The Construction of a Williams Design and Randomization in Cross-Over Clinical Trials Using SAS

Bing-Shun Wang, Xiao-Jin Wang, Li-Kun Gong

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A Williams design is a special and useful type of cross-over design. Balance is achieved by using only one particular Latin square if there are even numbers of treatments, and by using only two appropriate squares if there are odd numbers of treatments. PROC PLAN of SAS/STAT is a practical tool, not only for random construction of the Williams square, but also for randomly assigning treatment sequences to the subjects, which makes integration of the two procedures possible. The present paper provides a general SAS program for the random construction of a Williams design and the relevant procedure for randomization. Examples of a three-treatment, three-period (3 x 3) and a four-treatment, four-period (4 x 4) cross-over designs are given to illustrate the function of the SAS program. The results can be regenerated and replicated with the same random number seed. The general SAS program meets the practical needs of researchers in the application of Williams designs.

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