Description Usage Arguments Details Note Author(s) References Examples
This function assesses the pre-specified alpha(s) for the BE decision in Adaptive Sequential Two-Stage Designs (TSDs) with sample size re-estimation based on simulations in order to control the consumer risk α at the nominal level.
1 2 3 4 5 6 7 8 | check.TSD(Var1, PE1, n1, Var, PE, N, type = 1, usePE = FALSE, GMR,
alpha0 = 0.05, alpha1 = 0.0294, alpha2 = 0.0294, theta1, theta2,
target = 0.80, pmethod = c("shifted", "nct", "exact"),
int.pwr = TRUE, min.n2 = 0, max.n = Inf, Nmax = Inf,
fCrit = c("PE", "CI"), fClow = 0, nsims = 1e6, setseed = TRUE,
tol = 1e-8, pa = FALSE, skip = TRUE, algo = 1, plot.it = FALSE,
valid = FALSE, expl = 3, Xover = TRUE, stop1 = FALSE,
KM = FALSE, KM.des = c("TSD", "TSD-1", "TSD-2"), CIs = FALSE)
|
Var1 |
Vector of observed variability in the first stage.
If four elements are given, the CV is calculated from the confidence
interval by PowerTOST’s function
|
PE1 |
Observed point estimate in the first stage.
In the case of a four-element vector of |
n1 |
Sample size of the first stage of the study. In a parallel design with
unequal group sizes may be given as a two-element vector where the first
element is the group-size under Test and the second one under Reference.
If |
Var |
Vector of observed variability in the final (pooled) analysis.
If four elements are given, the CV is calculated from the confidence interval (taking the degrees of freedom of the stage-term into account):
|
PE |
Observed point estimate in the final (pooled) analysis.
In the case of a four-element vector of |
N |
Total sample size of the the study. If |
type |
‘Type’ of the Two-Stage Design ( |
usePE |
If |
GMR |
‘True’ or assumed bioavailability ratio for the sample size re-estimation. |
alpha0 |
Type I error (TIE) probability (α; nominal level of the test). Per convention
commonly set to |
alpha1 |
Specified adjusted α of the test in the interim. Defaults to |
alpha2 |
Specified adjusted α of the test in the final (pooled) analysis. Defaults to |
theta1 |
Lower acceptance limit for BE. Defaults to |
theta2 |
Upper acceptance limit for BE. Defaults to |
target |
Power threshold in the first step of ‘Type 1’ designs and power to achieve in the sample size re-estimation step. |
pmethod |
Power calculation method; also to be used in the sample size re-estimation
for stage 2. |
int.pwr |
If |
min.n2 |
Minimum sample size of stage 2. Defaults to 0 (as in all references). |
max.n |
If |
Nmax |
Futility criterion. If set to a finite value all simulated studies in which
a sample size |
fCrit |
Futility criterion to use for the point estimate or confidence interval in
the interim. Acceptable values are |
fClow |
Lower futility limit for |
nsims |
Number of simulations to be performed to estimate the (‘empiric’) TIE error and in optimizing adjusting α. The default value 1,000,000 = 1e+6 should not be lowered. |
setseed |
Simulations are dependent on the starting point of the (pseudo)random number
generator.To avoid differences in power for different runs, |
tol |
Desired accuracy (convergence tolerance) of |
pa |
Should results of the power analysis for adjusted α be shown? Defaults to |
skip |
Should optimization of α be
skipped if the TIE with the specified α already preserves the consumer risk ( |
algo |
Defaults to |
plot.it |
Should a comparative plot of PE and CI int the final analysis be made?
Defaults to |
valid |
Should one of the validation examples be assessed? Defaults to |
expl |
Number of the validation examples (
|
Xover |
Defaults to |
stop1 |
Defaults to |
KM |
Should a fully adaptive design according to Karalis & Macheras or Karalis be
used? Defaults to |
KM.des |
Design-specification of Karalis & Macheras or Karalis. Acceptable values: |
CIs |
Defaults to |
The calculations follow in principle the simulations as described in the references.
The underlying subject data are assumed to be evaluated after log-transformation.
Instead of – time-consuming – simulating subject data, the statistics PE1, PE, and
MSE1, SS2 are simulated via their associated distributions (normal and
χ²) as suggested by Zheng et al.
The code tries to reconstruct the applied method from the study’s conditions. In the strict sense applying a specified α is only justified if the study’s conditions were within the validated range (e.g., n1, CV1, GMR, target power, etc) given in the references.
Hoping to get in simulations an empiric Type I Error of exactly 0.05 (as
– unoffically – demanded by the EMA’s Biostatistics
Working Party) is futile. Already rounding the confidence interval in fixed sample
designs to two digits according to the guideline (i.e., 79.995% upwards
to 80.00% or 125.004% downwards to 125.00%) may transform into a TIE
of up to 0.0508.
