PowerTOST / Power2Stage [R for BE/BA]

posted by Helmut Homepage – Vienna, Austria, 2018-10-31 11:08 (819 d 00:32 ago) – Posting: # 19507
Views: 2,085

Hi fyy…,

» […] why there is not selection for 3-ways crossover design in sample size estimate.

Simple: Yung-jin didn’t implement it. ;-)

» If there are other soft could estimate sample size for 3-ways crossover design?

I recommend package PowerTOST.1 These designs are currently supported:
  1. 2 parallel groups (T|R)
  2. Paired means (TR or RT)
  3. 2×2×2 crossover (TR|RT)
  4. 3×3 crossover (Latin Squares ABC|BCA|CAB)
  5. 3×6×3 crossover (Williams’ design: ABC|ACB|BAC|BCA|CAB|CBA)
  6. 4×4 crossover (Latin Squares: ABCD|BCDA|CDAB|DABC or any of the Williams’ designs)
  7. 2×2×3 full replicate (TRT|RTR)
  8. 2×2×4 full replicate (TRTR|RTRT)
  9. 2×4×4 full replicate (TRTR|RTRT|TTRR|RRTT)
  10. 2×3×3 partial replicate (TRR|RTR|RRT)
  11. 2×4×2 full replicate (Balaam’s design: TR|RT|TT|RR)
  12. 2×2×2r (Liu’s repeated crossover)
Sample size / power for average bioequivalence (ABE) is provided for all designs. Reference-scaling for the FDA’s method (RSABE) and the EMA’s / WHO’s / Health Canada’s method (ABEL) is implemented (#VII–XII) as is the FDA’s for NTIDs (#VII–VIII). Note that simulations are required for all reference-scaling methods. Dose proportionality according to the power model and one-sided tests (for non-inferiority or non-superiority) are implemented as well.

In most functions power can be calculated by the shifted t-distribution (crude approximation), the noncentral t-distribution (like in bear), or exact methods (preferred). Details in the online manual.

Example for a 3×3 design:

sampleN.TOST(CV=0.2, theta0=0.95, targetpower=0.8, design="3x3x3")


+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
Study design:  3x3 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
True ratio = 0.95,  CV = 0.2

Sample size (total)
 n     power
18   0.808949

If you are not assuming a common variance for all pairwise comparions (very good idea: see there) estimate the sample size for the common 2×2×2 design instead:

sampleN.TOST(CV=0.2, theta0=0.95, targetpower=0.8, design="2x2x2")

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
True ratio = 0.95,  CV = 0.2

Sample size (total)
 n     power
20   0.834680

If you are interested in Two-Stage Designs (group-sequential and adaptive TSDs with sample size re-estimation: parallel groups and 2×2×2 crossovers) consider package Power2Stage.2 Online manual.

  1. Labes D, Schütz H, Lang B. PowerTOST: Power and Sample Size Based on Two One-Sided t-Tests (TOST) for (Bio)Equivalence Studies. 2018-04-12: version 1.4-7. CRAN, GitHub.
  2. Labes D, Lang B, Schütz H. Power2Stage: Power and Sample-Size Distribution of 2-Stage Bio­equivalence Studies. 2018-04-03: version 0.5-1. CRAN, GitHub.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Complete thread:

 Admin contact
21,316 posts in 4,446 threads, 1,489 registered users;
online 5 (0 registered, 5 guests [including 1 identified bots]).
Forum time: Wednesday 11:41 CET (Europe/Vienna)

Nothing fails like success because you do not learn anything from it.
The only thing we ever learn from is failure.
Success only confirms our superstitions.    Kenneth E. Boulding

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz