,
n,
nsim,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': Response - toxicity, - 'H0[2]': Response - no toxicity, - 'H0[3]': No Response - toxicity, - 'H0[4]': No Response - no toxicity |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': Response - toxicity, - 'H1[2]': Response - no toxicity, - 'H1[3]': No Response - toxicity, - 'H1[4]': No Response - no toxicity. |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_resp_i:
Futility boundary for response at the ith analysis
- fut_boundary_tox_i:
Futility boundary for toxicity at the ith analysis
- sup_boundary_resp_i:
Superiority boundary for response at the ith analysis
- sup_boundary_tox_i:
Superiority boundary for toxicity at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
Examples
oc_joint<-get_boundary_oc_efftox(
H0=c(0.15,0.30, 0.15, 0.40),
H1= c(0.18,0.42, 0.02, 0.38),
n = c(10, 5, 5),
nsim = 1000,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power",
seed = 1
)
Computes both the boundary and corresponding operating characteristics for nested endpoints
Description
Computes both the boundary and corresponding operating characteristics for nested endpoints
Usage
get_boundary_oc_nested(
H0,
H1,
n,
nsim,
lambda,
gamma,
eta = NULL,
method = "power",
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': CR: Complete remission, - 'H0[2]': PR: Partial remission, - 'H0[3]': 1-(CR+PR), |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': CR: Complete remission, - 'H1[2]': PR: Partial remission, - 'H1[3]': 1-(CR+PR), |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_resp_i:
Futility boundary for response at the ith analysis
- fut_boundary_tox_i:
Futility boundary for toxicity at the ith analysis
- sup_boundary_resp_i:
Superiority boundary for response at the ith analysis
- sup_boundary_tox_i:
Superiority boundary for toxicity at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
Examples
oc_nested<-get_boundary_oc_nested(
H0=c(0.15,0.15, 0.70),
H1= c(0.25,0.25, 0.50),
n = c(10, 5, 5),
nsim = 1000,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power",
seed = 1
)
Compute Probability Cutoffs for Futility and efficacy Stopping
Description
This function computes the probability cutoffs for futility stopping using two methods: power and O'Brien-Fleming type function.
Usage
get_cf_cs_values(n, lambda = NULL, gamma = NULL, eta = NULL, method = "power")
Arguments
n |
A numeric vector representing the additional patients enrolled at each interim analysis. The value at index 'i' indicates the number of new patients added at interim analysis 'i'. The total sample size at interim 'i' is the cumulative sum of the values in 'n' up to that index. For example, for four interim analyses with total sample sizes of 10, 15, 20, and 30, the vector would be represented as 'n = c(10, 5, 5, 10)', where: - 10 is the number of patients enrolled at interim 1, - 5 (15 - 10) is the additional number of patients enrolled at interim 2, - 5 (20 - 15) is the additional number of patients enrolled at interim 3, - 10 (30 - 20) is the additional number of patients enrolled at interim 4. |
lambda |
A vector of values for parameter 'lambda' of the cut-off probability (i.e common for both efficacy and futility cut-off probability) |
gamma |
A vector of values for parameter 'gamma' of the cut-off probability for futility |
eta |
A vector of values for parameter 'eta' of the cut-off probability for efficacy |
method |
type of function to be used for the cut off probability for superiority. The default is "power" type function. method=OF is an alternative for "O'Brien-Fleming" |
Value
A list containing two elements:
cf_values |
A matrix of cutoff values for futility stopping. |
cs_values |
A matrix of cutoff values for efficacy. |
Operating characteristics for binary Endpoint
Description
Operating characteristics for binary Endpoint
Usage
get_oc_binary(p, n, nsim, fb, sb, seed = NULL)
Arguments
p |
Response rate |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation |
fb |
vector/matrix of futility boundary at each interim analysis specified in the following order: c(f_1,..., f_length(n)) |
sb |
vector/matrix of superiority boundary at each interim analysis specified in the following order: c(s_1,..., s_length(n)) |
seed |
for reproducibility |
Value
A data frame with the following columns
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
- earlystopfuti_mean:
Average number of early stopping due to futility
- earlystopsupe_mean:
Average number of early stopping for futility due to efficacy
- ss_mean:
Average sample size
- rejectnull_mean:
Average number of hypothesis rejection at the final analysis (aka Type-I error if the response rate is the null rate or Power if the response rate is the alternative rate.
