Bioequivalence and Bioavailability Forum

Hi Christian,

❝ How to use Bear for sample size calculation for Crossover study 2x2, power=80, CVintra=.16, BE margins=80-125

Not sure why you posted a function-dump. Did you get an error?
With your values I got:

---------------------------------------------------------------------------
                            <<Sample Size Estimation>>                     
                                                                           
  Upper acceptance limit = 125 %
  Lower acceptance limit = 80 %
      Expected ratio T/R = 95.00 %
            Target power = 80.00 %
        Intra-subject CV = 16.0 %

  study     2x2x2        2x2x3       2x2x4
  design  crossover   replicated   replicated
 ------- ----------- ------------ ------------
    N        14          12           8

         Estimated power =   84.866 %
--------------------------------------------------------------------------

**Ref.:
 1. Hauschke D, Steinijans VW, Diletti E and Burke M.  Sample size         
    determination for bioequivalence assessment using a multiplicative model.
    Journal of Pharmacokinetics and Biopharmaceutics. 20, 557-561 (1992). 
 2. Julious SA. Tutorial in biostatistics: Sample sizes for clinical trials
    with normal data.  Statistics in Medicine. 23, 1921-1986 (2004).       
 3. Hauschke D, Steinijans VW and Pigeot I.  Bioequivalence studies in drug
    development methods and applications. John Wiley & Sons, New York     
    (2007).                                                               

 Note: The algorithms we use here have been validated with Dr. David Dubins'
 FARTSSIE, which is a very excellant Excel VBA program for many sample size
 estimation functions.  Website: http://individual.utoronto.ca/ddubins.   

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bear is a nice package, but the sample size estimation is limited to 2×2×2 crossovers and parallel designs. The sample sizes for the replicate designs are given as ≥75% (2×2×3) and ≥50% (2×2×4) of the 2×2×2 – which is only a rule of thumb.

If you want more flexibility (e.g., designs, α different from 0.05, sample sizes for FDA’s RSABE and EMA’s ABEL,…) consider package PowerTOST:

library(PowerTOST)
sampleN.TOST(alpha=0.05, targetpower=0.8, theta0=0.95, theta1=0.8,
             theta2=1.25, CV=0.16, design="2x2")

+++++++++++ 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
Null (true) ratio = 0.95,  CV = 0.16

Sample size (total)
 n     power
14   0.848665

Note that α 0.05, target power 0.8, T/R 0.95, acceptance range 0.80–1.25, and 2×2×2 are the function’s defaults – which are applicable in your case. Hence, you will get the same output by simply using sampleN.TOST(CV=0.16).