| Title: | Bayesian Single-Arm Design with Survival Endpoints |
|---|---|
| Description: | The proposed event-driven approach for Bayesian two-stage single-arm phase II trial design is a novel clinical trial design and can be regarded as an extension of the Simon’s two-stage design with the time-to-event endpoint. This design is motivated by cancer clinical trials with immunotherapy and molecularly targeted therapy, in which time-to-event endpoint is often a desired endpoint. |
| Authors: | Chia-Wei Hsu [aut, cre], Haitao Pan [aut], Jianrong Wu [aut] |
| Maintainer: | Chia-Wei Hsu <[email protected]> |
| License: | GPL-2 |
| Version: | 0.1.1 |
| Built: | 2024-10-31 20:49:03 UTC |
| Source: | CRAN |
Obtain design parameters, type I error, power and operating characteristics of the Bayesian Single-Arm Phase II Trial Designs with Time-to-Event Endpoints (Wu et al. 2021). The exponential distribution is assumed for the survival time. The gamma prior is used here
optimal_OneStage(alphacutoff, powercutoff, S0, x, ta, tf, a = 2, delta, ntrial, complete = "partial", seed = 8232)optimal_OneStage(alphacutoff, powercutoff, S0, x, ta, tf, a = 2, delta, ntrial, complete = "partial", seed = 8232)
alphacutoff |
the desired type I error to be controlled |
powercutoff |
the desired power to be achieved |
S0 |
the survival probability at timepoint x |
x |
the survival probability S0 at timepoint x |
ta |
accrual duration |
tf |
follow-up duration |
a |
shape parameter of prior distribution. The default value is a = 2 |
delta |
hazard ratio |
ntrial |
the number of simulated trials |
complete |
whether output the full or partial information. The default value is complete = "partial". If want to show full results, it would be complete = "complete" |
seed |
the seed. The default value is seed = 8232 |
optimal_OneStage() depending on the argument "complete", it returns a vector of partial information/complete information which includes:
partial information: (1) m: number of events of the whole design (2) n: number of patients of the whole design (3) k: total observation time of the whole design (4) typeI: type I error of the whole design (5) power: power of the whole design (6) ES1: expected sample size under alternative hypothesis (7) ES0: expected sample size under null hypothesis
full information: (1) eta: cutoff point of "Go" at final stage of analysis (2) zeta: cutoff point of "no-Go" at final stage of analysis (3) m: number of events of the whole design (4) n: number of patients of the whole design (5) k: total observation time of the whole design (6) typeI: type I error of the whole design (7) power: power of the whole design (8) ES1: expected sample size under alternative hypothesis (9) ES0: expected sample size under null hypothesis
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Bayesian Single-Arm Phase II Trial Designs with Time-to-Event Endpoints." Pharmaceutical Statistics. Accepted
### Design 1 # H0 vs. H1: 17% vs. 40% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.517 # x = 4 optimal_OneStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.517, ntrial = 10) ### Design 2 # H0 vs. H1: 17% vs. 30% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.679 # x = 4 optimal_OneStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.679, ntrial = 10)### Design 1 # H0 vs. H1: 17% vs. 40% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.517 # x = 4 optimal_OneStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.517, ntrial = 10) ### Design 2 # H0 vs. H1: 17% vs. 30% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.679 # x = 4 optimal_OneStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.679, ntrial = 10)
Obtain design parameters, type I error, power and operating characteristics of the Bayesian Single-Arm Phase II Trial Designs with Time-to-Event Endpoints (Wu et al. 2021). The exponential distribution is assumed for the survival time. The gamma prior is used here
optimal_TwoStage(alphacutoff, powercutoff, S0, x, ta, tf, a = 2, delta, frac = .5, ntrial, complete = "partial", seed = 8232)optimal_TwoStage(alphacutoff, powercutoff, S0, x, ta, tf, a = 2, delta, frac = .5, ntrial, complete = "partial", seed = 8232)
alphacutoff |
the desired type I error to be controlled |
