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
QC . . . . . . . . . . . . . . . . 262
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
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