final.tsd.in {Power2Stage}

Analysis after second stage of 2-stage 2x2 crossover design based on the Inverse Normal method

Description

Following the design scheme according to power.tsd.in the function performs the analysis after the second stage has been performed.

Usage

final.tsd.in(alpha, weight, max.comb.test = TRUE, GMR1, CV1, n1, df1 = NULL,
             SEM1 = NULL, GMR2, CV2, n2, df2 = NULL, SEM2 = NULL,
             theta1, theta2)

Arguments

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.
If missing, defaults to ⁠0.05⁠.

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. ⁠weight⁠ must either contain one element (in case of ⁠max.comb.test = FALSE⁠) or two elements (in case of ⁠max.comb.test = TRUE⁠).
If missing, defaults to ⁠0.5⁠ for ⁠max.comb.test = FALSE⁠ and to ⁠c(0.5, 0.25)⁠ for ⁠max.comb.test = TRUE⁠.

max.comb.test

Logical; if ⁠TRUE⁠ (default) the maximum combination test will be used, otherwise the standard combination test.

GMR1

Observed ratio of geometric means (T/R) of stage 1 data (use e.g., 0.95 for 95%).

CV1

Observed coefficient of variation of the intra-subject variability of stage 1 (use e.g., 0.3 for 30%).

n1

Sample size of stage 1.

df1

Optional; Error degrees of freedom of stage 1 that can be specified in addition to n1.

SEM1

Optional; Standard error of the difference of means of stage 1 that can be specified in addition to CV1. Must be on additive scale (i.e. usually log-scale).

GMR2

Observed ratio of geometric means (T/R) of (only) stage 2 data (use e.g., 0.95 for 95%).

CV2

Observed coefficient of variation of the intra-subject variability of (only) stage 2 (use e.g., 0.3 for 30%).

n2

Sample size of stage 2.

df2

Optional; Error degrees of freedom of (only) stage 2 that can be specified in addition to n2.

SEM2

Optional; Standard error of the difference of means of (only) stage 2 that can be specified in addition to CV2. Must be on additive scale (i.e. usually log-scale).

theta1

Lower bioequivalence limit. Defaults to 0.8.

theta2

Upper bioequivalence limit. Defaults to 1.25.

Details

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).

Value

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 max.comb.test = FALSE or maximum combination test statistic in case of max.comb.test = TRUE)

z2

Combination test statistic for second null hypothesis (standard combination test statistic in case of max.comb.test = FALSE or maximum combination test statistic in case of max.comb.test = TRUE)

RCI

Repeated confidence interval for stage 2.

MEUE

Median unbiased point estimate as estimate for the final adjusted geometric mean ratio after stage 2.

stop_BE

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

Author(s)

B. Lang

References

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; 37(10): 1587–1607. 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.

See Also

power.tsd.in, interim.tsd.in

Examples

# 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)
# Example 2 from Potvin et al.
final.tsd.in(GMR1 = 1.0876, CV1 = 0.18213, n1 = 12,
             GMR2 = 0.9141, CV2 = 0.25618, n2 = 8)