Generate operating characteristics for Two-Stage Screened Selection Design for Randomized Phase II Trials with Time-to-Event Endpoints

Description

Obtain the operating characteristics of Two-Stage Screened Selection Design for Randomized Phase II Trials with Time-to-Event Endpoints. The arguments for this function are from outputs of the functions of optimal() and sample_size()

Usage

get_oc(shape, m0, mA, hr, frac, ta, tf, c1, c,
       diff, n, nsim, seed = 2483)

Arguments

Value

get_oc() returns: (1) n: total sample size for each arm (2) SSD.Arm.A: selection probability of Arm A (3) SSD.Arm.B: selection probability of Arm B (4) SSD.No.Arm: the probability of no arms selected (5) diff: the equivalence margin (6) Mean.N.Arm.A: the average number of patients allocated to Arm A (7) Mean.N.Arm.B: the average number of patients allocated to Arm B

Author(s)

Chia-Wei Hsu, Haitao Pan, Jianrong Wu

References

Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted

Examples

## c1, n, c they all come from optimal function. Details are shown as follows:
## Not run: optimal(shape = 1, m0 = 1, ms = 2.4, tf = 3,
                 ta = 24, tot_size = 19, dist = "WB")
| alpha | beta | n1 |   c1   |  n |    c   |   t1    | MTSL |   ESS   |   PS
|  0.05 | 0.08 | 15 | 0.0508 | 19 | 1.6434 | 17.9751 |  27  | 16.5183 | 0.5203

## End(Not run)

get_oc(shape = 1, m0 = 1, mA = 2.4, hr = 0.6, frac = 15/19,
       ta = 24, tf = 3, c1 = 0.0508, c = 1.6434,
       diff = 0.25, n = 19, nsim = 10000)

Generate operating characteristics for Two-Stage Screened Selection Design for Randomized Phase II Trials with Time-to-Event Endpoints for 3 arms

Description

Obtain the operating characteristics of Two-Stage Screened Selection Design for Randomized Phase II Trials with Time-to-Event Endpoints for 3 arms. The arguments for this function are from outputs of the functions of optimal() and sample_size_3arm()

Usage

get_oc_3arm(shape, m0, mA, hr2, hr3, frac, ta, tf, c1, c,
            diff, n, nsim, seed = 2483)

Arguments

Value

get_oc_3arm() returns: (1) n: total sample size for each arm (2) SSD.Arm.A: selection probability of Arm A (3) SSD.Arm.B: selection probability of Arm B (4) SSD.Arm.C: selection probability of Arm C (5) SSD.No.Arm: the probability of no arms selected (6) diff: the equivalence margin (7) Mean.N.Arm.A: the average number of patients allocated to Arm A (8) Mean.N.Arm.B: the average number of patients allocated to Arm B (9) Mean.N.Arm.C: the average number of patients allocated to Arm C

Author(s)

Chia-Wei Hsu, Haitao Pan, Jianrong Wu

References

Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted

Examples

## c1, n, c they all come from optimal function. Details are shown as follows:
## Not run: optimal(shape = 1, m0 = 1, ms = 2, tf = 3,
                 ta = 24, tot_size = 21, dist = "WB")
| alpha | beta | n1 |    c1   |  n |   c   |   t1    | MTSL |   ESS   |   PS
|  0.05 | 0.14 | 16 | -0.0463 | 21 | 1.644 | 17.8248 |  27  | 18.3983 | 0.4815

## End(Not run)

get_oc_3arm(shape = 1, m0 = 1, mA = 2, hr2 = 1, hr3 = 0.6,
            frac = 16/21, ta = 24, tf = 3, c1 = -0.0463,
            c = 1.644, diff = 0, n = 21, nsim = 10000,
            seed = 2483)

Find optimal parameters

Description

Find the optimal parameters used in the get_oc() function

Usage

optimal(shape, m0, ms, tf, ta,
        tot_size, dist)

