optimal_TwoStage {BayesDesign}

Obtain design settings for two-stage Bayesian Single-Arm Phase II Trial with Time-to-Event Endpoints

Description

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

Usage

optimal_TwoStage(alphacutoff, powercutoff, S0, x,
                 ta, tf, a = 2, delta, frac = .5,
                 ntrial, complete = "partial", seed = 8232)

Arguments

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

Value

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

Author(s)

Chia-Wei Hsu, Haitao Pan, Jianrong Wu

References

Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Bayesian Single-Arm Phase II Trial Designs with Time-to-Event Endpoints." Pharmaceutical Statistics. Accepted

Examples

### 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)