binding: equivalence and binding futility boundaries in group...
In gset: Group Sequential Design in Equivalence Studies

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

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

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binding(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)

`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`	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`	pverall 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(-gammat.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`	number of randomly simulated samples in 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.

`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

Fang Liu (fang.liu.131@nd.edu)

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)

nonbinding,equivonly,nminmax,nfix,oc,figureE,figureEF

 ## 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)
  
  
  # default 
  # there are two ways to generate the boundary plots
  # 1. specify plot=TRUE (default) in "binding()"
  binding(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  <- binding(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=TRUE)
  bound
  figureEF(bound, K)
  
## End(Not run)