Finding optimal and balanced group-sequential designs

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Description

optgs is used to find a one-sided multi-stage design that balances four optimality criteria for a RCT with normally distributed outcomes

Usage

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optgs(delta0 = 0, delta1 = 1/3, J = 2, sigma = 1, sd.known = TRUE,
    alpha = 0.05, power = 0.9, weights = c(0.95, 0, 0, 0.05),
    initial = NULL)

Arguments

delta0

mean difference in treatment effect under the null hypothesis (default: 0)

delta1

clinically relevant difference used to power the trial (default: 1/3)

J

number of stages in the trial (default: 2)

sigma

assumed standard deviation of treatment responses (default: 1)

sd.known

logical value indicating if sigma will be treated as known; if FALSE, a quantile substitution method will be used to modify the stopping boundaries (default TRUE)

alpha

one-sided type-I error rate required (default: 0.05)

power

power required (default: 0.9)

weights

vector of length 4 giving the weights put on the four optimality criteria (default: c(0.95,0,0,0.05)). See details for more information

initial

starting values for the Nelder-Mead algorithm if the user wishes to override the default (default: NULL). Initial values must be specified as a two-dimensional vector where both entries are between -0.5 and 0.5.

Details

optgs uses the extended power-family of group-sequential tests, and searches for the values of the futility and efficacy shape parameters that optimise the specified weighting. A description of the extended power-family and optgs is provided in Wason (2012). The ‘weights’ argument corresponds to the weight put on: 1) the expected sample size at delta=delta0; 2) the expected sample size at delta=delta1; 3) the maximum expected sample size; 4) the maximum sample size (i.e. J*groupsize).

Value

groupsize

the number of patients required per arm, per stage

futility

the futility boundaries for the design

efficacy

the efficacy boundaries for the design

ess

the expected sample size at the delta0; the expected sample size at the delta1; and the maximum expected sample size

typeIerror

the actual type-I error rate of the design

power

the actual power of the design

References

Wason, J.M.S. OptGS: an R package for finding near-optimal group-sequential designs. Journal of Statistical Software, 66(2), 1-13. http://www.jstatsoft.org/v66/i02/

Examples

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##Find a three-stage design that minimises the maximum expected sample size.
threestagedeltaminimax=optgs(J=3,weights=c(0,0,1,0)) 
plot(threestagedeltaminimax)