spass (version 1.2)

n.1subgroup: Sample Size Calculation for a One Subgroup Design

Description

n.1subgroup calculates the required sample size for proving a desired alternative when testing for an effect in the full or subpopulation. See 'Details' for more information.

Usage

n.1subgroup(alpha, beta, delta, sigma, tau, eps = 0.001,
  approx = c("conservative.t", "liberal.t", "normal"), k = 1, nmax = 1000,
  nmin = 0)

Arguments

alpha

level (type I error) to which the hypothesis is tested.

beta

type II error (power=1-beta) to which an alternative should be proven.

delta

vector of treatment effects to be proven, c(outside subgroup, inside subgroup).

sigma

vector of standard deviations, c(outside subgroup, inside subgroup).

tau

subgroup prevalence.

eps

precision parameter concerning the power calculation in the iterative sample size search algorithm.

approx

approximation method: Use a conservative multivariate t distribution ("conservative.t"), a liberal multivariate t distribution ("liberal.t") or a multivariate normal distribution ("normal") to approximate the joint distribution of the standardized teststatistics.

k

sample size allocation factor between groups: see 'Details'.

nmax

maximum total sample size.

nmin

minimum total sample size.

Value

n.1subgroup returns the required sample size within the control group and treatment group.

Details

This function performs sample size estimation in a design with a subgroup within a full population where we want to test for treatment effects between a control and a treatment group. Since patients from the subgroup might potentially benefit from the treatment more than patients not included in that subgroup, one might prefer testing hypothesis cercerning the full population and the subpopulation at the same time. Here standardized test statistics are their joined distributions are used to calculate the required sample size for the control and treatment group to prove an existing alternative delta with a specified power 1-beta when testing the global null hypothesis \(H_0: \Delta_F=\Delta_S=0\) to level alpha.

For sample sizes \(n_C\) and \(n_T\) of the control and treatment group, respectively, the argument k is the sample size allocation factor, i.e. \(k = n_T/n_C\).

See Also

#' bssr.1subgroup for blinded sample size reestimation within a running trial.

Examples

# NOT RUN {
#Calculate required sample size to correctly reject with
#80% probability when testing the global Nullhypothesis H_0: Delta_F=Delta_S = 0
#assuming the true effect Delta_S=1 is in the subgroup (no effect outside of the subgroup)
#with subgroup prevalence tau=0.4.
#The variances in and outside of the subgroup are unequal, sigma=c(1,1.2).

estimate<-n.1subgroup(alpha=0.025,beta=0.1,delta=c(0,1),sigma=c(1,1.2),tau=0.4,eps=0.0001,
approx="conservative.t",k=2)
summary(estimate)
# }