Bioequivalence and Bioavailability Forum

My Capt’n,

sorry to interfere.

❝ in either case we'd be working on y=Blah+e

❝ where Blah has two levels (Before and after, or Test and Reference), leaving out other fixed stuff here because it doesn't affect power.

In your OP you wrote about a 222 design – which has period+sequence in the model. The only application of paired designs I know of (in BA, not BE) are ones where you com­pare PK metrics in steady state to single dose (e.g., AUC_τ to AUC_∞ in order to assess deviation from linear PK). Naturally we have not sequence here (MD always after SD) and have to assume no period effect.

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Edit: Due to +1 df, the paired model is always more powerful than the cross-over.

library(PowerTOST)
known.designs()[c(3, 12), ]
    no design  df df2 steps bk bknif bkni            name
3    1  2x2x2 n-2 n-2     2  2   1/2  0.5 2x2x2 crossover
12 100 paired n-1 n-1     1  2   2/1  2.0    paired means

power.TOST(CV=0.2, n=18, design="2x2x2")
[1] 0.7912399
power.TOST(CV=0.2, n=18, design="paired")
[1] 0.793409

Dear Maestro/All,

❝ Could you possibly check what a result from Proc Power would then look like for corr=0.0 and e.g. gmr=0.95, CV=0.25, n=18 or something ? Would that coin­cide with the usual power calculations from the world's finest package for power calculations widely known as PowerTOST?

proc power;
   pairedmeans test=equiv_ratio
      lower = 0.8
      upper = 1.25
      meanratio = 0.95
      corr = 0
      cv = 0.25
      npairs = 18
      power = .;
run;


gives 0.583. This is the same as power.TOST(CV=0.25, n=18, design="paired"). If we change corr = 0 to for example corr = 0.6, proc power gives 0.940.

Interesting... I went back to equation (3.5) in Patterson and Jones* and calculated the variance of the estimator of the treatment difference when taking into account the correlation (imho equation (3.5) assumes s_B² = 0, i.e. rho = 0). When doing so I end up with 2/n * s_T² * (1-rho). But as we know s_T² * (1-rho) is exactly equal to s_W². So the variance of the estimator of the treatment effect remains the same, even when taking into account the correlation (). Thus, the power is always the same, regardless of the correlation. In light of the observation above from proc power this does not make sense ... On the other hand: A higher correlation will result in higher s_B² which is compensated for via the subject effect in the model. Also, when simulating data sets with correlated outcomes and checking the power, the same result was obtained (i.e. power always the same).

Any thoughts, apparently there must be some error somewhere...??

Best, Ben

* Bioequivalence and Statistics in Clinical Pharmacology