Arguments

Value

optimal() returns a list containing two blocks:

$param: (1) S0: historical survival probability at the landmark time point x0 (2) hr: hazard ratio of the hypothetical arm with “minimal clinical meaningful median survival time” to the historical arm (3) rate: accrual rate (calculated as tot_size/ta)

$Two_stage: (1) alpha: type I error (2) beta: type II error (3) n1: the required sample size for the first stage (4) c1: the cutoff point at the first stage (5) n: the required sample size for each arm (is equal to tot_size) (6) c: the cutoff point at the final stage (7) t1: the expected time of interim analysis (first stage) (8) MTSL: the maximum total study length (ta + tf) (9) ESS: the expected sample size for each arm (10) PS: the probability of early stopping

Note

(1) For optimal() function, if the ms is set to be equal to the less effective arm (e.g., say, the arm A is less effective than the arm B), with the rationale, by this way, the computed boundaries, c1, n1, c, would control the pre-specified type I (since both arms A and B are all under the same null case) while the power for the better arm B, would have at least pre-specified power 1-beta

(2) optimal() funcition will be applied to either two or three-arm cases to find the optimal cutoff bounaries, c1, n1, c

Author(s)

Chia-Wei Hsu, Haitao Pan, Jianrong Wu

References

Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted

Examples

## For 2 arms
## Not run: 
shape <- 1
m0 <- 1
ms <- 2.4
tf <- 3
ta <- 24
tot_size <- 19
dist <- "WB"

optimal(shape = shape, m0 = m0, ms = ms, tf = tf,
        ta = ta, tot_size = tot_size, dist = dist)

## End(Not run)

## For 3 arms
## Not run: 
shape <- 1
m0 <- 1
ms <- 2
tf <- 3
ta <- 24
tot_size <- 21
dist <- "WB"

optimal(shape = shape, m0 = m0, ms = ms, tf = tf,
        ta = ta, tot_size = tot_size, dist = dist)

## End(Not run)

Calculate the sample size for each arm

Description

Calculate the sample size for each arm in a two-arm trial

Usage

sample_size(kappa, mA, hr, ta, tf, diff, P)

Arguments

Value

sample_size() returns required sample size for each arm

Author(s)

Chia-Wei Hsu, Haitao Pan, Jianrong Wu

References

Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted

Examples

sample_size(kappa = 1, mA = 2.4, hr = 0.60, ta = 24,
            tf = 3, diff = 0.25, P = 0.9)

Calculate the sample size for each arm

Description

Calculate the sample size for each arm in a three-arm trial

Usage

sample_size_3arm(kappa, m0, mA, mB, delta, ta, tf, P, diff)

Arguments

Value

sample_size_3arm() returns required sample size for each arm

Author(s)

Chia-Wei Hsu, Haitao Pan, Jianrong Wu

References

Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted

Examples

sample_size_3arm(kappa = 1, m0 = 1, mA = 2, mB = 2, delta = 0.6,
                 ta = 24, tf = 3, P = 0.90, diff = 0)

sample_size_3arm(kappa = 1, m0 = 1, mA = 2, mB = 2, delta = 0.6,
                 ta = 24, tf = 3, P = 0.90, diff = 0.25)

Calculate the sample size for each arm

Description

Provide the required sample size (per arm) based on the one-stage selection design given the type I error rate and power. Details see the reference paper

Usage

sampsize_1stage_2arm(kappa, alpha, beta, m0, m1, ta, tf, delta)

Arguments

Value

sampsize_1stage_2arm() returns required sample size for each arm

Author(s)

Chia-Wei Hsu, Haitao Pan, Jianrong Wu

References

Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted

Examples

sampsize_1stage_2arm(kappa = 1, alpha = 0.05, beta = 0.1, m0 = 1,
                     m1 = 2.5, delta = 0.65, ta = 24, tf = 9)