本书目录如下： 1 Introduction 1 1.1 Repeated Measurements . . . . . . . . . . . . . . 1 1.2 Advantages and Disadvantages of Repeated Measurements Designs 2 1.3 Notation for Repeated Measurements . . . . . . . . . . .. 3 1.4 Missing Data . . . . . . . . . . . . . . . . . .. 4 1.5 Sample Size Estimation . . . . . . . . . . . . . 8 1.6 Outline of Topics . . . . . . .. . . . . . . . 9 1.7 Choosing the “Best” Method of Analysis . . . . . . . . . 12 2 Univariate Methods 15 2.1 Introduction . . . . . . . . . .. . .15 2.2 One Sample . . . . . .. . . . . . . .16 2.3 Multiple Samples . . . . .. . . . . 21 2.4 Comments . . . . . . . .. . . . . . . .26 2.5 Problems . . . . . . . . . . . . . . .28 3 Normal-Theory Methods: Unstructured Multivariate Approach 45 3.1 Introduction . . . . . . . . . 45 3.2 Multivariate Normal Distribution Theory . . . . . . . 46 3.2.1 The Multivariate Normal Distribution . . .. . . . .. 46 3.2.2 The Wishart Distribution . . . .. . . . . .. 46 3.2.3 Wishart Matrices . . . . . . . . 47 3.2.4 Hotelling’s T2 Statistic . . . . . .. 47 3.2.5 Hypothesis Tests . . . . . . . .. 48 3.3 One-Sample Repeated Measurements . . . . . .49 3.3.1 Methodology . . . .. . . . . . . . .. 49 3.3.2 Examples . . . . . . . . . . . . . 50 3.3.3 Comments . . . . . . . . . . . . .. 54 3.4 Two-Sample Repeated Measurements . . .. . . . . 55 3.4.1 Methodology . . . . . . . . . . . 55 3.4.2 Example . . . . . . . . . . . . . . 57 3.4.3 Comments . . . . . . . . . . . . .. 60 3.5 Problems . . . . . . . . . . 61 4 Normal-Theory Methods: Multivariate Analysis of Variance 73 4.1 Introduction . . . . . . . . 73 4.2 The Multivariate General Linear Model . . . . . 74 4.2.1 Notation and Assumptions . . . . .74 4.2.2 Parameter Estimation . . . . . . . . . . . 75 4.2.3 Hypothesis Testing . . . . . . . . 76 4.2.4 Comparisons of Test Statistics . . .. . . . . . . 77 4.3 Pro.le Analysis . . . . . . . . . . . . 78 4.3.1 Methodology . . . . . . . . . . 78 4.3.2 Example . . . . . . . . . . . . . . . . . 81 4.4 Growth Curve Analysis . . . . . . . . . . . 83 4.4.1 Introduction . . . . . . . . . . . . 83 4.4.2 The Growth Curve Model . . . . . . . 83 4.4.3 Examples . . .. . . . . . . . . . . . 87 4.5 Problems . . . . . .. . . . . 94 5 Normal-Theory Methods: Repeated Measures ANOVA 103 5.1 Introduction . . . . . .. . . . . . . 103 5.2 The Fundamental Model . . . . . . . . . . 104 5.3 One Sample . . . .. . . . . . . . . .106 5.3.1 Repeated Measures ANOVA Model . . . . . . . . . 106 5.3.2 Sphericity Condition . . . . . . . . . . 109 5.3.3 Example . . . . . . . . . . . . . 111 5.4 Multiple Samples . . . . . . . . . . . . 112 5.4.1 Repeated Measures ANOVA Model . . . . . . . . . . 112 5.4.2 Example . . . . . . . . . . . . . . . .115 5.5 Problems . . . . . .. . . . . . . . . . . .116 6 Normal-Theory Methods: Linear Mixed Models 125 6.1 Introduction . . . . . . . . . . . . .125 6.2 The Linear Mixed Model . . . . . . . . . . 126 6.2.1 The Usual Linear Model . . . . . . . . . .126 6.2.2 The Mixed Model . . . . . . . . .. . . . . 126 6.2.3 Parameter Estimation . . . . .. . . . . .127 6.2.4 Background on REML Estimation . . . . .. . . .128 6.3 Application to Repeated Measurements . . . . . 130 6.4 Examples . .. . . . . . .134 6.4.1 Two Groups, Four Time Points, No Missing Data . . . . 134 6.4.2 Three Groups, 24 Time Points, No Missing Data . . . . 