View source: R/power_type1_2TOST.R

power.2TOST | R Documentation |

Calculates the exact power of two simultaneous TOST procedures (where the two parameters of the two TOSTs are correlated with some correlation) for various study designs used in BE studies

power.2TOST(alpha = c(0.05, 0.05), logscale = TRUE, theta0, theta1, theta2, CV, n, rho, design = "2x2", robust = FALSE, nsims, setseed = TRUE, details = FALSE)

`alpha` |
Vector; contains one-sided significance level for each of the two TOSTs. |

`logscale` |
Should the data used on log-transformed ( |

`theta1` |
Vector; contains lower bioequivalence limit for each of the two TOSTs. |

`theta2` |
Vector; contains upper bioequivalence limit for each of the two TOSTS. |

`theta0` |
Vector; contains ‘true’ assumed bioequivalence ratio for each of the two TOSTs. |

`CV` |
Vector of coefficient of variations (given as as ratio, |

`n` |
Number of subjects under study. |

`rho` |
Correlation between the two PK metrics ( |

`design` |
Character string describing the study design. |

`robust` |
Defaults to |

`nsims` |
Number of studies to simulate. Defaults to 1E5. |

`setseed` |
Logical; if |

`details` |
Logical; if |

Calculations are based on simulations and follow the distributional
properties as described in Phillips. This is in contrast to the calculations
via the 4-dimensional non-central *t*-distribution as described in Hua *et al.*
which was implemented in versions up to 1.4-6.

The formulas cover balanced and unbalanced studies w.r.t (sequence) groups.

In case of parallel group design and higher order crossover designs
(replicate crossover or crossover with more than two treatments) the calculations
are based on the assumption of equal variances for Test and Reference products
under consideration.

The formulas for the paired means 'design' do not take an additional correlation
parameter into account. They are solely based on the paired *t*-test
(TOST of differences = zero).

Value of power.

If `n`

is given as scalar (total sample size) and this number is not
divisible by the number of (sequence) groups of the design an unbalanced design
with small imbalance is assumed. A corresponding message is thrown showing the
assumed numbers of subjects in (sequence) groups.

The function does not vectorize properly if design is a vector. Moreover,
`theta0`

and `CV`

must be of length two, thus further vectorizing is not possible.

Other vector input is not tested yet.

B. Lang, D. Labes

Phillips KF. *Power for Testing Multiple Instances of the Two One-Sided Tests Procedure.* Int J Biostat. 2009;5(1):Article 15.

Hua SY, Xu S, D’Agostino RB Sr. *Multiplicity adjustments in testing for bioequivalence.* Stat Med. 2015;34(2):215–31. doi: 10.1002/sim.6247

Lang B, Fleischer F. *Letter to the Editor: Comments on ‘Multiplicity adjustments in testing for bioequivalence.’* Stat Med. 2016;35(14):2479–80. doi: 10.1002/sim.6488

`sampleN.2TOST, known.designs`

# Power for the 2x2x2 cross-over design with 24 subjects, intra-subject # standard deviation of 0.3 (CV = 30.7%) and assumed ratios of 1.05 for both # parameters, and correlation 0.75 between parameters (using all the other # default values) power.2TOST(theta0 = rep(1.05, 2), CV = rep(se2CV(0.3), 2), n = 24, rho = 0.75) # should give: 0.38906 # Setting as before but use rho 1 and high number of simulations # to reproduce result of power.TOST() p1 <- power.2TOST(theta0 = rep(1.05, 2), CV = rep(se2CV(0.3), 2), n = 24, rho = 1, nsims=1E7) p2 <- power.TOST(theta0 = 1.05, CV = se2CV(0.3), n = 24) all.equal(p1, p2, tolerance = 1e-04)

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