The statistical design and analysis of experiments and combinatorial design

该提案由一系列相互关联的研究组成，这些研究可能在临床试验、制造业和农业中应用，旨在验证申请人杰出研究生涯中最有前途的统计调查“未解决的问题”。 重点是对实验设计的统计研究，特别是但不完全涉及比较中的处理具有相对复杂结构的情况。要研究的问题是：(I)一种特殊类型的设计，即不完全析因设计，用于医学临床试验，其预后因素来自于患者进入试验时的情况。此外，还将考虑“加权”因素，以便将因素的极端组合包括在内，从而使设计被判定为“合乎道德的”；(Ii)扩展到一种称为格子正方形设计的特定类型的设计，主要用于医疗应用及其与两阶段设计的联系。此外，格子正方形设计在工业中可能是自然的，用于研究制造过程中产品的可靠性。重点是提供设计或数据收集指导，以平衡协变量效应的最优估计和足够的统计能力，以检测不同处理效果之间的差异(如果存在)；(Iii)不完全区组设计与图表数学理论之间的关系的确定，这将增加对设计的稳健性程度的洞察，即，当一些观测缺失或虚假时，可以得出什么结论；以及(Iv)最近邻设计(配置)与广义数独平方的关系，该关系也提供了数据压缩的可能性。在9x9数独平方中，只有17个数字产生一个由81个数字组成的唯一平方。实际应用可能包括数据压缩或加密。尽管数独游戏最初是作为一种娱乐形式开发的，但它可能会揭示一些实验问题的统计设计，本身就是一个有趣的变体。

The proposal consists of a range of interrelated studies having potential applications in clinical trials, the manufacturing industry and agriculture, and aims to validate the most promising "loose ends" of statistical investigation in the applicant's distinguished research career. The focus is the statistical study of the design of experiments dealing especially but not exclusively with situations in which the treatments under comparison have a relatively complex structure. The issues to be studied are: (i) a special type of design, an incomplete factorial design, to be used in clinical trials in medicine with prognostic factors derived from the condition of the patient at entry to the trial. Also "weighted" factors will be considered in order for extreme combinations of factors to be included, thus permitting the designs to be judged to be "ethical"; (ii) extensions to a particular type of design called a plaid-square design, for use chiefly in medical applications and their link to two-phase designs. In addition, the plaid-square designs may be natural in industry for studies on reliability of products in manufacturing processes. The important point is to provide design or data-collection guidance which balances optimal estimation of covariate effects with sufficient statistical power to detect differences between various treatment effects if they were present; (iii) the determination of relationships between incomplete block designs and the mathematical theory of graphs which will add insight into the degree of robustness of a design, i.e. what conclusions can be made when some observations are missing or spurious; and (iv) the relationship of nearest-neighbour designs (configurations) and the generalized Sudoku square giving the possibility also of data compression. In the 9x9 Sudoku square, only seventeen numbers produce a unique square of 81 numbers. Practical applications might include data compression or encryption. Although the Sudoku puzzle was originally developed as a form of entertainment, it may shed light on some statistical design of experiment problems and be of itself an intriguing variation.