Repeated Measurements and Cross-Over Designs

DAMARAJU RAGHAVARAO, PhD, was Laura H. Carnell Professor and Chairperson in the Department of Statistics at Temple University. With more than fifty years of research experience in all aspects of experimental design, sampling, and multivariate analysis, Dr. Raghavarao authored eight additional books and over 135 journal articles throughout his career.LAKSHMI PADGETT, PhD, is Senior Manager at Janssen R&D. Dr. Padgett has authored approximately twenty journal articles, and her research interests include phase I, II, and III trials.

• Preface xi1. Introduction 11.1 Introduction 11.2 One-Sample RMD 21.3 k-Sample RMD 41.4 Split-Plot Designs 71.5 Growth Curves 131.6 Cross-Over Designs 141.7 Two-Period Cross-Over Designs 181.8 Modifications in Cross-Over Designs 191.9 Nonparametric Methods 22References 232. One-Sample Repeated Measurement Designs 252.1 Introduction 252.2 Testing for Sphericity Condition 262.3 Univariate ANOVA for One-Sample RMD 292.4 Multivariate Methods for One-Sample RMD 322.5 Univariate ANOVA Under Nonsphericity Condition 342.6 Numerical Example 352.7 Concordance Correlation Coefficient 412.8 Multiresponse Concordance Correlation Coefficient 442.9 Repeated Measurements with Binary Response 47References 513. k-Sample Repeated Measurements Design 533.1 Introduction 533.2 Test for the Equality of Dispersion Matrices and Sphericity Condition of k-Dispersion Matrices 543.3 Univariate ANOVA for k-Sample RMD 573.4 Multivariate Methods for k-Sample RMD 603.5 Numerical Example 633.6 Multivariate Methods with Unequal Dispersion Matrices 673.7 Analysis with Ordered Categorical Response 72References 754. Growth Curve Models 774.1 Introduction 774.2 Sigmoidal Curves 784.3 Analysis of Mixed Models 844.4 Simple Linear Growth Curve Model 904.5 Nonlinear Growth Curve Model 924.6 Numerical Example 934.7 Joint Action Models 100References 1035. Cross-Over Designs without Residual Effects 1055.1 Introduction 1055.2 Fixed Effects Analysis of CODWOR 1075.3 Connectedness in CODWOR 1135.4 Orthogonality in CODWOR 1155.5 Latin Square Designs 1165.6 Youden Square Design and Generalization 1185.7 F-Squares 1235.8 Lattice Square Designs 1235.9 Analysis of CODWOR when the Units Effects Are Random 1255.10 Numerical Example 1275.11 Orthogonal Latin Squares 131References 1336. Cross-Over Designs with Residual Effects 1356.1 Introduction 1356.2 Analysis of CODWR 1366.3 BRED 1436.4 PBCOD(m) 1486.5 Numerical Example 1526.6 Analysis with Unit (or Subject) Effects Random 1566.7 Concluding Remarks 159References 1607. Two-Period Cross-Over Designs with Residual Effects 1637.1 Introduction 1637.2 Two-Period Two-Treatment CODWR Analysis: Parametric Methods 1647.2.1 Analysis of the design based on the model (7.2.9) 1677.2.2 Decomposition of the model (7.2.9) into intra- and interunit components 1697.2.3 Estimating direct effects contrast using cross-over nature of the treatments 1707.2.4 Modified two-period two-treatment design 1717.2.5 Cost analysis 1717.3 Two-Period Two-Treatment CODWR Analysis: Nonparametric Methods 1737.4 Two-Period t Treatment Cross-Over Design 1747.5 Numerical Examples 177References 1868. Other Cross-Over Designs with Residual Effects 1898.1 Introduction 1898.2 Extra-Period Designs 1918.2.1 Residual effect of a treatment effect on itself is the same as residual effect on other treatments 1928.2.2 Residual effect of a treatment on itself is different from the residual effect on other treatments 1938.3 Residual Effects Proportional to Direct Effects 1948.4 Undiminished Residual Effects Designs 1958.5 Treatment Balanced Residual Effects Designs 1978.6 A General Linear Model for CODWR 1998.7 Nested Design 2018.8 Split-Plot Type CODWR 2038.9 CODWR in Circular Arrangement 2058.10 Numerical Examples 207References 2139. Some Constructions of Cross-Over Designs 2159.1 Introduction 2159.2 Galois Fields 2159.3 Generalized Youden Designs 2179.4 Williams’ Balanced Residual Effects Designs 2219.5 Other Balanced Residual Effects Designs 2269.6 Combinatorially Overall Balanced Residual Effects Designs 2299.7 Construction of Treatment Balanced Residual Effects Designs 2319.8 Some Construction of PBCOD (m) 2329.9 Construction of Complete Set of MOLS and Patterson’s BRED 2349.10 Balanced Circular Arrangements 2359.11 Concluding Remarks 236References 237Index 245