## Approximate Power [R for BE/BA]

Dear all,

Dieter Hauschke informed me that Jones’/Kenward’s code uses Satterthwaite’s approximation for degrees of freedom (for heterogenous variances), which was corrected in a recent book.[1]
In power calculations degrees of freedom are fixed by the number of subjects (and sequences).

If you want to play around again, please replace code line #22

df    <- sqrt(n2)*(nc1-nc2)/(2*t1)

with

df    <- n2

Power (CV=20%) by the (old) new codes for n=24 are:
 +======+=======+=======+ |  GMR |  old  |  new  | +------+-------+-------+ | 0.85 | 28.16 | 26.86 | | 0.90 | 64.08 | 63.73 | | 0.95 | 89.19 | 89.60 | | 1.00 | 96.28 | 96.72 | | 1.05 | 89.90 | 90.32 | | 1.10 | 70.02 | 69.89 | | 1.15 | 41.92 | 40.85 | | 1.20 | 18.30 | 17.04 | +======+=======+=======+

Power >80% (CV=20%) by the (old) new codes are:
 +======+=====+===========+===========+ |  GMR |  n  |    old    |    new    | +------+-----+-----------+-----------+ | 0.85 | 134 | 0.8014178 | 0.8017723 | | 0.90 |  38 | 0.8140704 | 0.8154940 | | 0.95 |  20 | 0.8300156 | 0.8346802 | | 1.00 |  16 | 0.8214263 | 0.8331980 | | 1.05 |  18 | 0.7950343 | 0.8001854 | | 1.10 |  32 | 0.8084890 | 0.8100682 | | 1.15 |  72 | 0.8035456 | 0.8042181 | | 1.20 | 294 | 0.8017617 | 0.8019247 | +======+=====+===========+===========+

Power is >80% for all combinations tested.

» Maybe somebody of you has access to SAS or software specialized in power analysis (e.g., PASS or NQuery) and would like to check these results?

According to Dieter Hauschke Owen’s exact method is implemented in nQuery Advisor.

Since there is still some confusion about different methods for sample size estimation in bioequivalence (software, tables, approximations) an entire chapter of a new book[2] will be devoted to this issue.
1. S Patterson and B Jones
Bioequivalence and Statistics in Clinical Pharmacology
Chapman & Hall/CRC, Boca Raton, pp 230 (2006)
2. D Hauschke, VW Steinijans and I Pigeot
Bioequivalence Studies in Drug Development: Methods and Applications
Wiley, New York (2007)

Cheers,
Helmut Schütz

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