Table of Contents
Preface iii
Chapter 1 Introduction to the Analysis of Cross-over Designs: Basic Principles and Some Useful Tools 1
1.1 A general method for coding treatment and carryover effects 1
1.1.1 Coding method illustrated using the data step of SAS 4
1.1.2 Coding using matrix operations 11
1.2 An omnibus test of the separability of treatment and carryover effects 16
1.3 Consequences of poor separability of treatment and carryover effects 31
1.4 Considering period effects as continuous, rather than categorical, variables 34
1.5 Testing whether effects are estimable in cross-over designs 37
1.6 Testing whether the residuals are normally distributed 41
Exercises 45
Chapter 2 Latin Square Designs 55
2.1 Optimum designs for separating treatment and carryover effects 55
2.2 Estimating period effects in digram-balanced Latin square designs 63
2.3 Analyzing Latin square designs not balanced for estimation of carryover effects 68
2.4 Mutually orthogonal Latin squares versus digram-balanced Latin squares 72
Exercises 74
Chapter 3 The 2-Treatment, 2-Period, 2-Sequence Design 77
3.1 The basic layout of the 2 x 2 cross-over trial 78
3.2 Tests of significance in the 2 x 2 cross-over design 88
3.3 An example of data analysis in the 2 x 2 cross-over design 92
3.4 Adding baseline measurements to the 2 x 2 cross-over design 96
3.5 Adding baseline and wash-out measurements to the 2 x 2 cross-over design 101
3.6 Adding baseline and two wash-out measurements to the 2 x 2 cross-over design 109
3.7 Recommendations about the use of the 2 x 2 cross-over design 116
Exercises 118
Chapter 4 Modifications of the 2-Treatment, 2-Period, 2-Sequence Design 121
4.1 Designs with two sequences and three periods 122
4.2 Designs with four sequences and two periods 133
4.3 Designs with four sequences and three periods 143
4.4 Other designs with more than two periods and/or two sequences 148
4.5 Recommendations about the use of the designs in this chapter 158
Exercises 159
Chapter 5 Cross-over Designs With Variance Balance 163
5.1 The variance-balanced cross-over designs of Patterson and Lucas 163
5.2 Analysis of balanced designs of Patterson and Lucas 167
5.3 The designs of Quenouille, Berenblut and Patterson 170
5.4 The designs of Balaam 171
5.5 Improving the efficiencies of two-period designs 177
5.6 The efficiency of an extra-period design versus a complete Latin square 181
Exercises 182
Appendix 5.A Index to balanced cross-over designs 185
Appendix 5.B Designs PL 1-29. Balanced designs with t = k 188
Appendix 5.C Designs PL 30-54. Extra-period balanced designs with t = k 197
Appendix 5.D Designs PL 55-75. Balanced designs with t > k 206
Appendix 5.E Designs PL 76-93. Extra-period balanced designs with t > k 214
Appendix 5.F Designs PL 94-98. Extra-period balanced designs with k = 2 221
Appendix 5.G Designs QBP 1-4. Quenouille-Berenblut-Patterson designs for 3 ≤ t ≤ 6 223
Chapter 6 Cross-over Designs Lacking Variance Balance 227
6.1 The partially-balanced cross-over designs of Patterson and Lucas 227
6.2 Analysis of partially-balanced designs of Patterson and Lucas 230
6.3 The designs of Davis and Hall 233
6.4 The designs of Federer and Atkinson 237
Exercises 243
Appendix 6.A Index to partially-balanced cross-over designs of Patterson and Lucas 244
Appendix 6.B Designs PL 99-124. Partially-balanced designs based on Bose et al. 246
Appendix 6.C Designs PL 125-130. Additional partially-balanced cross-over designs 261
Appendix 6.D Designs PL 131-152. Extra-period partially-balanced cross-over designs 264
Appendix 6.E Designs PL 153-160. Extra-period partially-balanced designs with k = 2 274
Appendix 6.F Designs DH 1-45. Cyclic change-over designs of Davis and Hall 278
Appendix 6.G Designs FA 1-2. Tied-double-change-over designs of Federer and Atkinson 290
Chapter 7 The Analysis of Categorical Data from Cross-over Designs 291
7.1 The 2-treatment, 2-period, 2-sequence binary cross-over design 293
7.2 The logit model for binary data 297
7.3 Hypothesis testing 305
7.4 Parameter estimation using SAS PROC CATMOD 308
7.5 The 2-treatment, 3-period, 2-sequenee binary cross-over design 316
7.6 The general model for cross-over designs having a multilevel categorical response 325
7.7 Recommendations about the techniques and designs in this chapter 343
Exercises 344
Appendix 7.A Methods for computing maximum likelihood estimates 347
Appendix 7.B Covariance matrix estimation 351
Chapter 8 Ordinary Least Squares Estimation Versus Other Criteria of Estimation: Justification for Using the Methodology Presented in This Book 353
8.1 The assumptions underlying OLS 353
8.2 Examining the various covariance structures 357
8.3 Consequences of using different covariance structures 366
8.4 Other methods of analysis 375
8.5 A time series approach to the correlation structure 382
Exercises 392
Appendix 8.A Formal test for uniform covariance structure 392
Appendix 8.B Formal test for Huynh-Feldt Type H structure 394
Chapter 9 Other Topics in Cross-over Designs 397
9.1 The Bayesian analysis of cross-over designs 397
9.2 Repeated measurements within a cross-over design 400
9.3 Optimality in cross-over experimental design 406
9.4 Missing values in cross-over designs 411
9.5 Summary and conclusions 415
Exercises 418
References 419
Solutions 425
Author Index 439
Subject Index 443
