power.mpe.atleast.one {MKpower}

Power for at least One Endpoint with Known Covariance

Description

The function calculates either sample size or power for continuous multiple primary endpoints for at least one endpoint with known covariance.

Usage

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

Arguments

K

number of endpoints

n

optional: sample size

delta

expected effect size

Sigma

A covariance of known matrix

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

Details

The function can be used to either compute sample size or power for continuous multiple primary endpoints with known covariance where a significant difference for at least one endpoint is expected. The implementation is based on the formulas given in the references below.

The null hypothesis reads \mu_{Tk}-\mu_{Ck}\le 0 for all 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.

Value

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

Note

The function first appeared in package mpe, which is now archived on CRAN.

Author(s)

Srinath Kolampally, Matthias Kohl [e-mail]

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.

Examples

## compute power
power.mpe.atleast.one(K = 2, delta = c(0.2,0.2), Sigma = diag(c(1,1)), power = 0.8)

## compute sample size
power.mpe.atleast.one(K = 2, delta = c(0.2,0.2), Sigma = diag(c(2,2)), power = 0.9)

## 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.atleast.one(K = 4, n = 60, delta = c(0.5, 0.75, 0.5, 0.75), Sigma = Sigma)
## equivalent: known SDs and correlation rho
power.mpe.atleast.one(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))