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:

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

gives

+++++++++++ 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.

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