Optimal TwoStage or ThreeStage Designs with Userspecified Combined Sample Size or Study Length
Description
Construct a twostage or threestage design with a timetoevent endpoint evaluated at a prespecified time (e.g., 6month progressionfree survival) comparing treatment versus either a historical control rate with possible stopping for futility (singlearm), or an active control arm with possible stopping for both futility and superiority (twoarm), after the end of Stage 1 utilizing time to event data. The design minimizes either the expected duration of accrual (EDA), the expected sample size (ES), or the expected total study length (ETSL). The maximum combined sample size for both stages is prespecifed by the user.
Usage
1 2 3 4 5  np.OptimDes(
B.init, m.init, alpha, beta, param, x, n = NULL, pn = NULL,
pt = NULL, target = c("EDA", "ETSL","ES"), sf=c("futility","OF","Pocock"),
num.arm,r=0.5,num.stage=2,pause=0,
control = OptimDesControl(), ...)

Arguments
B.init 
A vector of userspecified time points (B1, ..., Bb) that determine a set of time intervals with uniform accrual. 
m.init 
The projected
number of patients that can be accrued within the time intervals determined by 
alpha 
Type I error. 
beta 
Type II error. 
param 
Events should be defined as poor outcomes (e.g. death, progression). Computations
and reporting are based on the proportion without an event at a
prespecified time, 
x 
Prespecified time for the eventfree endpoint (e.g., 1 year). 
n 
Userspecified combined sample size for both stages. 
pn 
Combined sample size for both stages specified by the ratio of the targetted twostage sample size to the correponding sample size for a singlestage design. 
pt 
Combined sample size for both stages specified by the ratio of the targetted twostage study length to the correponding study length for a singlestage design. 
target 
The expected duration of
accrual (EDA) is minimized with 
sf 
Spending function for 
num.arm 
Number of arms: a singlearm design with 
r 
Proportion of patients randomized to the treatment arm when 
num.stage 
Number of stages: a twostage design with 
pause 
The pause in accrual following the scheduled times for interim
analyses. Data collected during the pause on the previously accrued
patients are included in the interim analysis conducted at the end of the
pause. Accrual resumes after the pause without interuption as if no pause had
occurred. Default is 
control 
An optional list of control settings. See

... 
No additional optional parameters are currently implemented 
Details
Plots (plot.OptimDes
) based on the ouput of
OptimDes
can be used to find compromise designs based on
different combined sample sizes with
near optimal values for both ETSL ES, and EDA. np.OptimDes
can be
used to compute ETSL, ES, EDA, and the other design parameters for any
specified total sample size.
The targeted combined sample size must be specified by one of
three equivalent approaches: n
, pn
, and pt
.
The design calculations assume Weibull distributions for the eventfree
endpoint in the treatment group, and for the (assumed known, "Null") control
distribution.
The function weibPmatch
can be used to select
Weibull parameters that yield a target eventfree rate at a
specified time.
Value
A list of class OptimDes
with the same output as function OptimDes
.
Author(s)
Bo Huang <bo.huang@pfizer.com> and Neal Thomas <neal.thomas@pfizer.com>
References
Huang B., Talukder E. and Thomas N. (2010). Optimal twostage Phase II designs with longterm endpoints. Statistics in Biopharmaceutical Research, 2, 51–61.
Case M. D. and Morgan T. M. (2003) Design of Phase II cancer trials evaluating survival probabilities. BMC Medical Research Methodology, 3, 7.
Lin D. Y., Shen L., Ying Z. and Breslow N. E. (1996) Group seqential designs for monitoring survival probabilities. Biometrics, 52, 1033–1042.
Simon R. (1989) Optimal twostage designs for phase II clinical trials. Controlled Clinical Trials, 10, 1–10.
See Also
OptimDes
, plot.OptimDes
,
weibPmatch
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 