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

Following the design scheme according to `power.tsd.in`

the function
performs the analysis after the second stage has been performed.

1 2 3 |

`alpha` |
If one element is given, the overall one-sided significance level (not the
adjusted level for stage 2). If two
elements are given, the adjusted one-sided alpha levels for
stage 1 and
stage 2, respectively. |

`weight` |
Pre-defined weight(s) of stage 1.
Note that using the notation from Maurer et al weight corresponds to
information fraction, other literature may refer to sqrt(weight) as
being the weight. |

`max.comb.test` |
Logical; if |

`GMR1` |
Observed ratio of geometric means (T/R) of
stage 1 data
(use |

`CV1` |
Observed coefficient of variation of the intra-subject variability of
stage 1 (use |

`n1` |
Sample size of stage 1. |

`df1` |
Optional; Error degrees of freedom of
stage 1 that can be specified in
addition to |

`SEM1` |
Optional; Standard error of the difference of means of
stage 1 that can be specified in
addition to |

`GMR2` |
Observed ratio of geometric means (T/R) of (only)
stage 2 data
(use |

`CV2` |
Observed coefficient of variation of the intra-subject variability of (only)
stage 2 (use |

`n2` |
Sample size of stage 2. |

`df2` |
Optional; Error degrees of freedom of (only)
stage 2 that can be specified in
addition to |

`SEM2` |
Optional; Standard error of the difference of means of (only)
stage 2 that can be specified in
addition to |

`theta1` |
Lower bioequivalence limit. Defaults to 0.8. |

`theta2` |
Upper bioequivalence limit. Defaults to 1.25. |

The observed values `GMR1`

, `CV1`

, `n1`

must be obtained
using data from stage 1 only, and `GMR2`

, `CV2`

, `n2`

must
be obtained using data from stage 2 only. This may be done via the usual
ANOVA approach.

The optional arguments `df1`

, `SEM1`

, `df2`

and `SEM2`

require a somewhat advanced knowledge (provided in the raw output from for
example the software SAS, or may be obtained via `emmeans::emmeans`

).
However, it has the advantage that if there were missing data the exact
degrees of freedom and standard error of the difference can be used,
the former possibly being non-integer valued (e.g. if the
Kenward-Roger method was used).

Returns an object of class `"evaltsd"`

with all the input arguments and results
as components. As part of the input arguments a component `cval`

is also
presented, containing the critical values for stage 1 and 2 according to the
input based on `alpha`

, `weight`

and `max.comb.test`

.

The class `"evaltsd"`

has an S3 print method.

The results are in the components:

`z1` |
Combination test statistic for first null hypothesis (standard
combination test statistic in case of |

`z2` |
Combination test statistic for second null hypothesis (standard
combination test statistic in case of |

`RCI` |
(Exact) repeated confidence interval for stage 2. |

`MEUE` |
Median unbiased point estimate as estimate for the final geometric mean ratio after stage 2. |

`stop_BE` |
Logical, indicating whether BE can be concluded after stage 2 or not. |

B. Lang

König F, Wolfsegger M, Jaki T, Schütz H, Wassmer G.

*Adaptive two-stage bioequivalence trials with early stopping and sample size re-estimation.*

Vienna: 2014; 35^{th} Annual Conference of the International Society for Clinical Biostatistics. Poster P1.2.88

doi: 10.13140/RG.2.1.5190.0967.

Patterson SD, Jones B. *Bioequivalence and Statistics in Clinical Pharmacology.*

Boca Raton: CRC Press; 2^{nd} edition 2017.

Maurer W, Jones B, Chen Y. *Controlling the type 1 error rate in two-stage
sequential designs when testing for average bioequivalence.*

Stat Med. 2018;1–21. doi: 10.1002/sim.7614.

Wassmer G, Brannath W. *Group Sequential and Confirmatory Adaptive Designs
in Clinical Trials.*

Springer 2016. doi: 10.1007/978-3-319-32562-0.

1 2 3 | ```
# Example from Maurer et al.
final.tsd.in(GMR1 = exp(0.0424), CV1 = 0.3682, n1 = 20,
GMR2 = exp(-0.0134), CV2 = 0.3644, n2 = 36)
``` |

```
TSD with 2x2 crossover
Inverse Normal approach
- Maximum combination test with weights for stage 1 = 0.5 0.25
- Significance levels (s1/s2) = 0.02635 0.02635
- Critical values (s1/s2) = 1.93741 1.93741
- BE acceptance range = 0.8 ... 1.25
Final analysis after second stage
- Derived key statistics:
z1 = 3.22781, z2 = 3.07901,
Repeated CI = (0.88233, 1.14761)
Median unbiased estimate = 1.0100
- Decision: BE achieved
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.