OptimDes: Construct Optimal Two-stage or Three-stage Designs with...

In OptInterim: Optimal Two and Three Stage Designs for Single-Arm and Two-Arm Randomized Controlled Trials with a Long-Term Binary Endpoint

Description

Construct an optimal two-stage or three-stage designs with a time-to-event endpoint evaluated at a pre-specified time (e.g., 6 months) 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 I utilizing time to event data. The design minimizes either the expected duration of accrual (EDA), expected sample size (ES), or the expected total study length (ETSL).

Usage

OptimDes(
B.init, m.init, alpha, beta, param, x, 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. A large number of potential patients results in long execution times for OptimDes, so unrealistically large values should not be entered.
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).
target	The expected duration of accrual (EDA) is minimized with target="EDA", the expected total study length is minimized with target="ETSL", or 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

OptimDes finds an two-stage or three-stage design with a time to event endpoint evaluated at a pre-specified time with potential stopping after the first stage.

For single arm designs, it implements the Case and Morgan (2003) and Huang, Talukder and Thomas (2010) generalizaton of the Simon (1989) two-stage design for comparing a treatment to a known standard rate with possible stopping for futility at the interim.

For randomized two-arm comparative designs, it allows an early stopping for both futility and superiority. The spending function for superiority can be chosen with argument sf.

The design minimizes either the expected duration of accrual (EDA), expected sample size (ES), or the expected total study length (ETSL).

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. Estimation is based on the Kaplan-Meier or Nelson-Aalen estimators evaluated at a target time (e.g., 1 year). The full treatment and control distributions and the accrual distribution affect power (and alpha level in some settings), see Case and Morgan (2003)).

Accrual rates are specified by the user. These rates can differ across time intervals specified by the user (this generalizes the results in Case and Morgan).

A package vignette as user manual can be found in the /doc subdirectory of the OptInterim package. It can be accessed from the HTML help page for the package.

Value

A list with components:

target	The optimizaton target ("EDA" or "ETSL" or "ES").
sf	The alpha spending function ("futility" or "OF" or "Pocock").
test	A vector giving the type I error alpha, type II error beta, Weibull parameters param and survival time of interest x.
design	A vector giving the number of study arms num.arm, treatment randomization rate r, the number of study stages num.stage, the pause in accrual before an interim analysis pause.
accrual	A list containing the input vectors B.init and m.init.
result	A 5-element vector containing the expected duration of accrual (EDA), the expected total study length (ETSL), the expected sample size of the optimal design (ES), and the probability of stopping under the Null (pstopNULL) and Alternative hypotheses (pstopAlt).
n	A two (or three)-element vector containing the sample size for the interim analysis and the sample size if all stages are completed.
stageTime	A 3 (or 4)-element vector giving the times for the interim and final analyses, and maximum duration of accrual. Interim times are given for the beginning of any pause before the analysis occurs.
boundary	A vector giving the rejection cutpoints (see Test2stage) for the test statistic and decision rules.
se	A vector of length 4 (or 6) with the asymptotic standard errors at the iterim and final analysis under the null hypothesis, followed by the corresponding SEs under the alternative hypothesis. These SEs must be divided by the square root of sample size.
u	A two (or three)-element vector giving means of interim test statistics under H1. See detailed description. It is also used to compute conditional power.
exposure	The expected total exposure of patients at the time of the planned interim analysis (including any accrual pause). Patient exposure is truncated by both the interim analysis time (including any pause) and the target surival time (i.e., no exposure after x). Exposure is a vector of length 1 or 2. The first value is the expected exposure at the first interim analysis. For two-stage, single-group designs, the second value is exposure with the Case-Morgan finite sample adjustment. For 3-stage designs, the second value is the exposure at the second interim analysis. For two-stage, two-group designs, exposure is a scalar indicating the expected exposure at the first interim analysis.
all.info	A data frame containing the results for all of the evaluated sample sizes.
single.stage	A six-element vector giving the sample size fix.n, duration of accrual DA, study length SL, and corresponding values based on the exact binomial test for a one-arm single-stage design and the Fisher exact test for a two-arm single-stage design with the design distributional assumptions.

Note

The algorithm will search for the optimal n between the sample size for a single-stage design and the user specified maximum sample size sum(m.init).

When the length of B.init or m.init is 1, the accrual rate is constant as in Lin et al. (1996), Case and Morgan (2003).

Author(s)

Bo Huang <[e-mail]> and Neal Thomas <[e-mail]>

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

np.OptimDes, print.OptimDes, plot.OptimDes, weibPmatch

Examples

## 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

object12 <- OptimDes(B.init,m.init,alpha,beta,param,x,target="EDA",
sf="futility",num.arm=1,num.stage=2,control=OptimDesControl(n.int=c(1,5),trace=TRUE))
print(object12)


m.init <- 4*c(15, 20, 25, 20, 15)
object2 <- OptimDes(B.init,m.init,alpha,beta,param,x,target="EDA",sf="futility",num.arm=2)
print(object2)

object23O <- OptimDes(B.init,m.init,alpha,beta,param,x,target="ETSL",sf="OF",
num.arm=2,num.stage=3,control=OptimDesControl(trace=TRUE,aboveMin=c(1.05,1.10)))
print(object3)

## End(Not run)

OptInterim documentation built on May 2, 2019, 2:07 p.m.