MKpower (version 0.9)

power.mpe.known.var: Multiple Co-Primary Endpoints with Known Covariance

Description

The function calculates either sample size or power for continuous multiple co-primary endpoints with known covariance.

Usage

power.mpe.known.var(K, n = NULL, delta = NULL, Sigma, SD, rho,
  sig.level = 0.05, power = NULL, n.max = 1e5, tol = .Machine$double.eps^0.25)

Value

Object of class power.mpe.test, a list of arguments (including the computed one) augemented with method and note elements.

Arguments

K

number of co-primary endpoints

n

optional: sample size

delta

expected effect size (length K)

Sigma

known covariance matrix (dimension K x K)

SD

known standard deviations (length K)

rho

known correlations (length 0.5*K*(K-1))

sig.level

significance level (Type I error probability)

power

optional: power of test (1 minus Type II error probability)

n.max

upper end of the interval to be search for n via uniroot.

tol

the desired accuracy for uniroot.

Author

Srinath Kolampally, Matthias Kohl

Details

The function can be used to either compute sample size or power for continuous multiple co-primary endpoints with known covariance where a multivariate normal distribution is assumed. 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.

One has to specify either n or power, the other parameter is determined. Moreover, either covariance matrix Sigma or standard deviations SD and correlations rho must be given.

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

power.mpe.unknown.var

Examples

## compute power
power.mpe.known.var(K = 2, n = 20, delta = c(1,1), Sigma = diag(c(1,1)))

## compute sample size
power.mpe.known.var(K = 2, delta = c(1,1), Sigma = diag(c(2,2)), power = 0.9,
                    sig.level = 0.025)

## known covariance matrix
Sigma <- matrix(c(1.440, 0.840, 1.296, 0.840,
                  0.840, 1.960, 0.168, 1.568,
                  1.296, 0.168, 1.440, 0.420,
                  0.840, 1.568, 0.420, 1.960), ncol = 4)
## compute power
power.mpe.known.var(K = 4, n = 60, delta = c(0.5, 0.75, 0.5, 0.75), Sigma = Sigma)
## equivalent: known SDs and correlation rho
power.mpe.known.var(K = 4, n = 60,delta = c(0.5, 0.75, 0.5, 0.75),
                    SD = c(1.2, 1.4, 1.2, 1.4), 
                    rho = c(0.5, 0.9, 0.5, 0.1, 0.8, 0.25))