- earlystopfuti_sum:
Total number of early stopping due to futility
- earlystopsupe_sum:
Total number of early early stopping due to efficacy
- ss_sum:
Sum of sample sizes across simulation
- rejectnull_sum:
Total number of hypothesis rejection at the final analysis
Examples
H0 <- 0.2
a1 <- H0
b1 <- 1-a1
seed <- 123
n <- c(10, 5, 5)
method <- "power"
boundary_tab<- get_boundary_binary(H0=H0, a1=a1, b1=b1, n =n,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = method,
seed=seed)
test_oc<-get_oc_binary(
p = 0.2,
n = c(10, 5, 5),
nsim = 1000,
fb = boundary_tab$cnf,
sb = boundary_tab$cns,
seed = seed
)
Operating characteristics for for coprimary Endpoint
Description
Operating characteristics for for coprimary Endpoint
Usage
get_oc_coprimary(p1, p2, p3, p4, n, nsim, fb, sb, seed = NULL)
Arguments
p1 |
Response rate (Response - PFS6) |
p2 |
Response rate (Response - no PFS6) |
p3 |
Response rate (No Response - PFS6) |
p4 |
Response rate (No Response - no PFS6) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation |
fb |
vector/matrix of futility boundary at each interim analysis specified in the following order: c(resp_1,..., resp_length(n), PFS6_1, ..., PFS6_length(n)) |
sb |
vector/matrix of superiority boundary at each interim analysis specified in the following order: c(resp_1,..., resp_length(n), PFS6_1, ..., PFS6_length(n)) |
seed |
for reproducibility |
Value
A data frame with the following columns
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
- earlystopfuti_mean:
Average number of early stopping due to futility
- earlystopsupe_mean:
Average number of early stopping for futility due to efficacy
- ss_mean:
Average sample size"
- rejectnull_mean:
"Average number of hypothesis rejection at the final analysis (aka Type-I error if the response rate is the null rate or Power if the response rate is the alternative rate.
- earlystopfuti_sum:
Total number of early stopping due to futility
- earlystopsupe_sum:
Total number of early early stopping due to efficacy
- ss_sum:
Sum of sample sizes across simulation"
- rejectnull_sum:
Total number of hypothesis rejection at the final analysis
Examples
H0=c(0.05,0.05, 0.15, 0.75)
a <- H0
seed <- 123
n <- c(10, 5, 5)
method <- "power"
boundary_tab<- get_boundary_coprimary(H0=H0, a=a, n =n,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power",
seed=seed)
test_oc<-get_oc_coprimary(
p1 = 0.05,
p2 = 0.05,
p3 = 0.15,
p4 = 0.75,
n = c(10, 5, 5),
nsim = 1000,
fb = boundary_tab$cnf,
sb = boundary_tab$cns,
seed = seed
)
Operating characteristics for for joint Endpoint
Description
Operating characteristics for for joint Endpoint
Usage
get_oc_jointefftox(p1, p2, p3, p4, n, nsim, fb, sb, seed = NULL)
Arguments
p1 |
Response rate (Response - toxicity) |
p2 |
Response rate (Response - no toxicity) |
p3 |
Response rate (No Response - toxicity) |
p4 |
Response rate (No Response - no toxicity) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation |
fb |
vector/matrix of futility boundary at each interim analysis specified in the following order: c(resp_1,..., resp_length(n), tox_1, ..., tox_length(n)) |
sb |
vector/matrix of superiority boundary at each interim analysis specified in the following order: c(resp_1,..., resp_length(n), tox_1, ..., tox_length(n)) |
seed |
for reproducibility |
Value
A data frame with the following columns
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
- earlystopfuti_mean:
Average number of early stopping due to futility
- earlystopsupe_mean:
Average number of early stopping for futility due to efficacy
- ss_mean:
Average sample size"
- rejectnull_mean:
"Average number of hypothesis rejection at the final analysis (aka Type-I error if the response rate is the null rate or Power if the response rate is the alternative rate.
