gset (version 1.1.0)

nonbinding: equivalence and non-binding futility boundaries in group sequential equivalence studies

Description

Computation of equivalence and non-binding futility boundaries for group sequential designs in studies with equivalence hypothesis via Monte Carlo simulations

Usage

nonbinding(l, u, theta, sigma, n1, n2, t.vec, type1, type2, 
gamma = rep(-4, 2), crange = c(-10, 10), drange = c(-10, 10), 
force = TRUE, plot = TRUE, ll = 3, ul = 6, n.sim = 10000, seed = NULL)

Arguments

l

lower equivalence bound as given in the equivalence hypothesis

u

upper equivalence bound as given in the equivalence hypothesis

theta

true mean difference between 2 groups

sigma

between-subject standard deviation of the response variable for two independent groups; within subject standard deviation of the response variable for paired groups

n1

size (number of subjects) in group 1

n2

size (number of subjects) in group 2

t.vec

umulative time points for the interim looks assuming a constant accrual rate. For example, if a study has equally spaced 4 looks including the final look, then t.vec=1:4/4. It can any vector as long as it is increasing and the last element is 1.

type1

overall Type I error rate

type2

overall Type II error rate

gamma

The gamma parameter in the gamma cumulative error spending function (Hwang, Shih, and DeCani 1990). Error spending given a t.vec is = total error rate*(1-exp(-gamma*t.vec))/(1-exp(-gamma)). gamma= 1 produces Pocock-type error spending function; gamma = -4 produces O'Brien-Fleming type error spending function. Default gamma = -4

crange

a 2-dimensional vector containing the end-points of the interval from which the critical values for claiming equivalence will be solved. Default crange = c(-10,10)

drange

a 2-dimensional vector containing the end-points of the interval from which the critical values for claiming fultility will be solved. Default drange = c(-10,10)

force

Whether to force the futlitity boundaries to equal to the equilvence boundaries in the last look. Default force = TRUE

plot

Whether to generate the boundaries plot. Default plot = TRUE

ll

a parameter in the boundary plot. the short arm of the t(L) and t(U) axes

ul

a parameter in the boundary plot. the long arm of the t(L) and t(U) axes

n.sim

the number of randomly simulated samples in the computation of the boundaries via the Monte Carlo simulation approach. Default n.sim=1e4

seed

seed used in the Monte Carlo computation. If non-specified, the seed is set randomly.

Value

typeI

vector of cumulative stage Type I error rate

typeII

vector of cumulative stage Type II error rate

equivL

vector of the equivalence boundary c(L) at each stage

equivU

vector of the equivalence boundary c(U) at each stage

futilL

vector of the futility boundary d(L) at each stage

futilU

vector of the futility boundary d(U) at each stage

boundary plots

if plot=TRUE, a series of bounary plots will be produced, one for look

References

Liu, F. and Li, Q. (2014), Sequential Equivalence Testing based on the Exact Distribution of Bivariate Noncentral $t$-statistics, Computational Statistics and Data Analysis, 77:14-24

Liu, F. (2014), gset: an R package for exact sequential test of equivalence hypothesis based on bivariate non-central $t$-statistics, the R Journal (to appear)

See Also

binding,equivonly,nminmax,nfix, oc,figureE,figureEF

Examples

 ## Not run: 
#   L <- -0.2
#   U <- 0.2
#   theta <- 0
#   sigma <- 0.4  
#   alpha <- 0.05
#   beta  <- 0.2
#   K <- 4
#   r <- 1
#   # the sample size per group with a traditional nonsequential design
#   n.fix <- nfix(r, L,U,theta,sigma,alpha,beta)
#   
#   # there are two ways to generate the boundary plots
#   
#   # 1. specify plot=TRUE (default) in "binding()"
#   nonbinding(L, U, theta, sigma, n.fix$n1, n.fix$n2, 1:K/K, alpha, beta)             
#   
#   # 2. specify plot=FALSE in "binding()" and apply the "figureEF()" command 
#   bound  <- nonbinding(L, U, theta, sigma, n.fix$n1, n.fix$n2, 1:K/K, alpha, beta, plot=FALSE)  
#   figureEF(bound, K)
# 
#   # obtain nminmax
#   bound  <- nminmax(L, U, theta, sigma, n.fix$n1, n.fix$n2, 1:K/K, alpha, beta, binding=FALSE)
#   bound
#   figureEF(bound, K)
#   ## End(Not run)