Bioequivalence and Bioavailability Forum

Dear Dan!

❝ I am not a statistician or mathematician and therefore have to rely on expert statements.

You know: two experts = three opinions?

❝ We are currently planning a sequential replicate design BE study in cancer patients.

Since your patients are in steady state anyway, the replicate design is easy to perform; just an additional profile in each period – if you don't run into ethical problems (blood loss).

❝ Two different statisticians had no objections against the design …

See me first sentence.

❝ … and now you are telling me that there is no method available.

OK. It try to sort things out. There is an abundance of methods for designing and evaluating sequential and adaptive designs. These methods have their origin in testing for a significant difference, i.e., the Null-Hypothesis H₀ is ‘no difference’ and the Alternative Hypothesis H_a is a ‘significant difference’ between treatments. In bioequivalence the problem is formulated differently: H₀ is ‘bioinequivalence’, and H_a is ‘bioequivalence’. The latter is accepted by inclusion of the confidence interval in the acceptance range. This distinction in the formulation of hypotheses is not trivial. Example (AR 80–125%, 90% CI):

95–105%: BE H₀ rejected; ‘classical’ H₀ not rejected
85– 95%: BE H₀ rejected; ‘classical’ H₀ rejected
75– 85%: BE H₀ not rejected; ‘classical’ H₀ rejected
75–130%: BE H₀ not rejected; ‘classical’ H₀ not rejected

As you see these examples lead to contradictory results if the wrong set of hypotheses are employed. The problem with the extensive literature on sequential/adaptive designs is that to my knowledge (almost) all references deal with ‘classical’ significance testing. See the introductory section of Potvin et al. (2008)¹ and a general overview in Gould (1995).² If a method based on the wrong hypotheses is used, patient's risk may be inflated (i.e., to an unknown degree higher than 5 %). None of the ‘classical’ approaches are validated for cross-over studies and the formulation of the test problem in bioequivalence (inclusion rule or two one-sided t-tests).
Don’t get me wrong, of course it’s possible to push the button to run a macro in SAS – but IMHO up to now no method is published showing no inflation of the alpha-risk in an sequential/adaptive replicate design study. BTW, such a simulation study would have to be extremely large: whereas the conventional 2×2 crossover assumes a common variance, setting up a simulation for different variances of test and reference would be challenging at least.

1. Potvin D, Diliberti CE, Hauck WW, Parr AF, Schuirmann DJ, and RA Smith
   Sequential design approaches for bioequivalence studies with crossover designs
   Pharmaceut. Statist. 7/4, 245–62 (2008), DOI: 10.1002/pst.294
   Online abstract
   
2. LA Gould
   Group Sequential Extension of a Standard Bioequivalence Testing Procedure
   J Pharmacokinet Biopharm 23(1), 57–86 (1995)
   Online abstract