Description Usage Arguments Details Value References See Also Examples

View source: R/power.known.var.R

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

1 2 |

`K` |
number of co-primary endpoints |

`n` |
optional: sample size |

`delta` |
expected effect size (length |

`Sigma` |
known covariance matrix (dimension |

`SD` |
known standard deviations (length |

`rho` |
known correlations (length |

`sig.level` |
significance level (Type I error probability) |

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

`tol` |
the desired accuracy for |

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.

Object of class `power.mpe.test`

, a list of arguments (including the
computed one) augemented with method and note elements.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
## 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))
``` |

```
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
```

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