Power2Stage (version 0.5.2)

power.tsd.ssr: Power of 2-stage BE studies in 2x2 crossover designs with interim sample size re-estimation

Description

This function calculates the ‘empiric’ power (via simulations) of 2-stage BE studies with interim sample size re-estimation (i.e., but no BE decision after ). The sample size re-estimation can be done blinded or unblinded.

Usage

power.tsd.ssr(alpha = 0.05, n1, GMR, CV, targetpower = 0.8,
              pmethod = c("nct", "exact", "shifted", "ls"), blind = FALSE,
              usePE = FALSE, min.n = 0, max.n = Inf, theta0, theta1, theta2,
              npct = c(0.05, 0.5, 0.95), nsims, setseed = TRUE, details = FALSE)

Arguments

alpha

Nominal type I error. Has to be adjusted in case of inflation of the Type I Error.

n1

Sample size of .

GMR

Ratio T/R to be used in the sample size re-estimation. Defaults to 0.95 if missing.

CV

Coefficient of variation of the intra-subject variability (use e.g., 0.3 for 30%). Anticipated population value.

targetpower

Power to achieve in the sample size estimation step.

pmethod

Power calculation method to be used in the sample size re-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. Also implemented is the large sample approximation as used in the references. Defaults to "nct" as a reasonable compromise between speed and accuracy in the sample size estimation step.

blind

If TRUE the blinded estimate of the intra-subject variance, i.e., the estimate from the period differences, is used in sample size estimation. If FALSE the usual MSE from is used. Defaults to FALSE since most BE studies are open.

usePE

If TRUE the point estimate from the interim analysis is used in the sample size re-estimation. Defaults to FALSE. usePE = TRUE doesn<U+2019>t make sense if blind = TRUE. In that case the function issues a warning and usePE is reset to usePE = FALSE.

min.n

If min.n>n1, the re-estimated sample size (N) is set to max(min.n,N). If min.n=0 (the default), no minimal sample size is applied.

max.n

If max.n is set to a finite value the re-estimated sample size (N) is set to min(max.n,N). Defaults to Inf which is equivalent to not constrain the re-estimated sample size. Attention! max.n is here not a futility criterion like Nmax in other functions of this package.

theta0

Assumed ratio of geometric means (T/R) for simulations. If missing, defaults to GMR.

theta1

Lower bioequivalence limit. Defaults to 0.8.

theta2

Upper bioequivalence limit. Defaults to 1.25.

npct

Percentiles to be used for the presentation of the distribution of n(total)=n1+n2. Defaults to c(0.05, 0.5, 0.95) to obtain the 5% and 95% percentiles and the median.

nsims

Number of studies to simulate. If missing, nsims is set to 1E+05 = 100,000 or to 1E+06 = 1 Mio if estimating the empiric Type I Error ('alpha'), i.e., with theta0 at the border or outside the acceptance range theta1 … theta2.

setseed

Simulations are dependent on the starting point of the (pseudo) random number generator. To avoid differences in power for different runs a set.seed(1234567) is issued if setseed=TRUE, the default. Set this argument to FALSE to view the variation in power between different runs.

details

If set to TRUE the function prints the results of time measurements of the simulation steps. Defaults to FALSE.

Value

Returns an object of class class "pwrtsd" with all the input arguments and results as components. The class class "pwrtsd" has a S3 print method. The results are in the components:

pBE

Fraction of studies found BE.

pct_s2

Percentage of studies continuing to .

nmean

Mean of n(total).

nrange

Range (min, max) of n(total).

nperc

Percentiles of the distribution of n(total).

ntable

Object of class "table" summarizing the discrete distribution of n(total) via its unique values and counts of occurences of these values. ntable is only given back if usePE = FALSE

Details

The calculations follow in principle the simulations as described in Potvin et al. The underlying subject data are assumed to be evaluated after log-transformation. But instead of simulating subject data, the statistics pe1, mse1 and pe2, SS2 are simulated via their associated distributions (normal and distributions).

References

Golkowski D, Friede T, Kieser M. Blinded sample size re-estimation in crossover bioequivalence trials. Pharm Stat. 2014; 13(3):157--62. 10.1002/pst.1617

Jones B, Kenward MG. Design and Analysis of Cross-Over Trials. Boca Raton: CRC Press; 3 edition 2014. Chapter 12.

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. 10.1002/pst.294

See Also

power.tsd for 2-stage studies with interim BE decision.

Examples

# NOT RUN {
# Not run to comply with CRAN policy about examples' run-time;
# minimum number of sim's should be 1E5 for 'power', 1E6 sim's for 'alpha'
# }
# NOT RUN {
power.tsd.ssr(alpha=0.05, n1=10, GMR=1, CV=0.239, targetpower=0.9,
              pmethod="ls", blind=TRUE, theta0=1.25)
# should give an alpha-inflation 0.072359 (run time <5 seconds)
# repeated with noncentral t-approximation
power.tsd.ssr(alpha=0.05, n1=10, GMR=1, CV=0.239, targetpower=0.9,
              pmethod="nct", blind=TRUE, theta0=1.25)
# should give an alpha-inflation 0.069789 (run time ~20 seconds)
#
# adjusted alpha to control the Type I Error, noncentral t-approx.
power.tsd.ssr(alpha=0.03505, n1=10, GMR=1, CV=0.239, targetpower=0.9,
              pmethod="nct", blind=TRUE, theta0=1.25)
# should control the TIE with 0.049877
# }