139 6.4.3 Four Groups, Unequally Spaced Repeated Measurements, Time-Dependent Covariate . .. 145 6.5 Comments . . . . . . . . .. 149 6.5.1 Use of the Random Intercept and Slope Model . . . . . .. 149 6.5.2 E.ects of Choice of Covariance Structure on Estimates and Tests151 6.5.3 Performance of Linear Mixed Model Test Statisticsand Estimators155 6.6 Problems . . . . . . . .156 7 Weighted Least Squares Analysis of Repeated Categorical Outcomes169 7.1 Introduction . . . . . . . . 169 7.2 Background . . . . . . . . . 170 7.2.1 The Multinomial Distribution . . . .. . . . 170 7.2.2 Linear Models Using Weighted Least Squares . . . . . .171 7.2.3 Analysis of Categorical Data Using Weighted Least Squares . . . . .175 7.2.4 Taylor Series Variance Approximations for Nonlinear Response Functions . 178 7.3 Application to Repeated Measurements . . . . . . 184 7.3.1 Overview . . . . . . . . . 184 7.3.2 One Population, Dichotomous Response, Repeated Measurements Factor Is Unordered 184 7.3.3 One Population, Dichotomous Response, Repeated Measurements Factor Is Ordered. 187 7.3.4 One Population, Polytomous Response . . . . . . . . 191 7.3.5 Multiple Populations, Dichotomous Response . . . . 196 7.4 Accommodation of Missing Data . . . . . . . . . . . . . . . 204 7.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . 204 7.4.2 Ratio Estimation for Proportions . . . . . . . . . . . 204 7.4.3 One Population, Dichotomous Response . . . . . . . 205 7.4.4 Multiple Populations, Dichotomous Response . . . . 209 7.4.5 Assessing the Missing-Data Mechanism . . . . . . . 214 7.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 8 Randomization Model Methods for One-Sample Repeated Measurements 239 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 8.2 The Hypergeometric Distribution and Large-Sample Tests of Randomness for 2 × 2 Tables 240 8.2.1 The Hypergeometric Distribution . . . . . . . . . . . 240 8.2.2 Test of Randomness for a 2 × 2 Contingency Table . 241 8.2.3 Test of Randomness for s 2 × 2 Contingency Tables 242 8.3 Application to Repeated Measurements: Binary Response, Two Time Points .. . . 244 8.4 The Multiple Hypergeometric Distribution and Large-Sample Tests of Randomness for r × c Tables . . . . . . . . 246 8.4.1 The Multiple Hypergeometric Distribution . . . . . 247 8.4.2 Test of Randomness for an r × c Contingency Table 248 8.4.3 Test of Randomness for s r × c Tables . . . . . . . . 249 8.4.4 Cochran–Mantel–Haenszel Mean Score Statistic . . . 251 8.4.5 Cochran–Mantel–Haenszel Correlation Statistic . . . 253 8.5 Application to Repeated Measurements: Polytomous Response, Multiple Time Points . 253 8.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 253 8.5.2 The General Association Statistic QG . . . . . . . . 255 8.5.3 The Mean Score Statistic QM and the Correlation Statistic QC . 255 8.6 Accommodation of Missing Data . . . . . . . . . . . . . . . 258 8.6.1 General Association Statistic QG . . . . . . . . . . . 258 8.6.2 Mean Score Statistic QM . . . . . . . . . . . . . . . 260 8.6.3 Correlation Statistic 8.7 Use of Mean Score and Correlation Statistics for Continuous Data263 8.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 9 Methods Based on Extensions of Generalized Linear Models 273 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 9.2 Univariate Generalized Linear Models . . . . . . . . . . . . 274 9.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 274 9.2.2 Random Component . . . . . . . . . . . . . . . . . . 275 9.2.3 Systematic Component . . . . . . . . . . . . . . . . 279 9.2.4 Link Function . . . . . . . . . . . . . . . . . . . . . . 279 9.2.5 Canonical Links . . . . . . . . . . . . . . . . . . . . 279 9.2.6 Parameter Estimation . . . . . . . . . . . . . . . . . 281 9.3 Quasilikelihood . . . . . . . . . . . . . . . . . . . . . . . . . 286 9.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 286 9.3.2 Construction of a Quasilikelihood Function . . . . . 287 9.3.3 Quasilikelihood Estimating Equations . . . . . . . . 289 9.3.4 Comparison Between Quasilikelihood and Generalized Linear Models 291 9.4 Overview of Methods for the Analysis of Repeated Measurements .. . . 291 9.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 291 9.4.2 Marginal Models . . . . . . . . . . . . . . . . . . . . 292 9.4.3 Random-E.ects Models . . . . . . . . . . . . . . . . 293 9.4.4 Transition Models . . . . . . . . . . . . . . . . . . . 293 9.4.5 Comparisons of the Three Approaches . . . . . . . . 294 9.5 The GEE Method . . . . . . . . . . . . . . . . . . . . . . . 295 9.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 295 9.5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . 296 9.5.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . 301 9.5.4 Hypothesis Tests Using Wald Statistics . . . . . . . 308 9.5.5 Assessing Model Adequacy . . . . . . . . . . . . . . 309 9.5.6 Sample Size Estimation . . . . . . . . . . . . . . . . 310 9.5.7 Studies of the Properties of GEE . . . . . . . . . . . 311 9.5.8 Computer Software . . . . . . . . . . . . . . . . . . . 312 9.5.9 Cautions Concerning the Use of GEE . . . . . . . . 313 9.6 Subsequent Developments . . . . . . . . . . . . . . . . . . . 314 9.6.1 Alternative Procedures for Estimation of GEE Association Parameters 314 9.6.2 Other Developments and Extensions . . . . . . . . . 316 9.6.3 GEE1 and GEE2 . . . . . . . . . . . . . . . . . . . . 316 9.6.4 Extended Generalized Estimating Equations (EGEE) 317 9.6.5 Likelihood-Based Approaches . . . . . . . . . . . . . 318 9.7 Random-E.ects Models . . . . . . . . . . . . . . . . . . . . 318 9.8 Methods for the Analysis of Ordered Categorical Repeated Measurements 320 9.8.1 Introduction . . . . . . . . . . 320 9.8.2 Univariate Cumulative Logit Models for Ordered Categorical Outcomes 321 9.8.3 The Univariate Proportional-Odds Model . . . . . . . . . . . . . 322 9.8.4 The Stram–Wei–Ware Methodology for the Analysis of Ordered Categorical Repeated Measurements . . . . . . . . . . . . . 324 9.8.5 Extension of GEE to Ordered Categorical Outcomes . . . . 331 9.9 Problems . . . . . . . . . . . . .. . . . . 332 10 Nonparametric Methods 347 10.1 Introduction . . . . . . . . . . . . 347 10.2 Overview . . . . . . . . . . . . . .. 348 10.3 Multivariate One-Sample and Multisample Tests for Complete Data .. 350 10.3.1 One Sample . . . . . . . . . . .. 350 10.3.2 Multiple Samples . . . . . . . . . . 350 10.4 Two-Sample Tests for Incomplete Data . . . . . 355 10.4.1 Introduction . . . . . . . .355 10.4.2 The Wei–Lachin Method . . . . . .355 10.4.3 The Wei–Johnson Method . . . . 356 10.4.4 Examples . . . . . . . .. . . . . . . . . ..362 10.5 Problems . . . . . . . . . . . . . . . . . 364 Bibliography 373 Author Index 405 Subject Index 412 |