Description Usage Arguments Details Value References See Also Examples

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

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

1 2 3 |

`K` |
number of co-primary endpoints |

`n` |
optional: sample size |

`delta` |
expected effect size (length |

`Sigma` |
unknown covariance matrix (dimension |

`SD` |
unknown standard deviations (length |

`rho` |
unknown correlations (length |

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

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

`M` |
Number of replications for the required simulations. |

`min.n` |
Starting point of search interval for sample size |

`max.n` |
End point of search interval for sample size, must be larger than |

`tol` |
the desired accuracy for |

`use.uniroot` |
Finds one root of one equation |

The function can be used to either compute sample size or power for continuous multiple co-primary endpoints with unknown covariance. 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. An approach to calculate sample size `n`

, is to first call
`power.known.var`

and use the result as `min.n`

. The input for
`max.n`

must be larger then `min.n`

. Moreover, either covariance
matrix `Sigma`

or standard deviations `SD`

and correlations `rho`

must be given.

The sample size is calculated by simulating Wishart distributed random matrices, hence the results include a certain random variation.

Object of class `power.mpe.test`

, a list of arguments (including the
computed one) augmented 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 18 19 20 21 22 23 24 25 26 | ```
## compute power
## Not run:
power.unknown.var(K = 2, n = 20, delta = c(1,1), Sigma = diag(c(1,1)))
## To compute sample size, first assume covariance as known
power.known.var(K = 2, delta = c(1,1), Sigma = diag(c(2,2)), power = 0.9,
sig.level = 0.025)
## The value of n, which is 51, is used as min.n and max.n must be larger
## then min.n so we try 60.
power.unknown.var(K = 2, delta = c(1,1), Sigma = diag(c(2,2)), power = 0.9,
sig.level = 0.025, min.n = 51, max.n = 60)
## More complex example with unknown covariance matrix assumed to be
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.unknown.var(K = 4, n = 90, delta = c(0.5, 0.75, 0.5, 0.75), Sigma = Sigma)
## equivalent: unknown SDs and correlation rho
power.unknown.var(K = 4, n = 90, 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))
## End(Not run)
``` |

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