Prescott P
Department of Mathematics, Southampton University, U.K.
Stat Med. 1999 Feb 15;18(3):265-72. doi: 10.1002/(sici)1097-0258(19990215)18:3<265::aid-sim13>3.0.co;2-q.
Cross-over designs balanced for simple carry-over effects are commonly applied in clinical studies for the comparison of treatments for chronic conditions such as hypertension or asthma. Uniform-balanced cross-over designs have the desirable property that the treatment sequences are arranged so that, in the full design, each treatment is followed by every other treatment equally often. Such designs for an even number of treatments and the same number of sequences and periods are readily constructed using suitable cyclic Latin squares. For an odd number of treatments, pairs of squares may be combined to give uniform-balanced designs. Recently, computer search techniques have been used to find nearly-balanced Latin squares which may be combined in pairs or in sets of three to produce designs with the overall properties of uniformity and balance. In this paper, simple generating formulae are described which will give, for any odd number of treatments t > 3, uniform-balanced cross-over designs with p = t periods and n = kt treatment sequences for any k > or = 2. Tables of cross-over designs obtained from these simple formulae are presented for t < or = 15.
针对简单延滞效应进行平衡的交叉设计常用于临床研究，以比较高血压或哮喘等慢性病的治疗方法。均匀平衡交叉设计具有这样的理想特性：治疗序列的安排使得在完整设计中，每种治疗后面跟着其他每种治疗的次数相同。对于偶数种治疗以及相同数量的序列和周期，使用合适的循环拉丁方很容易构建这样的设计。对于奇数种治疗，可以将成对的方阵组合起来得到均匀平衡设计。最近，计算机搜索技术已被用于寻找近似平衡的拉丁方，这些拉丁方可以成对或三个一组进行组合，以产生具有均匀性和平衡性总体特性的设计。本文描述了简单的生成公式，对于任何大于3的奇数种治疗t，该公式将给出具有p = t个周期和n = kt个治疗序列的均匀平衡交叉设计，其中k≥2。给出了t≤15时根据这些简单公式得到的交叉设计表。
