Following the design scheme according to power.tsd.in
the function
performs the interim analysis of the first stage data.
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"))
If one element is given, the overall one-sided significance level (not
the adjusted level for ). In this
case the adjusted alpha levels will be calcualted internally. If two
elements are given, the argument refers to the two adjusted one-sided
alpha levels for and
, respectively.
If missing, defaults to 0.05
.
Pre-defined weight(s) of , 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. 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.
Desired (overall) target power to declare BE at the end of the trial.
Observed ratio of geometric means (T/R) of data (use e.g., 0.95 for 95%).
Sample size of .
Observed coefficient of variation of the intra-subject variability of (use e.g., 0.3 for 30%).
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).
Lower bioequivalence limit. Defaults to 0.8.
Upper bioequivalence limit. Defaults to 1.25.
Assumed ratio of geometric means (T/R) to be used in power calculation for and sample size re-estimation for . If missing, defaults to 0.95.
If TRUE
the sample size re-estimation is done with the observed
point estimate (PE) of the treatment difference in
.
Defaults to FALSE
.
Note: The futility inspection via the power of stage 1 is always done with
the planning value GMR
.
Minimum sample size of . Defaults to 4.
If the sample size re-estimation step gives a sample size for
less than min.n2
, then
min.n2
will be used for .
Maximum overall sample size +
.
This is not a futility criterion regarding the maximum sample size! If
max.n
is set to a finite value and the sample size re-estimation gives a
sample size for (n2
) such
that n1 + n2 > max.n
, then the sample size for
will be set to n2 = max.n - n1
.
Defaults to Inf
, i.e., no constraint on the re-estimated sample size.
Threshold for power monitoring step to decide on futility for cases where
BE has not been achieved after
: If BE has not been
achieved after and the power for
is greater than or equal to
fCpower
, then the study will be considered a failure.
See ‘Details’ for more information on the choice of
fCpower
.
Futility criterion to use: "No"
(no futility criterion regarding
observed point estimate, confidence interval and maximum sample size),
"PE"
(observed point estimate of the geometric mean ratio from
),
"CI"
(90% confidence interval of the geometric mean ratio from
), "Nmax"
(overall maximum
sample size); or a combination thereof (concatenate abbreviations).
Defaults to "CI".
Lower futility limit for the PE or CI of
.
If the PE or CI is completely outside of fClower
… fCupper
the study is to be stopped due to futility (not BE).
May be missing. If "PE"
or "CI"
is specified within fCrit
,
the default will be set to 0.8 for fCrit = "PE"
or 0.95 for fCrit = "CI"
.
If neither "PE"
nor "CI"
is specified within fCrit
, there
will be no futility constraint regarding point estimate or confidence interval
from (regardless of any
specification of fClower
and/or fCupper
).
Upper futility limit for the PE or CI of
.
Analogous to fClower
: Will be set to 1/fClower
if missing.
Futility criterion regarding maximum sample size. If the determined sample size
for (n2
) is such that
n1 + n2 > fCNmax
, the study will not continue to
and stopped due to futility (not
BE).
If "Nmax"
is specified within fCrit
and argument fCNmax
is missing, the value will be set to fCNmax = 4*n1
. If "Nmax"
is
not specified within fCrit
, then there will be no futility constraint
regarding maximum sample size (regardless of any specification of fCNmax
).
Method for sample size re-estimation step: "no"
does not use
conditional error rates nor the estimated conditional target power for
the second stage, "error"
uses conditional error rates for the
second stage, and "error_power"
uses both conditional error rates
and the estimated conditional target power for the second stage.
Defaults to "error_power"
.
See also ‘Details’.
Power calculation method, also to be used in the sample size estimation for
.
Implemented are "nct"
(approximate calculations via non-central
t-distribution, "exact"
(exact calculations via Owen<U+2019>s Q),
and "shifted"
(approximate calculation via shifted central t-distribution
like in the paper of Potvin et al.)
In contrast to power.tsd.in
the default value here is "exact"
.
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:
Observed p-value for first hypothesis.
Observed p-value for second hypothesis.
z statistic value for first null hypothesis.
z statistic value for second null hypothesis.
(Exact) repeated confidence interval for .
Three dimensional vector with either 0 or 1. The first
component represents futility due to Power of first stage > fCpower
,
the second futility due to CI
(or PE
) outside of
fClower ... fCupper
, the third futility due to
n1 + n2 > fCNmax
.
Note that the futility rules can be applied in a non-binding manner.
90% Confidence interval for observed ratio of geometric means
from . If fCrit != "CI"
result will be NULL
.
Calculated power of .
Logical, indicating whether to stop after (due to BE or due to futility).
Logical, indicating whether study is recommended to be stopped after due to futility.
Logical, indicating whether BE could be concluded after or not (regardless of any futility criterion).
Required (total) sample size for (will be zero if BE has been shown after ).
Only applicable if BE has not been shown after
. Contains
alpha values for the two hypotheses required for sample size re-calculation.
If ssr.conditional = "no"
the result is equal to alpha
,
otherwise it contains the conditional error rates for the standard combination
test (in case of max.comb.test = FALSE
) or maximum combination test (in
case of max.comb.test = TRUE
).
Only applicable if BE has not been shown after . Contains the geometric mean ratio used for sample size re-calculation (accounts for adaptive planning step).
Only applicable if BE has not been shown after . Contains the target power used for the sample size re-calculation (see also 'Details').
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 non-integer valued (e.g. if the
Kenward-Roger 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, 1-w) 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, 1-w) and (w*, 1-w*).
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 re-estimation 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 re-calculation will be set
to targetpower
.
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
interim.tsd.in(GMR1 = exp(0.0424), CV1 = 0.3682, n1 = 20, max.n = 4000)
# }
Run the code above in your browser using DataCamp Workspace