Statistical methods for the analysis of repeated measurements

Title:

Personal Author:

Davis, Charles S. (Charles Shaw), 1952-

Series:

Springer texts in statistics

Publication Information:

New York, NY : Springer, 2002

ISBN:

9780387953700

Subject Term:

Multivariate analysis

Experimental design

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000004598144	QA278 D38 2002	Open Access Book	Book	Searching... Unknown

I have endeavored to provide a comprehensive introduction to a wide - riety of statistical methods for the analysis of repeated measurements. I envision this book primarily as a textbook, because the notes on which it is based have been used in a semester-length graduate course I have taught since1991.Thiscourseisprimarilytakenbygraduatestudentsinbiostat- tics and statistics, although students and faculty from other departments have audited the course. I also anticipate that the book will be a useful r- erence for practicing statisticians. This assessment is based on the positive responses I have received to numerous short courses I have taught on this topic to academic and industry groups. Althoughmyintentistoprovideareasonablycomprehensiveoverviewof methodsfortheanalysisofrepeatedmeasurements,Idonotviewthisbook as a de?nitive "state of the art" compendium of research in this area. Some general approaches are extremely active areas of current research, and it is not feasible, given the goals of this book, to include a comprehensive summary and list of references. Instead, my focus is primarily on methods that are implemented in standard statistical software packages. As a result, thelevelofdetailonsometopicsislessthaninotherbooks,andsomemore recent methods of analysis are not included. One particular example is the topic of nonlinear mixed models for the analysis of repeated measurements (Davidian and Giltinan, 1995; Vonesh and Chinchilli, 1996). With respect to some of the more recent methods of analysis, I do attempt to mention some of the areas of current research.

Reviews 1

Choice Review

Davis's work is designed primarily as a resource for a one-semester graduate course and provides a comprehensive introduction to numerous statistical methods used in analyzing repeated measurements. Davis focuses on methods that are used in standard statistical software packages with orientation directed primarily toward statistical practitioners rather than statistical researchers. Numerous problems that concentrate on biomedical examples are included along with 80 real-data sets. Knowledge of such topics as categorical data analysis, generalized linear models, and multivariate normal distribution theory is necessary for proper understanding of the material. Additional prerequisites include mathematical statistics at the level of Robert V. Hogg and Allen T. Craig's Introduction to Mathematical Statistics (5th ed., 1995) and ANOVA and linear regression at the level of Applied Linear Statistical Analysis, John Neter et al. (2nd ed., 1985). Highly recommended for graduate students and professionals/practitioners. D. J. Gougeon University of Scranton

