Following the design scheme according to power.tsd.in
the function
performs the analysis after the second stage has been performed.
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)
If one element is given, the overall one-sided significance level (not the
adjusted level for ). If two
elements are given, the adjusted one-sided alpha levels for
and
, respectively.
If missing, defaults to 0.05
.
Pre-defined weight(s) of .
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
.
Logical; if TRUE
(default) the maximum combination test will be
used, otherwise the standard combination test.
Observed ratio of geometric means (T/R) of data (use e.g., 0.95 for 95%).
Observed coefficient of variation of the intra-subject variability of (use e.g., 0.3 for 30%).
Sample size of .
Optional; Error degrees of freedom of
that can be specified in
addition to n1
.
Optional; Standard error of the difference of means of
that can be specified in
addition to CV1
. Must be on additive scale (i.e. usually log-scale).
Observed ratio of geometric means (T/R) of (only) data (use e.g., 0.95 for 95%).
Observed coefficient of variation of the intra-subject variability of (only) (use e.g., 0.3 for 30%).
Sample size of .
Optional; Error degrees of freedom of (only)
that can be specified in
addition to n2
.
Optional; Standard error of the difference of means of (only)
that can be specified in
addition to CV2
. Must be on additive scale (i.e. usually log-scale).
Lower bioequivalence limit. Defaults to 0.8.
Upper bioequivalence limit. Defaults to 1.25.
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 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:
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
)
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
)
(Exact) repeated confidence interval for .
Median unbiased point estimate as estimate for the final geometric mean ratio after stage 2.
Logical, indicating whether BE can be concluded after or not.
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).
K<U+00F6>nig F, Wolfsegger M, Jaki T, Sch<U+00FC>tz H, Wassmer G. Adaptive two-stage bioequivalence trials with early stopping and sample size re-estimation. Vienna: 2014; 35 Annual Conference of the International Society for Clinical Biostatistics. Poster P1.2.88 10.13140/RG.2.1.5190.0967.
Patterson SD, Jones B. Bioequivalence and Statistics in Clinical Pharmacology. Boca Raton: CRC Press; 2 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. 10.1002/sim.7614.
Wassmer G, Brannath W. Group Sequential and Confirmatory Adaptive Designs in Clinical Trials. Springer 2016. 10.1007/978-3-319-32562-0.
# NOT RUN {
# 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)
# }
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