For more details see a description in the doc subdirectory of the package.
So far the author did not came across a TIE after optimization of
>0.05001. The question whether this is acceptable to the BSWP
remains open.
Program offered for Use without any Guarantees and Absolutely No Warranty.
No Liability is accepted for any Loss and Risk to Public Health Resulting from Use of this Code
Helmut Schütz
O’Brien PC, Fleming TR. A Multiple Testing Procedure for Clinical Trials.
Biometrics. 1979;35(3):549–56.
Armitage P. Interim Analysis in Clinical Trials.
Stat Med. 1991;10(6):925–37. doi: 10.1002/sim.4780100613
Potvin D, DiLiberti CE, Hauck WW, Parr AF, Schuirmann DJ, Smith RA. Sequential design approaches for bioequivalence studies with crossover designs.
Pharm Stat. 2008;7(4):245–62. doi: 10.1002/pst.294
Montague TH, Potvin D, DiLiberti CE, Hauck WW, Parr AF, Schuirmann DJ. Additional results for ‘Sequential design approaches for bioequivalence studies with crossover designs’.
Pharm Stat. 2012;11(1):8–13. doi: 10.1002/pst.483
Zheng Ch, Wang J, Zhao L. Testing bioequivalence for multiple formulations with power and sample size calculations.
Pharm Stat. 2012;11(4):334–41. doi: 10.1002/pst.1522
Fuglsang A. Sequential Bioequivalence Trial Designs with Increased Power and Controlled Type I Error Rates.
AAPS J. 2013;15(3):659–61. doi: 10.1208/s12248-013-9475-5
Karalis V, Macheras P. An Insight into the Properties of a Two-Stage Design in Bioequivalence Studies.
Pharm Res. 2013;30(7):1824–35. doi: 10.1007/s11095-013-1026-3
Karalis V. The role of the upper sample size limit in two-stage bioequivalence designs.
Int J Pharm. 2013;456(1):87–94. doi: 10.1016/j.ijpharm.2013.08.013
Fuglsang A. Futility Rules in Bioequivalence Trials with Sequential Designs.
AAPS J. 2014;16(1):79–82. doi: 10.1208/s12248-013-9540-0
Fuglsang A. Sequential Bioequivalence Approaches for Parallel Designs.
AAPS J. 2014;16(3):373–8. doi: 10.1208/s12248-014-9571-1
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Pharm Stat. 2015;14(3):180–8. doi: 10.1002/pst.1672
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Pharm Stat. 2015;15(1):15–27. doi: 10.1002/pst.1721
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | # Potvin et al., Example 2, 'Method B'
# Not run: Due to timing policy of CRAN for examples.
## Not run:
check.TSD(Var1=c(0.032634, "MSE"), PE1=c(0.08396, "difflog"), n1=12,
Var=c(0.045896, "MSE"), PE=c(0.014439, "difflog"), N=20,
pmethod="shifted", type=1)
# or simply using a built-in dataset
check.TSD(valid=TRUE, expl=3)
# Should give TIE 0.04307 and acceptance of the reported results.
#
# As above but variabilities and PEs calculated from CIs and alpha(s).
# Varibility as a 4-element vector, and PEs not given.
# Not run: Due to timing policy of CRAN for examples.
check.TSD(Var1=c(0.9293, 1.2728, 0.0294, "CI"), n1=12,
Var=c(0.8845, 1.1638, 0.0294, "CI"), N=20,
pmethod="shifted", type=1)
# Slightly different TIE (0.04300) since the precision of the input
# is limited.
#
# Potvin et al., Example 2, 'Method C'
check.TSD(Var1=c(0.032634, "MSE"), PE1=c(0.08396, "difflog"), n1=12,
Var=c(0.045896, "MSE"), PE=c(0.014439, "difflog"), N=20,
pmethod="shifted", type=2, plot.it=TRUE)
# or using the built-in dataset
check.TSD(valid=TRUE, expl=4)
# Should give TIE 0.05062 and optimized alpha 0.02858 (TIE 0.04992).
# Original and adjusted results agree; can accept the reported results.
#
# Xu et al., 'Method E' for high CVs
check.TSD(Var1=c(0.483, "CV"), PE1=c(0.943, "ratio"), n1=48,
Var=c(0.429, "CV"), PE=c(1.01, "ratio"), N=104,
pmethod="shifted", type=1, fCrit="CI", fClow=0.9305,
alpha1=0.0254, alpha2=0.0357)
# or using the built-in dataset
check.TSD(valid=TRUE, expl=8)
## End(Not run)
# Should give TIE 0.04953 and acceptance of reported results.
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