Bioequivalence and Bioavailability Forum

Hi Shuanghe,

BEQool is right.

There is indeed a “ranking” in the sense that only certain sequences truly satisfy the balance criteria for a Williams design. In a four‐treatment crossover, there are exactly six acceptable Williams designs that guarantee each treatment immediately follows every other treatment exactly once. Your design Y is one of those six, whereas design X is not. Take a look at the excellent article prepared by Helmut regarding Higher-Order Crossover Designs, especially at Acknowledgment section 

Design Y is generally considered superior to Design X when the primary concern is the first-order carryover effect (the direct influence of one treatment on the immediately following treatment). Design Y ensures that every treatment follows every other treatment exactly once. This provides the most balanced estimate of first-order carryover effects. It allows you to estimate the direct carryover effect of A on B, B on A, A on C, C on A, etc., with equal precision.