SimDes: Simulation Studies for Two-Stage or Three-Stage Designs from...
In OptInterim: Optimal Two and Three Stage Designs for Single-Arm and Two-Arm Randomized Controlled Trials with a Long-Term Binary Endpoint

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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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)

`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.

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.

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.

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

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.

OptimDes, TestStage, weibPmatch

## 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)