Description Usage Arguments Details Value Author(s) References See Also Examples
Following the design scheme according to power.tsd.in
the function
performs the interim analysis of the first stage data.
1 2 3 4 5 6  interim.tsd.in(alpha, weight, max.comb.test = TRUE, targetpower = 0.8,
GMR1, n1, CV1, df1 = NULL, SEM1 = NULL, theta1, theta2,
GMR, usePE = FALSE, min.n2 = 4, max.n = Inf,
fCpower = targetpower, fCrit = "CI", fClower, fCupper, fCNmax,
ssr.conditional = c("error_power", "error", "no"),
pmethod = c("exact", "nct", "shifted"))

alpha 
If one element is given, the overall onesided significance level (not
the adjusted level for stage 1). In this
case the adjusted alpha levels will be calcualted internally. If two
elements are given, the argument refers to the two adjusted onesided
alpha levels for stage 1 and
stage 2, respectively. 
weight 
Predefined weight(s) of stage 1, see
'Details' for more information. 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 
targetpower 
Desired (overall) target power to declare BE at the end of the trial. 
GMR1 
Observed ratio of geometric means (T/R) of stage 1 data (use e.g., 0.95 for 95%). 
n1 
Sample size of stage 1. 
CV1 
Observed coefficient of variation of the intrasubject variability of stage 1 (use e.g., 0.3 for 30%). 
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 
theta1 
Lower bioequivalence limit. Defaults to 0.8. 
theta2 
Upper bioequivalence limit. Defaults to 1.25. 
GMR 
Assumed ratio of geometric means (T/R) to be used in power calculation for stage 1 and sample size reestimation for stage 2. If missing, defaults to 0.95. 
usePE 
If 
min.n2 
Minimum sample size of stage 2. Defaults to 4. 
max.n 
Maximum overall sample size stage 1 +
stage 2. 
fCpower 
Threshold for power monitoring step to decide on futility for cases where
BE has not been achieved after
stage 1: If BE has not been
achieved after stage 1 and the power for
stage 1 is greater than or equal to

fCrit 
Futility criterion to use: 
fClower 
Lower futility limit for the PE or CI of
stage 1. 
fCupper 
Upper futility limit for the PE or CI of
stage 1. 
fCNmax 
Futility criterion regarding maximum sample size. If the determined sample size
for stage 2 ( 
ssr.conditional 
Method for sample size reestimation step: 
pmethod 
Power calculation method, also to be used in the sample size estimation for
stage 2. 
The observed values of stage 1 (e.g. GMR1
, n1
, CV1
) may
be obtained based on the first stage data via the usual ANOVA approach.
The optional arguments df1
and SEM1
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 noninteger valued (e.g. if the
KenwardRoger method was used).
The weight
argument always refers to the first weight of a pair of
weights. For example, in case of max.comb.test = FALSE
the standard
combination test requires two weights (w, 1w) but only the first one, w,
is required as input argument here because the second weight is
automatically specified once the first is given. Similarly for
max.comb.test = TRUE
, w and w* need to be specified, which in turn
define the two pairs of weights (w, 1w) and (w*, 1w*).
If ssr.conditional = "error_power"
, the design scheme generally
calculates the estimated conditional target power of the second stage and
uses this value as desired target power in the sample size reestimation process.
If fCpower
> targetpower
, then the conditional target power
may actually be negative. This does not seem sensible. Therefore, for such
cases the desired target power for the sample size recalculation will be set
to targetpower
.
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:
p11 
Observed pvalue for first hypothesis. 
p12 
Observed pvalue for second hypothesis. 
z1 
z statistic value for first null hypothesis. 
z2 
z statistic value for second null hypothesis. 
RCI 
(Exact) repeated confidence interval for stage 1. 
futility 
Three dimensional vector with either 0 or 1. The first
component represents futility due to Power of first stage > 
CI90 
90% Confidence interval for observed ratio of geometric means
from stage 1. If 
Power Stage 1 
Calculated power of stage 1. 
stop_s1 
Logical, indicating whether to stop after stage 1 (due to BE or due to futility). 
stop_fut 
Logical, indicating whether study is recommended to be stopped after stage 1 due to futility. 
stop_BE 
Logical, indicating whether BE could be concluded after stage 1 or not (regardless of any futility criterion). 
n2 
Required (total) sample size for stage 2 (will be zero if BE has been shown after stage 1). 
alpha_ssr 
Only applicable if BE has not been shown after
stage 1. Contains
alpha values for the two hypotheses required for sample size recalculation.
If 
GMR_ssr 
Only applicable if BE has not been shown after stage 1. Contains the geometric mean ratio used for sample size recalculation (accounts for adaptive planning step). 
targetpower_ssr 
Only applicable if BE has not been shown after stage 1. Contains the target power used for the sample size recalculation (see also 'Details'). 
B. Lang
König F, Wolfsegger M, Jaki T, Schütz H, Wassmer G.
Adaptive twostage bioequivalence trials with early stopping and sample size reestimation.
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 twostage
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: 10.1007/9783319325620.
1 2  # Example from Maurer et al
interim.tsd.in(GMR1 = exp(0.0424), CV1 = 0.3682, n1 = 20, max.n = 4000)

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
 Observed point estimate from stage 1 is not used for SSR
 With conditional error rates and conditional estimated target power
Interim analysis after first stage
 Derived key statistics:
z1 = 2.16918, z2 = 1.52869,
Repeated CI = (0.82575, 1.31819)
 No futility criterion met
 Test for BE not positive (not considering any futility rule)
 Calculated n2 = 36
 Decision: Continue to stage 2 with 36 subjects
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