MKinfer (version 1.2)

mpe.z.test: Intersection-Union z-Test for Testing Multiple Co-Primary Endpoints

Description

The function computes the intersection-union z-test.

Usage

mpe.z.test(X, Y, Sigma, conf.level = 0.975)

Value

Object of class "mpe.test".

Arguments

X

matrix with observations of group 1 in rows

Y

matrix with obersvations of group 2 in rows

Sigma

known covariance matrix.

conf.level

confidence level of the interval.

Author

Srinath Kolampally, Matthias Kohl

Details

The function computes the intersection-union z-test. The implementation is based on the formulas given in the references below.

The null hypothesis reads \(\mu_{Tk}-\mu_{Ck}\le 0\) for at least one \(k\in\{1,\ldots,K\}\) where Tk is treatment k, Ck is control k and K is the number of co-primary endpoints (i.e. number of columns of X and Y).

References

Sugimoto, T. and Sozu, T. and Hamasaki, T. (2012). A convenient formula for sample size calculations in clinical trials with multiple co-primary continuous endpoints. Pharmaceut. Statist., 11: 118-128. doi:10.1002/pst.505

Sozu, T. and Sugimoto, T. and Hamasaki, T. and Evans, S.R. (2015). Sample Size Determination in Clinical Trials with Multiple Endpoints. Springer Briefs in Statistics, ISBN 978-3-319-22005-5.

See Also

mpe.t.test

Examples

library(mvtnorm)
delta <- c(0.25, 0.5)
Sigma <- matrix(c(1, 0.75, 0.75, 1), ncol = 2)
n <- 50
X <- rmvnorm(n=n, mean = delta, sigma = Sigma)
Y <- rmvnorm(n=n, mean = rep(0, length(delta)), sigma = Sigma)
mpe.z.test(X = X, Y = Y, Sigma = Sigma)