Bioequivalence and Bioavailability Forum

Dear ioanam!

❝ Would you like to explain the design of an 'incomplete 3 x 3 cross over design'?

This is not a design, but a statement about the data.
‘Incomplete’ means that subject(s) dropped out from a ‘3×3 cross-over’ study and/or periods were missing.

Here is the only reference I could find for an evaluation; you may contact the authors for details (which probably were published previously: N Lim & S Park; Assessing Bioequivalence in 3×3 Cross-over Design with Unbalanced Data, The Korean Communications in Statistics 14/2, 345-356, 2001).

It’s possible to recover some information by applying a mixed effects model (instead of fixed). Unfortunatelly this is not possible in some pieces of commercial PK software (e.g., Kinetica); if you can’t afford SAS, you may opt for Pineirho/Bates’ package nlme for R.

Quoting Senn (2002)*

As far as is possible I go for the maximum incorporation of data into the analysis. If a patient drops out I always use data from the periods which he did complete.
In practice, of course, if a fixed effect model is used, then a patient cannot contribute information regarding treatment unless he received at least two treatments and in any case he can hardly contribute much information except indirectly (in an analogous manner to incomplete blocks) regarding any given treatment contrast unless he received both treatments represented in the contrast. There is no practical difficulty, however, in incorporating such patients into an analysis using proc glm of SAS^®. The analysis is carried out in the ordinary way and the program will extract what information is to be extracted under the fixed effects model using ordinary least squares. If a random effects model is used the some further information is recoverable […]. Usually the amount of information is extremely small. In the context of drug development, however, it will be important to specify beforehand which approach (fixed or random) will be used.

Please note that a 3×3 (Latin Square) design is an inappropriate design anyway; a 6×3 Williams’ design is strongly recommended (otherwise even for a complete data set pairwise comparisons will be inbalanced).

---

• S Senn
  Drop-outs, protocol violations and missing observations
  In: S Senn, Cross-over Trials in Clinical Research
  John Wiley & Sons, Chichester, pp 286–7 (2002)