gset (version 1.1.0)

oc: examination of the operating characteristics of a group sequential design for equivalence studies

Description

empirical examination of the operating characteristics of a group sequential design via the Monte Carlo simulation approach. users need to supply the design, including the lower and upper bounds of the equivalence hypothesis, the true difference between 2 groups, and the corresponding variance parameter, and the number of looks (including the final look), the group sizes, and the equivalence and futility boundaries. It outputs empirical type I or type II error rates, expected sample sizes in the 2 groups, and the probability of stopping at each stage due to either equivalence or futility

Usage

oc(l, u, theta, sigma, K, n1, n2, boundaries, 
futility = TRUE, binding = FALSE, n.sim = 10000)

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 deviaton of the response variables for two indepedent groups; within subject standard deviaton of the response variables for paired groups

K

number of looks/stages

n1

size (number of subjects) in group 1 in the actual study

n2

size (number of subjects) in group 2 in the actual study

boundaries

a list that contains four vectors that correspond to the stagewise lower equivalence boundaries c(L), upper equivalence boundaries c(U), lower futility boundaries d(L), and upper futility boundaries d(U), respectively. the boundaries can be obtained using functions binding(), nonbinding(), and nminmax().

futility

whether the stop will stop for futility; default = TRUE

binding

whether hte futility boundaries are binding; default = FALSE

n.sim

number of randomly simulated studies for the empirical examination of the operating characteristics of a group sequential design via the Monte Carlo simulation approach. Default n.sim=1e4

Value

reject.rate

rate of rejection of H0 (non-equivalence). If H0 is true, then reject.rate is the empirical type I error rate; if H1 is true, then reject.rate is the empirical power

En1

sample size that is expected to spend in group 1; smaller than n1.minmax due to early stopping

En2

sample size that is expected to spend in group 2; smaller than n2.minmax due to early stopping

prob.stop

probability of stopping at each stage due to either equivalence or futility

prob.stopE

probability of stopping at each stage due to equivalence

prob.stopF

probability of stopping at each stage due to futility

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,equivonly,nminmax,nfix,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
#   n.fix <- nfix(r, L,U,theta,sigma,alpha,beta)
#   
#   bound1 <- nonbinding(L,U,theta,sigma, n.fix$n1, n.fix$n2, 1:K/K, alpha,beta, plot=FALSE) 
#   bound2<- nminmax(L, U, theta, sigma, n.fix$n1, n.fix$n2, 1:K/K, alpha, beta)
#   
#   theta <- L 
#   oc1 <- oc(L, U, theta, sigma, K, n.fix$n1, n.fix$n2, bound1, futility=TRUE)
#   oc2 <- oc(L, U, theta, sigma, K, bound2$n1minmax, bound2$n2minmax, bound2, futility=TRUE)
#   
#   theta <- 0 
#   oc3 <- oc(L, U, theta, sigma, K, n.fix$n1, n.fix$n2, bound1, futility=TRUE)
#   oc4 <- oc(L, U, theta, sigma, K, bound2$n1minmax, bound2$n2minmax, bound2, futility=TRUE)
#   ## End(Not run)