nonbinding: equivalence and non-binding futility boundaries in group... In gset: Group Sequential Design in 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

 ```1 2 3``` ```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

Author(s)

Fang Liu ([email protected])

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)

`binding`,`equivonly`,`nminmax`,`nfix`, `oc`,`figureE`,`figureEF`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ``` ## 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) ```