- earlystopfuti_sum:
Total number of early stopping due to futility
- earlystopsupe_sum:
Total number of early early stopping due to efficacy
- ss_sum:
Sum of sample sizes across simulation"
- rejectnull_sum:
Total number of hypothesis rejection at the final analysis
Examples
H0=c(0.15,0.30, 0.15, 0.40)
a <- H0
seed <- 123
n <- c(10, 5, 5)
method <- "power"
boundary_tab<- get_boundary_jointefftox(H0=H0, a=a, n =n,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = "power",
seed=seed)
test_oc<-get_oc_jointefftox(
p1 = 0.15,
p2 = 0.30,
p3 = 0.15,
p4 = 0.40,
n = c(10, 5, 5),
nsim = 1000,
fb = boundary_tab$cnf,
sb = boundary_tab$cns,
seed = seed
)
Operating characteristics for Nested Endpoint
Description
Operating characteristics for Nested Endpoint
Usage
get_oc_nested(p1, p2, p3, n, nsim, fb, sb, seed = NULL)
Arguments
p1 |
Response rate (CR: Complete remission) |
p2 |
Response rate (PR: Partial remission) |
p3 |
Response rate (1-(CR+PR)) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation |
fb |
vector/matrix of futility boundary at each interim analysis specified in the following order: c(CR_1,..., CR_length(n), CR/PR_1, ..., CR/PR_length(n)) |
sb |
vector/matrix of superiority boundary at each interim analysis specified in the following order: c(CR_1,..., CR_length(n), CR/PR_1, ..., CR/PR_length(n)) |
seed |
for reproducibility |
Value
A data frame with the following columns
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
- earlystopfuti_mean:
Average number of early stopping due to futility
- earlystopsupe_mean:
Average number of early stopping for futility due to efficacy
- ss_mean:
Average sample size"
- rejectnull_mean:
"Average number of hypothesis rejection at the final analysis (aka Type-I error if the response rate is the null rate or Power if the response rate is the alternative rate.
- earlystopfuti_sum:
Total number of early stopping due to futility
- earlystopsupe_sum:
Total number of early early stopping due to efficacy
- ss_sum:
Sum of sample sizes across simulation"
- rejectnull_sum:
Total number of hypothesis rejection at the final analysis
Examples
H0=c(0.15, 0.15, 0.70)
a <- H0
seed <- 123
n <- c(10, 5, 5)
method <- "power"
boundary_tab<- get_boundary_nested(H0=H0, a=a, n =n,
lambda = seq(0, 1, l = 11),
gamma = seq(0, 1, l = 11),
eta = seq(0, 3, l = 31),
method = method,
seed=seed)
test_oc<-get_oc_nested(
p1 = 0.15,
p2 = 0.15,
p3 = 0.70,
n = c(10, 5, 5),
nsim = 1000,
fb = boundary_tab$cnf,
sb = boundary_tab$cns,
seed = seed
)
Plot the cut-off probability and simulation results for BOP2FE designs
Description
Plot the objects returned by other functions, including (1) cut-off probability; (2) boundary values; (3) operating characteristics
Usage
## S3 method for class 'bop2fe'
plot(x, ...)
Arguments
x |
the object returned by BOP2FE_xx |
... |
additional parameters |
Value
plot() returns a figure depending on the object entered
Search optimal parameters for binary endpoint
Description
'search_optimal_pars_binary()' is a helper function and calls 'get_boundary_oc_binary()' to obtain the optimal parameter combinations with type I error less than t1e and sorted according to power.
Usage
search_optimal_pars_binary(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric value for the response rate under the null hypothesis |
H1 |
A numeric value for the response rate under the alternative hypothesis |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search |
lambda2 |
ending value for 'lambda' values to search |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2 |
gamma1 |
starting value for 'gamma' values to search |
gamma2 |
ending value for 'gamma' values to search |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2 |
eta1 |
starting value for 'eta' values to search |
eta2 |
ending value for 'eta' values to search |
grid3 |
number of eta values to consider between eta1 and eta2 |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_i:
Futility boundary at the ith analysis
- sup_boundary_i:
Superiority boundary at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:2
eta values for cut-off probability
Examples
test_binary <- search_optimal_pars_binary(
H0=0.2,
H1= 0.4,
n = c(10, 5, 5),
nsim = 1000,
t1e = 0.1,
method = "power",
lambda1 = 0,
lambda2 = 1,
grid1 = 11,
gamma1 = 0,
gamma2 = 1,
grid2 = 11,
eta1 = 0,
eta2 = 3,
grid3 = 31,
seed = 123
)
Search optimal parameters for co primary endpoint
Description
'search_optimal_pars_coprimary()' is a helper function and calls 'get_boundary_oc_coprimary()' to obtain the optimal parameter combinations with type I error less than t1e and sorted according to power.
