Balanced designs for multiple crossover studies.

Experimental situations are considered, in which t different treatments are administered to n cases (volunteers, patients, animals etc.) during p periods (p less than or equal to t) in a way that each of these cases receives p different treatments in sequence (crossover designs). In order to minimize the influence of carry-over effects the designs of the trials are constructed with regard to three conditions of balance: (a) Each case receives the same number of treatments, (b) each treatment is applied the same number of times in each period, and (c) each possible transition between two consecutive periods appears the same number of times during the experiment. The minimal numbers of cases are given for complete (p = t) and incomplete (p less than t) designs balanced according to all the above mentioned conditions. Furthermore, the designs themselves (plans of the experiments) are also listed for the minimal number of cases for 2 less than or equal to p less than or equal to t less than or equal to 10.