Simulation Studies for Two-Stage or Three-Stage Designs from function OptimDes

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Description

Simulation experiments to compare the alpha level, power and other features of two-stage or three-stage designs from function OptimDes with the targetted values.

Usage

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SimDes(object,B.init,m.init,weib0,weib1,interimRule='e1',
       sim.n=1000,e1conv=1/365,CMadj=F,attainI=1,attainT=1,FixDes="F", 
       Rseed)

Arguments

object

Output object of function OptimDes.

B.init

A vector of user-specified time points (B1, ..., Bb) that determine a set of time intervals with uniform accrual. This vector needs to be specified only if its values differ from the call to OptimDes.

m.init

The projected number of patients that can be accrued within the time intervals determined by B.init. This vector needs to be specified only if its values differ from the call to OptimDes.

weib0

A vector with the shape and scale for the Weibull distribution under the null hypothesis. These need to be specified only if they differ from the input to OptimDes.

weib1

A vector with the shape and scale for the Weibull distribution under the alternative hypothesis. These need to be specified only if they differ from the input to OptimDes.

interimRule

The interim analysis is performed when the planned n1 patients are accrued regardless of the time required when interimRule='n1'. The interim analysis is performed at the planned time t1 regardless of the number of patients accrued when interimRule='t1'. The interim analysis is performed when the truncated (by x) total exposure matches the total expected exposure when interimRule='e1'. The default is 'e1'.

sim.n

The number of simulation replications.

e1conv

Convergence criteria for matching the truncated exposure when interimRule='e1'. The default is 1/365, which is appropriate provided B.init is specified in years

CMadj

If true, the n, n1, and t1 are adjusted by the ratio of the exact binomial to asymptotic normal sample size for the single stage design, as in Case and Morgan (2003). Proportional adjustment of times and sample sizes are made even if the accrual rates are not constant. The adjustment to the mda is made through the adjustment to n rather than by multiplication to ensure consistency with accrual boundaries. The truncated exposure time is matched to the adjusted time of the interim analysis. Default is false.

attainI

Samples sizes and times of the interim analyses often differ from the exact targetted values for operational reasons. The attainI permits simulations with a different interim time or sample size (depending on interimRule) by a specified fraction.

attainT

Simulations with a total sample size (assuming the trial does not stop based on the interim analysis) that differs from the planned total by a specified fraction.

FixDes

If FixDes="E" or "N", a fixed design is simulated with the sample size determined by the Exact or Normal approximation. All other options for modifying the simuations are ignored. The alpha level and power based on an exact test and the normal approximation are returned. All other output variables are 0. The default is "F"

Rseed

Optional integer for input to function set.seed. If unspecified, the random seed status at the time of the function call is used.

Details

sim.n(default is 1000) simulation experiments are conducted to assess how close the empirical type I and II error rates come to the target values.

Simulation studies can also be used to assess the performance of the optimal design under mis-specification of the design parameters. For example, if the Weibull shape and scale parameters of the time to event distributions are changed, or if the accrual rates are changed. (see Case and Morgan, 2003, for discussion of this topic).

The function weibPmatch can be used to select Weibull parameters that yield a target event-free rate at a specified time.

Value

A vector with:

alphaExact

Estimated alpha level using an exact test for the final test. It is NA if the design allows interim stopping for superiority.

alphaNorm

Estimated alpha level using approximately normal tests.

powerExact

Estimated power using an exact test for the final test. It is NA if the design allows interim stopping for superiority.

powerNorm

Estimated power using approximately normal tests.

eda

Estimated mean duration of accrual under the null hypothesis.

etsl

Estimated mean total study length under the null hypothesis.

es

Estimated mean total sample size under the null hypothesis.

edaAlt

Estimated mean duration of accrual under the alternative hypothesis.

etslAlt

Estimated mean total study length under the alternative hypothesis.

esAlt

Estimated mean total sample size under the alternative hypothesis.

pstopNull

The proportion of trials stopped for futility at the interim analysis under the null hypothesis.

pstopAlt

The proportion of trials stopped for futility at the interim analysis under the alternative hypothesis.

pstopENull

The proportion of trials stopped for efficacy at the interim analysis under the null hypothesis.

pstopEAlt

The proportion of trials stopped for efficacy at the interim analysis under the alternative hypothesis.

aveE

Average total (truncated at x) exposure at time of interim analysis.

pinfoNull

The proportion of the total information obtained at the interim analysis under the null hypothesis.

pinfoNull2

The proportion of the total information obtained at the second interim analysis under the null hypothesis when num.stage=3.

pinfoAlt

The proportion of the total information obtained at the interim analysis under the alternative hypothesis.

n1

Average sample size at interim.

n2

Average sample size at second interim.

t1

Average time at interim.

t2

Average time at second interim.

difIntSupL

Lowest interim survival rate difference stopped for efficacy.

difIintSupH

Highest interim survival rate difference not stopped for efficacy.

difIntFutL

Lowest interim survival rate difference continued to final analysis based on the normal approximation.

difIntFutH

Highest interim survival rate difference resulting in futility terimination based on the normal approximation.

difFinSupL

Lowest final survival rate difference rejecting null based on the normal approximation.

difFinFutH

Highest final survival rate difference without rejecting null based on the normal approximation.

Author(s)

Bo Huang <bo.huang@pfizer.com> and Neal Thomas <neal.thomas@pfizer.com>

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, 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

object1 <- OptimDes(B.init,m.init,alpha,beta,param,x,target="EDA",sf="futility",num.arm=1)

SimDes(object1,sim.n=100)

### Stopping based on pre=planned time of analysis
SimDes(object1,interimRule='t1',sim.n=100)

### accrual rates differ from planned
SimDes(object1,m.init=c(5,5,25,25,25),sim.n=100)

## End(Not run)