Optimal and/or Efficient Cross-Over Designs Balanced for Carry-Over of Active Treatments

The experimenters have limited flexibility as far as the number of experimental units are concerned; this could be unsuitable in bioavailability/bioequivalence study. In cross-over design literature, most of the designs require an even number of subjects, few of them are available for 3, 9 or 15 subjects, but designs are not available for number of subjects like 5, 7, 11. A new class called active balanced cross-over designs is defined and constructed for carry-over models through a 5M active balanced computer search algorithm for addressing this gap in literature. The newly generated cross-over designs are more variance efficient under self and mixed carry-over model than the two treatments three periods cross-over designs. Many cross-over designs, which have been unavailable so far, are obtained for five carry-over models in this paper. A new optimal cross-over design in the class of balanced two treatments three periods cross-over designs is also generated. An exhaustive list of optimal and/or efficient cross-over designs have been provided for designs in 4 to 13 experimental units. In this list, 10 new included designs are optimal for one of the carry-over models and 7 new included designs are optimal and/or efficient when fitting to all four plausible carry-over models.