Bioequivalence and Bioavailability Forum

Dear Helmut,

Let Y_i.k the sequence-by-period means (i=sequence, k=period) of the PK parameters under consideration (log-transformed if necessary).
The expected values of these are under the usual model (without carry-over):
                period
sequence    1      2      3
1 TRR     µT+p1  µR+p2  µR+p3
2 RTR     µR+p1  µT+p2  µR+p3
3 RRT     µR+p1  µR+p2  µT+p3
where the p_i are the period effects and µ_T and µ_R the formulation effects (means adjusted for period effects).

The contrast
F=1/6{2*Y1.1-Y1.2-Y1.3
      -Y2.1+2*Y2.2-Y2.3
      -Y3.1-Y3.2+2*Y3.3}
is then an estimate of the difference between Test and Reference.
This estimate can be shown to have variance (derivation omitted due to length)
var(F)=1/6{1/n1 + 1/n2 + 1/n3}*sigma2e
where the n_i are the number of subjects in the sequence groups and sigma²_e the error variance (intra-subject).

With the same number of subjects in each sequence this reduces to
var(F)=1/2*(1/n)*sigma2e
      =3/2*(1/N)*sigma2e
where N is now the total number of subjects.

This is the same as the variance of the appropriate contrast of sequence-by-period means for the usual 2x2x3 design (f.i. TRT/RTR) which is (see Chow, Liu "Design and Analysis of Bioavailability and Bioequivalence Studies", chapter 9.3.1)
var(F)=3/8*{1/n1 + 1/n2}*sigma2e
      =3/4*(1/n)*sigma2e
      =3/2*(1/N)*sigma2e

Thus we can use the design constant 1.5 also for the partial replicated design (sequences TRR/RTR/RRT)!
Or the rule 0.75*N for a 2x2 design, but now as a multiple of 3.

This concludes your definitive rehabilitation .
Someone out there to prove me wrong?

BTW: The exact sample size for the partial replicate design assuming expected CV 40%, expected T/R 95%, target power 80% and BE margins 75%-133.333333% is N=27, achieved power=0.801380
BE margins 75%-133%: N=27, achieved power=0.799982