Optimal crossover designs

This monograph presents a comprehensive and up-to-date account of the developments in optimality aspects of crossover designs. Crossover designs are immensely useful in various areas of human investigation including agriculture, animal nutrition, clinical trials, pharmaceutical studies, biological assays, weather modification experiments, sensory evaluation of food products and learning experiments. Research on the optimality aspects of crossover designs has developed only in the last three decades, and it has now emerged as a potential field for further investigation. This book is the first comprehensive treatise on this subject. It covers optimal crossover designs at length by consolidating vast amounts of material from the literature, and includes many recent and deep results. It is expected that this book will not only provide a one-stop reference for the available results, but also encourage further research in this area of substantial practical relevance. Contents......Page 8 Preface......Page 12 1.1 Prologue......Page 14 1.2 Notation, Terminology and Models......Page 21 1.3 Information Matrices......Page 25 1.4 Optimality Criteria and Tools......Page 31 1.5 Outline of the Book......Page 36 2.1 Introduction......Page 38 2.2 Definitions and Some Basic Results......Page 39 2.3 Optimality of Balanced Uniform Designs......Page 44 2.4 Optimality of Strongly Balanced Designs......Page 54 2.5 Some More Optimal Designs......Page 56 2.6 Constructions......Page 62 3.1 Introduction......Page 72 3.2 Designs with p t......Page 73 3.3 Two-period Designs......Page 82 3.4 Optimality of Patterson Designs......Page 89 3.5 Constructions......Page 97 4.1 Introduction......Page 104 4.2 Notation and Information matrices......Page 106 4.3 Quadratic Function for Direct Effects Associated with a Sequence......Page 110 4.4 Determining a, b and S......Page 113 4.5 Optimality Equations......Page 117 4.6 Optimal Symmetric Designs for Direct Effects......Page 119 4.7 Optimal Designs for Carryover Effects......Page 123 4.8 Design Efficiency......Page 127 5.1 Introduction......Page 130 5.2 A Model with Self and Mixed Carryover Effects......Page 131 5.3 A Model with Carryover Effects Proportional to Direct Effects and Optimal Designs......Page 144 6.1 Introduction......Page 160 6.2 Correspondence with a Factorial Experiment......Page 162 6.3 Optimality Results......Page 165 6.4 Optimality Under a Non-additive Random Subject Effects Model......Page 172 6.5 Optimality in the Presence of Higher Order Carryover Effects and Interaction......Page 175 7.1 Introduction......Page 180 7.2 Optimal Two-treatment Designs......Page 181 7.2.1 Optimal Designs under Uncorrelated Errors......Page 182 7.2.2 Optimal Designs under Correlated Errors......Page 183 7.2.3 Optimal Designs under Autoregressive Errors......Page 185 7.3 Optimal Designs under Correlated Errors for an Arbitrary Number of Treatments......Page 191 7.4 Optimal Designs for Test-Control Comparisons......Page 195 7.4.1 Optimal Designs with p > t + 1......Page 198 7.4.2 Optimal Designs with p = 2......Page 201 7.4.3 Optimal Designs with 3 p t +1......Page 202 7.5 Optimal Designs with Subject Dropout......Page 212 7.6 Some Additional Comments......Page 217 References......Page 222 Index......Page 236 1. Introduction. 1.1. Prologue. 1.2. Notation, terminology and models. 1.3. Information matrices. 1.4. Optimality criteria and tools. 1.5. Outline of the book -- 2. Optimality of balanced and strongly balanced designs. 2.1. Introduction. 2.2. Definitions and some basic results. 2.3. Optimality of balanced uniform designs. 2.4. Optimality of strongly balanced designs. 2.5. Some more optimal designs. 2.6. Constructions -- 3. Some optimal designs with p