atleast.one.endpoint: At least one Endpoint with Known Covariance

In mpe: Multiple Primary Endpoints

Description

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

Usage

atleast.one.endpoint(K, n = NULL, delta = NULL, Sigma, SD, rho, sig.level = 0.05/K,
                            power = NULL, 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)
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 <= 0 for all 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) augmented 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.

Examples

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

## compute sample size
atleast.one.endpoint(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
atleast.one.endpoint(K = 4, n = 60, delta = c(0.5, 0.75, 0.5, 0.75), Sigma = Sigma)
## equivalent: known SDs and correlation rho
atleast.one.endpoint(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 primary endpoints for at least one endpoint 

              n = 218.963
          delta = 0.2, 0.2
             SD = 1, 1
            rho = 0
      sig.level = 0.025
          power = 0.8

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

NOTE: n is number in *each* group


 Power calculation for multiple primary endpoints for at least one endpoint 

              n = 594.5002
          delta = 0.2, 0.2
             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 primary endpoints for at least one endpoint 

              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 = 0.0125
          power = 0.9024514

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 primary endpoints for at least one endpoint 

              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 = 0.0125
          power = 0.9024541

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.