Bioequivalence and Bioavailability Forum

Hi Datacollector,

❝ […] a regular 2 way crossover […] comfortably met the usual bioequivalence criteria.

Congratulations.

❝ The less good news was that there were significant period and sequence effects for both AUC and Cmax.

AUC and C_max are highly correlated. If you see significant effects for one likely you see them for the other as well.

❝ We are assured we can ignore the sequence effect as the usual conditions for so doing apply.

Correct. A statistically significant sequence effect (better unequal carry-over because equal carry-over doesn’t matter) can be caused by

• a true sequence effect,
  
• a true carry-over effect,
  
• a true formulation-by-period interaction,
  
• a randomization failure,

or any possible combination of them. OK, the last one can be assessed in an audit/inspection. These effects are ‘confounded’ (i.e., cannot be separated by a statistical method in a non-replicative design). Hence, they can only be avoided by design (sufficiently long washout). It was shown by Freeman* that analysis of period data gives biased estimates and a potentially inflated type I error. It took the EMA 21 years to incorporate that in the BE-GL:

A test for carry-over is not considered relevant and no decisions regarding the analysis (e.g. analysis of the first period only) should be made on the basis of such a test. The potential for carry­over can be directly addressed by examination of the pre-treatment plasma concentrations in period 2 (and beyond if applicable).

❝ Looking at the period data (treating as two parallel studies) …

Given the above, why did you do that at all? The sequence effect is not relevant. Even more, the period effect is adjusted for in the crossover model anyway (it means out).

❝ … we find the T/R point estimator lies considerably below the acceptance range, while for period 2, it is rather higher than the BE acceptance range.

Are you looking for an explanation?
Since the two periods are now evaluated as parallel designs there are tons of reasons. If a study would have been planned (!) as a parallel design, the usual conditions should have been observed: It is of utmost importance to keep groups as similar as possible (sex, body weight, age-dependent clearance, …). If the drug is subjected to polymorphic metabolism, pheno- (or even better geno-) typing should be done. This was not the case – and with good reasons. Since in a crossover subjects act as their own reference, we don’t have to care about all that. It is quite possible that – by pure chance – groups were not similar: You think that your are comparing treatments but actually you are comparing treatments + unknown (!) group differences. Confounded effects again. Meaningless.

❝ … This has given rise to some concern.

By whom and why?

❝ Does the observation of the difference between periods negate the finding of equivalence?

Nope.

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• Freeman PR. The performance of the two-stage analysis of two-treatment, two-period cross-over trials. Stat Med. 1989;8(12):1421–32. doi:10.1002/sim.4780081202.