Bioequivalence and Bioavailability Forum

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