Preface p. v
1 Introduction	p. 1
1.1 Repeated Measurements	p. 1
1.2 Advantages and Disadvantages of Repeated Measurements Designs	p. 2
1.3 Notation for Repeated Measurements	p. 3
1.4 Missing Data	p. 4
1.5 Sample Size Estimation	p. 8
1.6 Outline of Topics	p. 9
1.7 Choosing the ""Best"" Method of Analysis	p. 12
2 Univariate Methods	p. 15
2.1 Introduction	p. 15
2.2 One Sample	p. 16
2.3 Multiple Samples	p. 21
2.4 Comments	p. 26
2.5 Problems	p. 28
3 Normal-Theory Methods: Unstructured Multivariate Approach	p. 45
3.1 Introduction	p. 45
3.2 Multivariate Normal Distribution Theory	p. 46
3.2.1 The Multivariate Normal Distribution	p. 46
3.2.2 The Wishart Distribution	p. 46
3.2.3 Wishart Matrices	p. 47
3.2.4 Hotelling's T 2 Statistic	p. 47
3.2.5 Hypothesis Tests	p. 48
3.3 One-Sample Repeated Measurements	p. 49
3.3.1 Methodology	p. 49
3.3.2 Examples	p. 50
3.3.3 Comments	p. 54
3.4 Two-Sample Repeated Measurements	p. 55
3.4.1 Methodology	p. 55
3.4.2 Example	p. 57
3.4.3 Comments	p. 60
3.5 Problems	p. 61
4 Normal-Theory Methods: Multivariate Analysis of Variance	p. 73
4.1 Introduction	p. 73
4.2 The Multivariate General Linear Model	p. 74
4.2.1 Notation and Assumptions	p. 74
4.2.2 Parameter Estimation	p. 75
4.2.3 Hypothesis Testing	p. 76
4.2.4 Comparisons of Test Statistics	p. 77
4.3 Profile Analysis	p. 78
4.3.1 Methodology	p. 78
4.3.2 Example	p. 81
4.4 Growth Curve Analysis	p. 83
4.4.1 Introduction	p. 83
4.4.2 The Growth Curve Model	p. 83
4.4.3 Examples	p. 87
4.5 Problems	p. 94
5 Normal-Theory Methods: Repeated Measures ANOVA	p. 103
5.1 Introduction	p. 103
5.2 The Fundamental Model	p. 104
5.3 One Sample	p. 106
5.3.1 Repeated Measures ANOVA Model	p. 106
5.3.2 Sphericity Condition	p. 109
5.3.3 Example	p. 111
5.4 Multiple Samples	p. 112
5.4.1 Repeated Measures ANOVA Model	p. 112
5.4.2 Example	p. 115
5.5 Problems	p. 116
6 Normal-Theory Methods: Linear Mixed Models	p. 125
6.1 Introduction	p. 125
6.2 The Linear Mixed Model	p. 126
6.2.1 The Usual Linear Model	p. 126
6.2.2 The Mixed Model	p. 126
6.2.3 Parameter Estimation	p. 127
6.2.4 Background on REML Estimation	p. 128
6.3 Application to Repeated Measurements	p. 130
6.4 Examples	p. 134
6.4.1 Two Groups, Four Time Points, No Missing Data	p. 134
6.4.2 Three Groups, 24 Time Points, No Missing Data	p. 139
6.4.3 Four Groups, Unequally Spaced Repeated Measurements, Time-Dependent Covariate	p. 145
6.5 Comments	p. 149
6.5.1 Use of the Random Intercept and Slope Model	p. 149
6.5.2 Effects of Choice of Covariance Structure on Estimates and Tests	p. 151
6.5.3 Performance of Linear Mixed Model Test Statistics and Estimators	p. 155
6.6 Problems	p. 156
7 Weighted Least Squares Analysis of Repeated Categorical Outcomes	p. 169
7.1 Introduction	p. 169
7.2 Background	p. 170
7.2.1 The Multinomial Distribution	p. 170
7.2.2 Linear Models Using Weighted Least Squares	p. 171
7.2.3 Analysis of Categorical Data Using Weighted Least Squares	p. 175
7.2.4 Taylor Series Variance Approximations for Nonlinear Response Functions	p. 178
7.3 Application to Repeated Measurements	p. 184
7.3.1 Overview	p. 184
7.3.2 One Population, Dichotomous Response, Repeated Measurements Factor Is Unordered	p. 184
7.3.3 One Population, Dichotomous Response, Repeated Measurements Factor Is Ordered	p. 187
7.3.4 One Population, Polytomous Response	p. 191
7.3.5 Multiple Populations, Dichotomous Response	p. 196
7.4 Accommodation of Missing Data	p. 204
7.4.1 Overview	p. 204
7.4.2 Ratio Estimation for Proportions	p. 204
7.4.3 One Population, Dichotomous Response	p. 205
7.4.4 Multiple Populations, Dichotomous Response	p. 209
7.4.5 Assessing the Missing-Data Mechanism	p. 214
7.5 Problems	p. 220
