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

In mpe: Multiple Primary Endpoints

Description

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

Usage

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

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)
tol	the desired accuracy for uniroot.

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 <= 0 for at least one k in {1,...,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) augemented with method and note elements.

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.unknown.var, mpe.z.test

Examples

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

## compute sample size
power.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.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.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))

Example output

Loading required package: mvtnorm

 Power calculation for multiple co-primary endpoints (covariance known) 

              n = 20
          delta = 1, 1
             SD = 1, 1
            rho = 0
      sig.level = 0.05
          power = 0.8750109

Sigma =
     [,1] [,2]
[1,]    1    0
[2,]    0    1

NOTE: n is number in *each* group


 Power calculation for multiple co-primary endpoints (covariance known) 

              n = 51.61514
          delta = 1, 1
             SD = 1.414214, 1.414214
            rho = 0
      sig.level = 0.025
          power = 0.9

Sigma =
     [,1] [,2]
[1,]    2    0
[2,]    0    2

NOTE: n is number in *each* group


 Power calculation for multiple co-primary endpoints (covariance known) 

              n = 60
          delta = 0.50, 0.75, 0.50, 0.75
             SD = 1.2, 1.4, 1.2, 1.4
            rho = 0.50, 0.90, 0.50, 0.10, 0.80, 0.25
      sig.level = 0.05
          power = 0.6207101

Sigma =
      [,1]  [,2]  [,3]  [,4]
[1,] 1.440 0.840 1.296 0.840
[2,] 0.840 1.960 0.168 1.568
[3,] 1.296 0.168 1.440 0.420
[4,] 0.840 1.568 0.420 1.960

NOTE: n is number in *each* group


 Power calculation for multiple co-primary endpoints (covariance known) 

              n = 60
          delta = 0.50, 0.75, 0.50, 0.75
             SD = 1.2, 1.4, 1.2, 1.4
            rho = 0.50, 0.90, 0.50, 0.10, 0.80, 0.25
      sig.level = 0.05
          power = 0.6209287

Sigma =
      [,1]  [,2]  [,3]  [,4]
[1,] 1.440 0.840 1.296 0.840
[2,] 0.840 1.960 0.168 1.568
[3,] 1.296 0.168 1.440 0.420
[4,] 0.840 1.568 0.420 1.960

NOTE: n is number in *each* group

mpe documentation built on May 2, 2019, 2:04 a.m.