gset (version 1.1.0)

equivonly: equivalence boundaries in group sequential equivalence studies that only stop for equivalence

Description

Computation of equivalence boundaries for group sequential designs in studies with equivalence hypothesis that only stop for equivalence via Monte Carlo simulations

Usage

equivonly(l, u, sigma, n1, n2, t.vec, type1, gamma = -4, crange = c(-10, 10), 
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

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

cumulative 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

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)

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

equivL

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

equivU

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

boundary plots

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

Details

The exactly same equivalence boundaries can also be obtained using the command nonbinding

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

nonbinding,binding,nminmax,nfix,oc,figureE,figureEF

Examples

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