8 Randomization Model Methods for One-Sample Repeated Measurements	p. 239
8.1 Introduction	p. 239
8.2 The Hypergeometric Distribution and Large-Sample Tests of Randomness for 2 × 2 Tables	p. 240
8.2.1 The Hypergeometric Distribution	p. 240
8.2.2 Test of Randomness for a 2 × 2 Contingency Table	p. 241
8.2.3 Test of Randomness for s 2 × 2 Contingency Tables	p. 242
8.3 Application to Repeated Measurements: Binary Response, Two Time Points	p. 244
8.4 The Multiple Hypergeometric Distribution and Large-Sample Tests of Randomness for r × c Tables	p. 246
8.4.1 The Multiple Hypergeometric Distribution	p. 247
8.4.2 Test of Randomness for an r × c Contingency Table	p. 248
8.4.3 Test of Randomness for s r × c Tables	p. 249
8.4.4 Cochran-Mantel-Haenszel Mean Score Statistic	p. 251
8.4.5 Cochran-Mantel-Haenszel Correlation Statistic	p. 253
8.5 Application to Repeated Measurements: Polytomous Response, Multiple Time Points	p. 253
8.5.1 Introduction	p. 253
8.5.2 The General Association Statistic Q G	p. 255
8.5.3 The Mean Score Statistic Q M and the Correlation Statistic Qc	p. 255
8.6 Accommodation of Missing Data	p. 258
8.6.1 General Association Statistic Q G	p. 258
8.6.2 Mean Score Statistic Q M	p. 260
8.6.3 Correlation Statistic Q C	p. 262
8.7 Use of Mean Score and Correlation Statistics for Continuous Data	p. 263
8.8 Problems	p. 264
9 Methods Based on Extensions of Generalized Linear Models	p. 273
9.1 Introduction	p. 273
9.2 Univariate Generalized Linear Models	p. 274
9.2.1 Introduction	p. 274
9.2.2 Random Component	p. 275
9.2.3 Systematic Component	p. 279
9.2.4 Link Function	p. 279
9.2.5 Canonical Links	p. 279
9.2.6 Parameter Estimation	p. 281
9.3 Quasilikelihood	p. 286
9.3.1 Introduction	p. 286
9.3.2 Construction of a Quasilikelihood Function	p. 287
9.3.3 Quasilikelihood Estimating Equations	p. 289
9.3.4 Comparison Between Quasilikelihood and Generalized Linear Models	p. 291
9.4 Overview of Methods for the Analysis of Repeated Measurements	p. 291
9.4.1 Introduction	p. 291
9.4.2 Marginal Models	p. 292
9.4.3 Random-Effects Models	p. 293
9.4.4 Transition Models	p. 293
9.4.5 Comparisons of the Three Approaches	p. 294
9.5 The GEE Method	p. 295
9.5.1 Introduction	p. 295
9.5.2 Methodology	p. 296
9.5.3 Example	p. 301
9.5.4 Hypothesis Tests Using Wald Statistics	p. 308
9.5.5 Assessing Model Adequacy	p. 309
9.5.6 Sample Size Estimation	p. 310
9.5.7 Studies of the Properties of GEE	p. 311
9.5.8 Computer Software	p. 312
9.5.9 Cautions Concerning the Use of GEE	p. 313
9.6 Subsequent Developments	p. 314
9.6.1 Alternative Procedures for Estimation of GEE Association Parameters	p. 314
9.6.2 Other Developments and Extensions	p. 316
9.6.3 GEE1 and GEE2	p. 316
9.6.4 Extended Generalized Estimating Equations (EGEE)	p. 317
9.6.5 Likelihood-Based Approaches	p. 318
9.7 Random-Effects Models	p. 318
9.8 Methods for the Analysis of Ordered Categorical Repeated Measurements	p. 320
9.8.1 Introduction	p. 320
9.8.2 Univariate Cumulative Logit Models for Ordered Categorical Outcomes	p. 321
9.8.3 The Univariate Proportional-Odds Model	p. 322
9.8.4 The Stram-Wei-Ware Methodology for the Analysis of Ordered Categorical Repeated Measurements	p. 324
9.8.5 Extension of GEE to Ordered Categorical Outcomes	p. 331
9.9 Problems	p. 332
10 Nonparametric Methods	p. 347
10.1 Introduction	p. 347
10.2 Overview	p. 348
10.3 Multivariate One-Sample and Multisample Tests for Complete Data	p. 350
10.3.1 One Sample	p. 350
10.3.2 Multiple Samples	p. 350
10.4 Two-Sample Tests for Incomplete Data	p. 355
10.4.1 Introduction	p. 355
10.4.2 The Wei-Lachin Method	p. 355
10.4.3 The Wei-Johnson Method	p. 356
10.4.4 Examples	p. 362
10.5 Problems	p. 364

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