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Cover image for Models for discrete longitudinal data
Title:
Models for discrete longitudinal data
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Series:
Springer series in statistics
Publication Information:
New York, NY : Springer, 2005
ISBN:
9780387251448
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Item Category 1
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30000004589978 QA278 M64 2005 Open Access Book Book
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Summary

Summary

The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000 book.

Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package.

The authors received the American Statistical Association's Excellence in Continuing Education Award based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004.


Author Notes

Geert Molenberghs is Professor of Biostatistics at the Universiteit Hasselt in Belgium and has published methodological work on surrogate markers in clinical trials, categorical data, longitudinal data analysis, and the analysis of non-response in clinical and epidemiological studies
Geert Verbeke is Professor of Biostatistics at the Biostatistical Centre of the Katholieke Universiteit Leuven in Belgium


Table of Contents

Prefacep. vii
Acknowledgmentsp. ix
I Introductory Materialp. 1
1 Introductionp. 3
2 Motivating Studiesp. 7
2.1 Introductionp. 7
2.2 The Analgesic Trialp. 8
2.3 The Toenail Datap. 8
2.4 The Fluvoxamine Trialp. 12
2.5 The Epilepsy Datap. 14
2.6 The Project on Preterm and Small for Gestational Age Infants (POPS) Studyp. 14
2.7 National Toxicology Program Datap. 17
2.8 The Sports Injuries Trialp. 23
2.9 Age Related Macular Degeneration Trialp. 24
3 Generalized Linear Modelsp. 27
3.1 Introductionp. 27
3.2 The Exponential Familyp. 27
3.3 The Generalized Linear Model (GLM)p. 28
3.4 Examplesp. 29
3.5 Maximum Likelihood Estimation and Inferencep. 30
3.6 Logistic Regression for the Toenail Datap. 31
3.7 Poisson Regression for the Epilepsy Datap. 32
4 Linear Mixed Models for Gaussian Longitudinal Datap. 35
4.1 Introductionp. 35
4.2 Marginal Multivariate Modelp. 36
4.3 The Linear Mixed Modelp. 36
4.4 Estimation and Inference for the Marginal Modelp. 39
4.5 Inference for the Random Effectsp. 41
5 Model Familiesp. 45
5.1 Introductionp. 45
5.2 The Gaussian Casep. 46
5.3 Model Families in Generalp. 47
5.4 Inferential Paradigmsp. 52
II Marginal Modelsp. 53
6 The Strength of Marginal Modelsp. 55
6.1 Introductionp. 55
6.2 Marginal Models in Contingency Tablesp. 56
6.3 British Occupational Status Studyp. 62
6.4 The Caithness Datap. 62
6.5 Analysis of the Fluvoxamine Trialp. 64
6.6 Extensionsp. 68
6.7 Relation to Latent Continuous Densitiesp. 79
6.8 Conclusions and Perspectivep. 80
7 Likelihood-based Marginal Modelsp. 83
7.1 Notationp. 84
7.2 The Bahadur Modelp. 86
7.3 A General Framework for Fully Specified Marginal Modelsp. 93
7.4 Maximum Likelihood Estimationp. 99
7.5 An Influenza Studyp. 99
7.6 The Multivariate Probit Modelp. 102
7.7 The Dale Modelp. 113
7.8 Hybrid Marginal-conditional Specificationp. 122
7.9 A Cross-over Trial: An Example in Primary Dysmenorrhoeap. 127
7.10 Multivariate Analysis of the POPS Datap. 131
7.11 Longitudinal Analysis of the Fluvoxamine Studyp. 134
7.12 Appendix: Maximum Likelihood Estimationp. 136
7.13 Appendix: The Multivariate Plackett Distributionp. 142
7.14 Appendix: Maximum Likelihood Estimation for the Dale Modelp. 147
8 Generalized Estimating Equationsp. 151
8.1 Introductionp. 151
8.2 Standard GEE Theoryp. 153
8.3 Alternative GEE Methodsp. 161
8.4 Prentice's GEE Methodp. 162
8.5 Second-order Generalized Estimating Equations (GEE2)p. 164
8.6 GEE with Odds Ratios and Alternating Logistic Regressionp. 165
8.7 GEE2 Based on a Hybrid Marginal-conditional Modelp. 168
8.8 A Method Based on Linearizationp. 169
8.9 Analysis of the NTP Datap. 170
8.10 The Heatshock Studyp. 174
8.11 The Sports Injuries Trialp. 181
9 Pseudo-Likelihoodp. 189
9.1 Introductionp. 189
9.2 Pseudo-Likelihood: Definition and Asymptotic Propertiesp. 190
9.3 Pseudo-Likelihood Inferencep. 192
9.4 Marginal Pseudo-Likelihoodp. 195
