nminmax: sample size calculation for group sequential equivalence...

In gset: Group Sequential Design in 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

Author(s)

Fang Liu ([e-mail])

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)

gset documentation built on May 2, 2019, 2:09 p.m.