Usage
search_optimal_pars_coprimary(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': Response - PFS6, - 'H0[2]': Response - no PFS6, - 'H0[3]': No Response - PFS6, - 'H0[4]': No Response - no PFS6 |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': Response - PFS6, - 'H1[2]': Response - no PFS6, - 'H1[3]': No Response - PFS6, - 'H1[4]': No Response - no PFS6 |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search |
lambda2 |
ending value for 'lambda' values to search |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2 |
gamma1 |
starting value for 'gamma' values to search |
gamma2 |
ending value for 'gamma' values to search |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2 |
eta1 |
starting value for 'eta' values to search |
eta2 |
ending value for 'eta' values to search |
grid3 |
number of eta values to consider between eta1 and eta2 |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_resp_i:
Futility boundary for response at the ith analysis
- fut_boundary_tox_i:
Futility boundary for toxicity at the ith analysis
- sup_boundary_resp_i:
Superiority boundary for response at the ith analysis
- sup_boundary_tox_i:
Superiority boundary for toxicity at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
Examples
test_comprimary <- search_optimal_pars_coprimary(
H0=c(0.05,0.05, 0.15, 0.75),
H1= c(0.15,0.15, 0.20, 0.50),
n = c(10, 5, 5),
nsim = 1000,
t1e = 0.1,
method = "power",
lambda1 = 0,
lambda2 = 1,
grid1 = 11,
gamma1 = 0,
gamma2 = 1,
grid2 = 11,
eta1 = 0,
eta2 = 3,
grid3 = 31,
seed = 123
)
Search optimal parameters for joint efficacy and toxicity endpoint
Description
'search_optimal_pars_efftox()' is a helper function and calls 'get_boundary_oc_efftox()' to obtain the optimal parameter combinations with type I error less than t1e and sorted according to power.
Usage
search_optimal_pars_efftox(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': Response - toxicity, - 'H0[2]': Response - no toxicity, - 'H0[3]': No Response - toxicity, - 'H0[4]': No Response - no toxicity |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': Response - toxicity, - 'H1[2]': Response - no toxicity, - 'H1[3]': No Response - toxicity, - 'H1[4]': No Response - no toxicity. |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search |
lambda2 |
ending value for 'lambda' values to search |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2 |
gamma1 |
starting value for 'gamma' values to search |
gamma2 |
ending value for 'gamma' values to search |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2 |
eta1 |
starting value for 'eta' values to search |
eta2 |
ending value for 'eta' values to search |
grid3 |
number of eta values to consider between eta1 and eta2 |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_resp_i:
Futility boundary for response at the ith analysis
- fut_boundary_tox_i:
Futility boundary for toxicity at the ith analysis
- sup_boundary_resp_i:
Superiority boundary for response at the ith analysis
- sup_boundary_tox_i:
Superiority boundary for toxicity at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
Examples
test_joint <- search_optimal_pars_efftox(
H0=c(0.15,0.30, 0.15, 0.40),
H1= c(0.18,0.42, 0.02, 0.38),
n = c(10, 5, 5),
nsim = 1000,
t1e = 0.1,
method = "power",
lambda1 = 0,
lambda2 = 1,
grid1 = 11,
gamma1 = 0,
gamma2 = 1,
grid2 = 11,
eta1 = 0,
eta2 = 3,
grid3 = 31,
seed = 123
)
Search optimal parameters for nested endpoint
Description
'search_optimal_pars_nested()' is a helper function and calls 'get_boundary_oc_nested()' to obtain the optimal parameter combinations with type I error less than t1e and sorted according to power.
Usage
search_optimal_pars_nested(
H0,
H1,
n,
nsim,
t1e = NULL,
method = "power",
lambda1,
lambda2,
grid1,
gamma1,
gamma2,
grid2,
eta1 = NULL,
eta2 = NULL,
grid3 = NULL,
seed = NULL
)
Arguments
H0 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H0[1]': CR: Complete remission, - 'H0[2]': PR: Partial remission, - 'H0[3]': 1-(CR+PR) |
H1 |
A numeric vector representing the null response rates for different outcomes, specified in the following order: - 'H1[1]': CR: Complete remission, - 'H1[2]': PR: Partial remission, - 'H1[3]': 1-(CR+PR) |
n |
A numeric vector representing the additional patients enrolled at each interim analysis.
