Locally balanced change-over designs

Abstract

Change-over designs are constructed which are balanced in conventional senses but have local balance too. Each design has an odd number n of treatments which are administered successively, over n successive periods, to each member of a set of n(n - 1) patients. The patients are grouped into (n - 1)/2 non-overlapping groups of 2n patients so that, for each i ≠ j, exactly two patients per group receive treatment T_i immediately after treatment T_j. Throughout periods 1 to (n + 1)/2, each group has exactly one patient receiving T_i immediately after T_j. In any two consecutive periods, exactly one patient receives T_i preceded by T_j. In the first (n ± 1)/2 periods, the sets of treatments received by the patients constitute the blocks of a balanced incomplete block design with (v, k, λ) = (n, (n ± 1)/2, (n ± 1)(n - 2 ± 1)/4). Published work of E.J. Williams, B.A. Anderson, P.J. Owens and R.A. Bailey is used to produce designs for prime values of n and for n = 9.