Bioequivalence and Bioavailability Forum

Hi BE-proff,

❝ In Russia we have two options to prove sample size: either demonstrate calculations with formulas …

See this presentation (slide 8). The procedure is always iterative (since the t-value in the formula to calculate power depends on the degrees of freedom and hence, the sample size itself). The approximation¹ by the shifted central t-distribution can be done with a pocket calculator (alternatively: paper-pencil-brain) and a t-table. The better approximation (noncentral t) already needs software, since no tables exist for a range of the noncentrality parameter. The exact method needs numeric integration of two integrals → software.

❝ … or provide literature reference.

What do you mean by that?

❝ The 1st option is not for me because I don't have relevant background so I'd prefer the 2nd way.

❝

❝ So, if somebody could share any literature reference in a journal (preferrable) which mentions PowerTOST I'd really appreciate it

Jones & Kenward²

The power and sample size for a bioequivalence trial can conveniently be calculated using the R package PowerTOST (Labes (2013)).^a
The power is calculated using the R package PowerTOST (Labes (2013)) with the “exact” option.^b
Using the PowerTOST (Labes (2013)) R library function, the power, for a true ratio of 1, for this estimated CV and a total sample size of 20 is just over 0.04.^c

PowerTOST is mentioned in Nadarajah et al.³

In the folder \library\PowerTOST\tests you find R-scripts to validate the various sample size functions against published data. See the man-pages of ct5.1, ct5.2, ct5.3, ct5.4.1, ct9.6.2, ct9.6.4, ct9.6.6, ct9.6.8, ctCW.III, ctSJ.VIII.10, and ctSJ.VIII.20 for the references.

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1. Hauschke, D, Steinijans, VW, Diletti E, Burke M. Sample Size Determination for Bioequivalence Assessment Using a Multiplicative Model.
   J Pharmacokin Biopharm 1992;20(5);557–61. doi:10.1007/BF01061471.
   
2. Jones B, Kenward MG. Design and Analysis of Cross-Over Trials.
   Boca Raton: CRC Press / Chapman & Hall; 3^rd ed. 2015.
   1. p.329
      
   2. p.373
      
   3. p.379
3. Nadarajah S, Sergey Bityukov S, Krasnikov N. Confidence distributions: A review.
   Stat Meth. 2015;22:23–46. doi:10.1016/j.stamet.2014.07.002.  open source.