Statistical methods for two-sequence three-period cross-over designs with incomplete data.

In clinical trials, and in bioavailability and bioequivalence studies, one often encounters replicate cross-over designs such as a two-sequence three-period cross-over design to assess treatment and carry-over effects of two formulations of a drug product. Because of the potential dropout (or for some administrative reason), however, the observed data set from a replicate cross-over design is incomplete or unbalanced so that standard statistical methods for a cross-over design may not apply directly. For inference on the treatment and carry-over effects, we propose a method based on differences of the observations that eliminates the random subject effects and thus does not require any distributional condition on the random subject effects. When no datum is missing, this method provides the same results as the ordinary least squares method. When there are missing data, the proposed method still provides exact confidence intervals for the treatment and carry-over effects, as long as the dropout is independent of the measurement errors. We provide an example for illustration.