optimal {frequentistSSD}

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

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

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)