The value at index
|
nsim |
number of simulation. A value at least 1000 for better result |
t1e |
Desired Type - I error rate. If specified it will only return results with type I error rate less the specified value |
method |
A character string specifying the method to use for calculating cutoff values for the efficacy stopping. Options are "power" (default) or "OF" for "O'Brien-Fleming". |
lambda1 |
starting value for 'lambda' values to search |
lambda2 |
ending value for 'lambda' values to search |
grid1 |
number of 'lambda' values to consider between lambda1 and lambda2 |
gamma1 |
starting value for 'gamma' values to search |
gamma2 |
ending value for 'gamma' values to search |
grid2 |
number of 'gamma' values to consider between gamma1 and gamma2 |
eta1 |
starting value for 'eta' values to search |
eta2 |
ending value for 'eta' values to search |
grid3 |
number of eta values to consider between eta1 and eta2 |
seed |
for reproducibility |
Value
A data frame with the following columns
- fut_boundary_resp_i:
Futility boundary for response at the ith analysis
- fut_boundary_tox_i:
Futility boundary for toxicity at the ith analysis
- sup_boundary_resp_i:
Superiority boundary for response at the ith analysis
- sup_boundary_tox_i:
Superiority boundary for toxicity at the ith analysis
- earlystopfuti_mean_h0:
Average number of early stopping due to futility under the null hypothesis
- earlystopsupe_mean_h0:
Average number of early stopping for futility due to efficacy under the null hypothesis
- ss_mean_h0:
Average sample size under the null hypothesis
- rejectnull_mean_h0:
Average number of hypothesis rejection at the final analysis under the null hypothesis
- earlystopfuti_mean_h1:
Average number of early stopping due to futility under the alternative hypothesis
- earlystopsupe_mean_h1:
Average number of early early stopping due to efficacy under the alternative hypothesis
- ss_mean_h1:
Average sample size under the alternative hypothesis
- rejectnull_mean_h1:
Average number of hypothesis rejection at the final analysis under the alternative hypothesis
- lambda:
lambda values for cut-off probability
- gamma:
gamma values for cut-off probability
- eta:
eta values for cut-off probability
Examples
test_nested <- search_optimal_pars_nested(
H0=c(0.15,0.15, 0.70),
H1= c(0.25,0.25, 0.50),
n = c(10, 5, 5),
nsim = 1000,
t1e = 0.1,
method = "power",
lambda1 = 0,
lambda2 = 1,
grid1 = 11,
gamma1 = 0,
gamma2 = 1,
grid2 = 11,
eta1 = 0,
eta2 = 3,
grid3 = 31,
seed = 123
)
Compute operating characteristics at the optimal boundary
Description
After identifying the optimal boundary that controls the Type I error rate less than or equal to 0.1 under H0 and maximize the power under H1, it might be of interest to compute the operating characteristics of the optimal boundary under a different H1 values. This function accepts a single or multiple values of additional H1 values and compute the operating characteristics for each of them.
Usage
simulate_oc(object, p, endpoint, seed = NULL)
Arguments
object |
the object returned by BOP2FE_xx |
p |
a single vector or a list of vector for which the operating characteristics is desired. |
endpoint |
the type of endpoint. Possible options are 'binary', 'nested', 'coprimary', and 'joint'. |
seed |
for reproducibility |
Value
simulate_oc() returns a data frame with the optimal pars and boundary from the given object as well
as the operating characteristics. If a single p vector is supplied the result will be a data frame
with a single row. If multiple p vectors are supplied the data frame will be have multiple rows each
corresponding to the p vectors in the order of their specification
Examples
test_nested <- BOP2FE_nested(
H0=c(0.15,0.15, 0.70),
H1= c(0.25,0.25, 0.50),
n = c(10, 5, 5),
nsim = 1000, t1e = 0.1, method = "power",
lambda1 = 0, lambda2 = 1, grid1 = 11,
gamma1 = 0, gamma2 = 1, grid2 = 11,
eta1 = 0, eta2 = 3, grid3 = 31,
seed = 123
)
# Compute operating characteristics for a single p vector
simulate_oc(test_nested, p=c(0.30,0.30,0.40),
endpoint = 'nested', seed=123)
# Compute operating characteristics for multiple p vector
simulate_oc(test_nested, p=list(c(0.30,0.30,0.40),c(0.35,0.35,0.30)),
endpoint = 'nested', seed=123)
summarize main results for a given BOP2FE designs
Description
summarize main results for a given BOP2FE designs
Usage
## S3 method for class 'bop2fe'
summary(object, ...)
Arguments
object |
the object returned by BOP2FE_xx |
... |
additional parameters |
Value
summary() returns a list depending on the object entered including design parameters,
boundary, operating characteristics.