OptInterim (version 3.0.1)

FixDes: Construct a Single-stage Design for a time-to-event Endpoint Evaluated at a Pre-specifed Time Versus Either a Known Standard Control or a Randomized Comparative Control

Description

Find the sample size, duration of accrual, and test boundary for a single-stage design with an event-free endpoint versus either a known standard control or a randomized comparative control. Testing is one-sided based on the Kaplan-Meier estimator evaluated at a user-specified time point.

Usage

FixDes(B.init, m.init, alpha, beta, param, x, num.arm, r=0.5)

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).

num.arm

Number of treatment arms. num.arm=1 for single-arm trial assuming a known standard control. num.arm=2 for two-arm randomized trial with a comparative control arm.

r

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

Value

A list with components:

n0

Fixed design sample size.

DA

Duration of accrual.

SL

Total study length (time, DA+x).

n0E

n0 based on exact binomial test.

DAE

DA based on exact binomial test.

SLE

SL based on exact binomial test.

C

Rejection cutpoint for the test statistic.

Details

Estimation is based on the Kaplan-Meier or Nelson-Aalen estimators evaluated at a target time (e.g., 1 year). The event-free rates at the target time are computed from Weibull distributions assumed for the treatment and control distributions, as is done in function OptimDes. The design depends only on the event-free rates at the target time (except for small changes due to rounding with different survival functions). The duration of accrual depends on the projected maximum accrual rates.

References

Huang B., Talukder E. and Thomas N. Optimal two-stage Phase II designs with long-term endpoints. Statistics in Biopharmaceutical Research, 2(1), 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, TestStage, SimDes

Examples

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

FixDes(B.init, m.init, alpha, beta, param, x,num.arm=1)

m.init <- 5*c(15, 20, 25, 20, 15)
FixDes(B.init, m.init, alpha, beta, param, x,num.arm=2)