powercutoff |
the desired power to be achieved |
S0 |
the survival probability at timepoint x |
x |
the survival probability S0 at timepoint x |
ta |
accrual duration |
tf |
follow-up duration |
a |
shape parameter of prior distribution. The default value is a = 2 |
delta |
hazard ratio |
frac |
a information fraction for interim analysis. The fefault value is frac = 0.5 |
ntrial |
the number of simulated trials |
complete |
whether output the full or partial information. The default value is complete = "partial". If want to show full results, it would be complete = "complete" |
seed |
the seed. The default value is seed = 8232 |
optimal() depending on the argument "complete", it returns a vector of partial information/complete information which includes:
partial information: (1) m1: number of events at stage 1 (2) n1: number of patients at stage 1 (3) k1: total observation time at stage 1 (4) m: number of events of the whole design (5) n: number of patients of the whole design (6) k: total observation time of the whole design (7) typeI: type I error of the whole design (8) power: power of the whole design (9) PET1: early stopping probabilites under alternative hypothesis (10) ES1: expected sample size under alternative hypothesis (11) PET0: early stopping probabilites under null hypothesis (12) ES0: expected sample size under null hypothesis
full information: (1) eta: cutoff point of "Go" at final stage of analysis (2) xi: cutoff point of "no-Go" at final stage of analysis (3) m1: number of events at stage 1 (4) n1: number of patients at stage 1 (5) k1: total observation time at stage 1 (6) m: number of events of the whole design (7) n: number of patients of the whole design (8) k: total observation time of the whole design (9) typeI: type I error of the whole design (10) power: power of the whole design (11) PET1: early stopping probabilites under alternative hypothesis (12) ES1: expected sample size under alternative hypothesis (13) PET0: early stopping probabilites under null hypothesis (14) ES0: expected sample size under null hypothesis
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Bayesian Single-Arm Phase II Trial Designs with Time-to-Event Endpoints." Pharmaceutical Statistics. Accepted
### Design 1 # H0 vs. H1: 17% vs. 40% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.517 # x = 4 optimal_TwoStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.517, ntrial = 10) ### Design 2 # H0 vs. H1: 17% vs. 30% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.679 # x = 4 optimal_TwoStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.679, ntrial = 10)### Design 1 # H0 vs. H1: 17% vs. 40% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.517 # x = 4 optimal_TwoStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.517, ntrial = 10) ### Design 2 # H0 vs. H1: 17% vs. 30% (4-month PFS) # that is, S0 = 0.17, and hazard ratio, e.g., delta = 0.679 # x = 4 optimal_TwoStage(alphacutoff = 0.1, powercutoff = 0.8, S0 = 0.17, x = 4, ta = 6, tf = 6, delta = 0.679, ntrial = 10)
Sum up transformed observation time for each patient to get U in order to determine the trial: (1) goes to second stage (2) stops for futility (3) declares the treatment is promising and warrants for further study in a large scale phase III trial (4) declares the treatment is unpromising and is not worth for further study.
tot_time(obs_time, S0, x)tot_time(obs_time, S0, x)
obs_time |
a vector. Each element represents an observation time of the patient |
S0 |
the survival probability at timepoint x |
x |
the survival probability S0 at timepoint x |
the function returns the total transformed observation time for all patients
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Bayesian Single-Arm Phase II Trial Designs with Time-to-Event Endpoints." Pharmaceutical Statistics. Accepted
obs_time <- c(3.003, 11.987, 4.306, 2.561, 1.575, 0.329, 1.940, 0.869, 7.481, 1.861, 7.279, 0.007, 6.485, 1.981, 4.257, 0.967, 2.619, 0.040, 0.426, 4.628) S0 <- 0.17 x <- 4 tot_time(obs_time = obs_time, S0 = S0, x = x)obs_time <- c(3.003, 11.987, 4.306, 2.561, 1.575, 0.329, 1.940, 0.869, 7.481, 1.861, 7.279, 0.007, 6.485, 1.981, 4.257, 0.967, 2.619, 0.040, 0.426, 4.628) S0 <- 0.17 x <- 4 tot_time(obs_time = obs_time, S0 = S0, x = x)