| Title: | Screened Selection Design with Survival Endpoints |
|---|---|
| Description: | A study based on the screened selection design (SSD) is an exploratory phase II randomized trial with two or more arms but without concurrent control. The primary aim of the SSD trial is to pick a desirable treatment arm (e.g., in terms of the median survival time) to recommend to the subsequent randomized phase IIb (with the concurrent control) or phase III. Though The survival endpoint is often encountered in phase II trials, the existing SSD methods cannot deal with the survival endpoint. Furthermore, the existing SSD won’t control the type I error rate. The proposed designs can “partially” control or provide the empirical type I error/false positive rate by an optimal algorithm (implemented by the optimal() function) for each arm. All the design needed components (sample size, operating characteristics) are supported. |
| 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: | 2024-11-28 06:28:02 UTC |
| Source: | CRAN |
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()
get_oc(shape, m0, mA, hr, frac, ta, tf, c1, c, diff, n, nsim, seed = 2483)get_oc(shape, m0, mA, hr, frac, ta, tf, c1, c, diff, n, nsim, seed = 2483)
shape |
the shape parameter of weibull distribution |
m0 |
the median survival time of historical data |
mA |
the median survival time of arm A |
hr |
the hazard ratio of arm B to arm A |
frac |
the ratio of sample size in stage 1 compared to total sample size (e.g., n1/n) |
ta |
the accrual duration |
tf |
the follow-up duration |
c1 |
the critical value at stage 1 |
c |
the critical value at stage 2 |
diff |
the equivalence margin |
n |
the total sample size for each arm |
nsim |
the number of simulated trials |
seed |
the seed. The default value is seed = 2483 |
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
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted
## 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)## 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)
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()
get_oc_3arm(shape, m0, mA, hr2, hr3, frac, ta, tf, c1, c, diff, n, nsim, seed = 2483)get_oc_3arm(shape, m0, mA, hr2, hr3, frac, ta, tf, c1, c, diff, n, nsim, seed = 2483)
shape |
the shape parameter of weibull distribution |
m0 |
the median survival time of historical data |
mA |
the median survival time of arm A |
hr2 |
the hazard ratio of arm B to arm A |
hr3 |
the hazard ratio of arm C to arm A |
frac |
the ratio of sample size in stage 1 compared to total sample size (e.g., n1/n) |
ta |
the accrual duration |
tf |
the follow-up duration |
c1 |
the critical value at stage 1 |
c |
the critical value at stage 2 |
diff |
the equivalence margin |
n |
the total sample size for each arm |
nsim |
the number of simulated trials |
seed |
the seed. The default value is seed = 2483 |
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
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted
## 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)## 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 the optimal parameters used in the get_oc() function
optimal(shape, m0, ms, tf, ta, tot_size, dist)optimal(shape, m0, ms, tf, ta, tot_size, dist)
shape |
the shape parameter of weibull distribution |
m0 |
the median survival time of historical data |
ms |
the minimal clinical meaningful median survival time |
tf |
the follow-up duration |
ta |
the accrual duration |
tot_size |
the required sample size for each arm |
dist |
the distribution |
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
(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
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted
## 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)## 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 in a two-arm trial
sample_size(kappa, mA, hr, ta, tf, diff, P)sample_size(kappa, mA, hr, ta, tf, diff, P)
kappa |
the shape parameter of weibull distribution |
mA |
the median survival time of arm A |
hr |
the hazard ratio of arm B to arm A |
ta |
the accrual duration |
tf |
the follow-up duration |
diff |
the equivalence margin |
P |
the chance of correctly selecting the superior arm |
sample_size() returns required sample size for each arm
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted
sample_size(kappa = 1, mA = 2.4, hr = 0.60, ta = 24, tf = 3, diff = 0.25, P = 0.9)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 in a three-arm trial
sample_size_3arm(kappa, m0, mA, mB, delta, ta, tf, P, diff)sample_size_3arm(kappa, m0, mA, mB, delta, ta, tf, P, diff)
kappa |
the shape parameter of weibull distribution |
m0 |
the median survival time of historical control with respect to both arm A, B and C |
mA |
the median survival time of arm A |
mB |
the median survival time of arm B |
delta |
the hazard ratio of arm C to arm A |
ta |
the accrual duration |
tf |
the follow-up duration |
P |
the chance of correctly selecting the superior arm |
diff |
the equivalence margin |
sample_size_3arm() returns required sample size for each arm
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted
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)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)
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
sampsize_1stage_2arm(kappa, alpha, beta, m0, m1, ta, tf, delta)sampsize_1stage_2arm(kappa, alpha, beta, m0, m1, ta, tf, delta)
kappa |
the shape parameter of weibull distribution |
alpha |
type I error rate |
beta |
type II error rate |
m0 |
the median survival time of historical control with respect to both arm A and B |
m1 |
the median survival time of arm A |
ta |
the accrual duration |
tf |
the follow-up duration |
delta |
the hazard ratio of arm B to arm A |
sampsize_1stage_2arm() returns required sample size for each arm
Chia-Wei Hsu, Haitao Pan, Jianrong Wu
Jianrong Wu, Haitao Pan, Chia-Wei Hsu (2021). "Two-Stage Screened Selection Designs for Randomized Phase II Trials with Time-to-Event Endpoints." Submitted
sampsize_1stage_2arm(kappa = 1, alpha = 0.05, beta = 0.1, m0 = 1, m1 = 2.5, delta = 0.65, ta = 24, tf = 9)sampsize_1stage_2arm(kappa = 1, alpha = 0.05, beta = 0.1, m0 = 1, m1 = 2.5, delta = 0.65, ta = 24, tf = 9)