Bioequivalence and Bioavailability Forum

Dear bears, dear all,

here some brief calculation results with 'true' ratio =1 and a classical 2x2 cross-over using the common acceptance limits 0.8 - 1.25:

                  sample size (alpha=0.05)
                 carved   uncertain 
      power CV   in stone   CV       ratio
--------------------------------------------
m=5   0.8   0.2     16      24        1.5
            0.25    24      36        1.5
            0.3     32      52        1.625
            0.35    42      68        1.619
            0.4     54      86        1.593
      0.9   0.2     20      36        1.8
            0.25    28      54        1.929
            0.3     40      76        1.9
            0.35    52     102        1.962
            0.4     66     130        1.967

Note that we cannot meet Joulious factors exactly because of the discrete nature of the sample size estimation (steps of 2, meeting target power with different excess). But we are very near of his theoretical derived factors (which do not depend on CV) of 1.652 for power=0.8 and 1.980 for power=0.9 .
Moreover it must be noted that Julious factors are derived with Z-quantiles instead of t-quantiles in the sample size formula i.e. are large sample results.

Same calculations with ratio=0.95 but only for power=80%:

                  sample size (alpha=0.05)
                 carved   uncertain 
      power CV   in stone   CV       ratio
--------------------------------------------
m=5   0.8   0.2     20      28        1.4
            0.25    28      44        1.571
            0.3     40      60        1.5
            0.35    52      80        1.538
            0.4     66     104        1.576

Stephen Senn in "Statistical issues in drug development": "Clinically relevant difference: That which is used to justify the sample size but will be claimed to have been used to find it."