PowerTOST / Power2Stage [🇷 for BE/BA]

posted by Helmut Homepage – Vienna, Austria, 2018-10-31 11:08 (1386 d 07:04 ago) – Posting: # 19507
Views: 2,481

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 [msg]there[/msg]) 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 🖖 [image]
Helmut Schütz
[image]

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

Complete thread:

UA Flag
Activity
 Admin contact
22,305 posts in 4,668 threads, 1,587 registered users;
online 11 (1 registered, 10 guests [including 6 identified bots]).
Forum time: Wednesday 19:13 CEST (Europe/Vienna)

There is no point in being precise when you don’t know
what you’re talking about.    attributed to John Tukey

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5