gset (version 1.1.0)

nminmax: sample size calculation for group sequential equivalence studies

Description

calculates sample size for group sequential designs in equivalence studies that can stop for equivalence, or for either equivalence or futility (binding or non-binding). The calculated samples size is referred to as n.minmax, "min" in the sense that the calculcated n is the minimunm required sample size to reach a given power level, "max" in the sense that it would the max spent sample size which only happens if the study stop in the last stage

Usage

nminmax(l, u, theta, sigma, n1.lower, n2.lower, t.vec, type1, type2, 
gamma = rep(-4, 2), binding = FALSE, n1.upper = ceiling(2 * n1.lower), 
n2.upper = ceiling(2 * n2.lower), 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.lower

the lower bound of the interval from which n.minmax in group 1 will be solved using a bisection method

n2.lower

the lower bound of the interval from which n.minmax in group 2 will be solved using a bisection method

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

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

binding

whether the futility boundaries are binding; default = FALSE

n1.upper

the upper bound of the interval from which n.minmax in group 1 will be solved using a bisection method; default = 2*n1.lower

n2.upper

the upper bound of the interval from which n.minmax in group 2 will be solved using a bisection method; default = 2*n2.lower

n.sim

number of randomly simulated samples in computation of n.minmax 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

n1minmax

n.minmax in group 1

n2minmax

n.minmax in group 2

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

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, 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)
#   
#   # nminmax with nonbinding futility
#   bound1  <- nminmax(L, U, theta, sigma, n.fix$n1, n.fix$n2, 1:K/K, alpha, beta)
#   figureEF(bound1, K)
# 
#   # nminmax with binding futility
#   bound2  <- nminmax(L, U, theta, sigma, n.fix$n1, n.fix$n2, 1:K/K, alpha, beta, binding=TRUE)
#   figureEF(bound2, K)
#   ## End(Not run)