Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

View source: R/sampleN_2TOST_sim.R

Estimates the necessary sample size to have at least a given power when two parameters are tested simultaneously.

1 2 3 4 |

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

`targetpower` |
Power to achieve at least. Must be >0 and <1. |

`logscale` |
Should the data used on log-transformed or on original scale? |

`theta0` |
Vector; contains ‘true’ assumed T/R ratio for each of the two TOSTs. |

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

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

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

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

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

`setseed` |
Logical; if |

`robust` |
Defaults to |

`print` |
If |

`details` |
If |

`imax` |
Maximum number of steps in sample size search. |

`nsims` |
Number of studies to simulate. Defaults to 100,000 = 1E5. |

The sample size is estimated via iterative evaluation of power of the two TOSTs.

Start value for the sample size search is taken from a large sample approximation
(one TOST) according to Zhang, modified.

The sample size is bound to 4 as minimum.

The estimated sample size gives always the *total* number of subjects (not subject/sequence in crossovers or subjects/group in parallel designs – like in some other software packages).

A list with the input and results will be returned.

The element name `"Sample size"`

contains the total sample size.

The function does not vectorize properly.

If you need sample sizes with varying CVs, use f.i. for-loops or the apply-family.

If both `theta0`

are near the acceptance limits then the starting value may not
be a good approximation resulting in a lot of iteration steps; `imax`

may need
to be increased to obtain the required sample size.

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

Zhang P. *A Simple Formula for Sample Size Calculation in Equivalence Studies.* J Biopharm Stat. 2003;13(3):529–538. doi: 10.1081/BIP-120022772

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# Sample size for 2x2x2 cross-over design, intra-subject CV = 30% and assumed
# ratios of 0.95 for both parameters, and correlation 0.9 between parameters
# (using all the other default values)
# Should give n=44 with power=0.80684
sampleN.2TOST(theta0 = rep(0.95, 2), CV = rep(0.3, 2), rho = 0.9)
# Sample size for a parallel group design,
# evaluation on the original (untransformed) scale
# BE limits 80 ... 120% = -20% ... +20% of reference,
# assumed true BE ratio 0.95% = -5% to reference mean for both parameters,
# total CV=20% for both parameters, and correlation 0.9 between parameters
# should give n=54 with power=0.8149
sampleN.2TOST(logscale=FALSE, theta0 = rep(-0.05, 2), CV = c(0.2, 0.2),
rho = 0.9, design = "parallel")
``` |

```
+++++++++++ Equivalence test - 2 TOSTs +++++++++++
Sample size estimation
--------------------------------------------------
Study design: 2x2 crossover
log-transformed data (multiplicative model)
alpha = 0.05, 0.05; target power = 0.8
BE margins = 0.8, 0.8 ... 1.25, 1.25
True ratios = 0.95, 0.95; CV = 0.3, 0.3
Correlation between the two metrics = 0.9
Sample size (total)
n power
44 0.808790
+++++++++++ Equivalence test - 2 TOSTs +++++++++++
Sample size estimation
--------------------------------------------------
Study design: 2 parallel groups
untransformed data (additive model)
alpha = 0.05, 0.05; target power = 0.8
BE margins = -0.2, -0.2 ... 0.2, 0.2
True diffs = -0.05, -0.05; SD = 0.2, 0.2
Correlation between the two metrics = 0.9
Sample size (total)
n power
52 0.800940
```

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