Optimal Two-Stage or Three-Stage Designs with User-specified Combined Sample Size or Study Length

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Description

Construct a two-stage or three-stage design with a time-to-event endpoint evaluated at a pre-specified time (e.g., 6-month progression-free survival) comparing treatment versus either a historical control rate with possible stopping for futility (single-arm), or an active control arm with possible stopping for both futility and superiority (two-arm), 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 pre-specifed by the user.

Usage

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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 user-specified 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 B.init.

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 pre-specified time, x. For constructing an optimal design, complete event-free distributions at all times must be specified for the control condition (Null), and for the alternative "effective" treatment. Weibull distributions are currently implemented. param is a vector of length 4: (shape null, scale null, shape alternative, scale alternative). The R parameterization of the Weibull distribution is used.

x

Pre-specified time for the event-free endpoint (e.g., 1 year).

n

User-specified combined sample size for both stages.

pn

Combined sample size for both stages specified by the ratio of the targetted two-stage sample size to the correponding sample size for a single-stage design.

pt

Combined sample size for both stages specified by the ratio of the targetted two-stage study length to the correponding study length for a single-stage design.

target

The expected duration of accrual (EDA) is minimized with target="EDA", the expected total study length is minimized with target="ETSL", and the expected sample size with target="ES".

sf

Spending function for alpha at the end of Stage 1. There are three types of spending functions: no efficacy stopping with sf="futility", O'Brien-Fleming boundaries with sf="OF", and Pocock boundaries with sf="Pocock".

num.arm

Number of arms: a single-arm design with num.arm=1, or a randomized two-arm design with num.arm=2.

r

Proportion of patients randomized to the treatment arm when num.arm=2. By default, r=0.5.

num.stage

Number of stages: a two-stage design with num.stage=2, or a three-stage design with num.stage=3.

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 pause=0.

control

An optional list of control settings. See OptimDesControl for the parameters that can be set and their default values.

...

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 event-free 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 event-free 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 two-stage Phase II designs with long-term 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 two-stage designs for phase II clinical trials. Controlled Clinical Trials, 10, 1–10.

See Also

OptimDes, plot.OptimDes, weibPmatch

Examples

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## Not run: 
B.init <- c(1, 2, 3, 4, 5)
m.init <- c(15, 20, 25, 20, 15)
alpha <- 0.05
beta <- 0.1
param <- c(1, 1.09, 2, 1.40)
x <- 1

# H0: S0=0.40 H1: S1=0.60

object14 <- np.OptimDes(B.init,m.init,alpha,beta,param,x,pt=1.1,target="ETSL",sf="futility",num.arm=1,num.stage=2)

## End(Not run)