9.5 Comparison with Generalized Estimating Equationsp. 199
9.6 Analysis of NTP Datap. 200
10 Fitting Marginal Models with SASp. 203
10.1 Introductionp. 203
10.2 The Toenail Datap. 203
10.3 GEE1 with Correlationsp. 204
10.4 Alternating Logistic Regressionsp. 212
10.5 A Method Based on Linearizationp. 215
10.6 Programs for the NTP Datap. 219
10.7 Alternative Software Toolsp. 221
III Conditional Modelsp. 223
11 Conditional Modelsp. 225
11.1 Introductionp. 225
11.2 Conditional Modelsp. 226
11.3 Marginal versus Conditional Modelsp. 233
11.4 Analysis of the NTP Datap. 234
11.5 Transition Modelsp. 236
12 Pseudo-Likehoodp. 243
12.1 Introductionp. 243
12.2 Pseudo-Likelihood for a Single Repeated Binary Outcomep. 244
12.3 Pseudo-Likelihood for a Multivariate Repeated Binary Outcomep. 245
12.4 Analysis of the NTP Datap. 246
IV Subject-specific Modelsp. 255
13 From Subject-specific to Random-effects Modelsp. 257
13.1 Introductionp. 257
13.2 General Model Formulationp. 257
13.3 Three Ways to Handle Subject-specific Parametersp. 258
13.4 Random-effects Models: Special Casesp. 260
14 The Generalized Linear Mixed Model (GLMM)p. 265
14.1 Introductionp. 265
14.2 Model Formulation and Approaches to Estimationp. 265
14.3 Estimation: Approximation of the Integrandp. 268
14.4 Estimation: Approximation of the Datap. 269
14.5 Estimation: Approximation of the Integralp. 273
14.6 Inference in Generalized Linear Mixed Modelsp. 276
14.7 Analyzing the NTP Datap. 277
14.8 Analyzing the Toenail Datap. 278
15 Fitting Generalized Linear Mixed Models with SASp. 281
15.1 Introductionp. 281
15.2 The GLIMMIX Procedure for Quasi-Likelihoodp. 282
15.3 The GLIMMIX Macro for Quasi-Likelihoodp. 287
15.4 The NLMIXED Procedure for Numerical Quadraturep. 290
15.5 Alternative Software Toolsp. 296
16 Marginal versus Random-effects Modelsp. 297
16.1 Introductionp. 297
16.2 Example: The Toenail Datap. 297
16.3 Parameter Interpretationp. 298
16.4 Toenail Data: Marginal versus Mixed Modelsp. 301
16.5 Analysis of the NTP Datap. 304
V Case Studies and Extensionsp. 307
17 The Analgesic Trialp. 309
17.1 Introductionp. 309
17.2 Marginal Analyses of the Analgesic Trialp. 310
17.3 Random-effects Analyses of the Analgesic Trialp. 314
17.4 Comparing Marginal and Random-effects Analysesp. 317
17.5 Programs for the Analgesic Trialp. 318
18 Ordinal Datap. 325
18.1 Regression Models for Ordinal Datap. 326
18.2 Marginal Models for Repeated Ordinal Datap. 329
18.3 Random-effects Models for Repeated Ordinal Datap. 331
18.4 Ordinal Analysis of the Analgesic Trialp. 332
18.5 Programs for the Analgesic Trialp. 334
19 The Epilepsy Datap. 337
19.1 Introductionp. 337
19.2 A Marginal GEE Analysisp. 337
19.3 A Generalized Linear Mixed Modelp. 340
19.4 Marginalizing the Mixed Modelp. 342
20 Non-linear Modelsp. 347
20.1 Introductionp. 347
20.2 Univariate Non-linear Modelsp. 349
20.3 The Indomethacin Study: Non-hierarchical Analysisp. 351
20.4 Non-linear Models for Longitudinal Datap. 355
20.5 Non-linear Mixed Modelsp. 357
20.6 The Orange Tree Datap. 358
20.7 Pharmacokinetic and Pharmacodynamic Modelsp. 360
20.8 The Songbird Datap. 368
20.9 Discrete Outcomesp. 376
20.10 Hypothesis Testing and Non-linear Modelsp. 379
20.11 Flexible Functionsp. 379
20.12 Using SAS for Non-linear Mixed-effects Modelsp. 384
21 Pseudo-Likelihood for a Hierarchical Modelp. 393
21.1 Introductionp. 393
21.2 Pseudo-Likelihood Estimationp. 394
21.3 Two Binary Endpointsp. 397
21.4 A Meta-analysis of Trials in Schizophrenic Subjectsp. 401
21.5 Concluding Remarksp. 403
22 Random-effects Models with Serial Correlationp. 405
22.1 Introductionp. 405
22.2 A Multilevel Probit Model with Autocorrelationp. 406
22.3 Parameter Estimation for the Multilevel Probit Modelp. 408
22.4 A Generalized Linear Mixed Model with Autocorrelationp. 410
22.5 A Meta-analysis of Trials in Schizophrenic Subjectsp. 412
22.6 SAS Code for Random-effects Models with Autocorrelationp. 415
22.7 Concluding Remarksp. 417
23 Non-Gaussian Random Effectsp. 419
23.1 Introductionp. 419
23.2 The Heterogeneity Modelp. 421
23.3 Estimation and Inferencep. 423
23.4 Empirical Bayes Estimation and Classificationp. 427
23.5 The Verbal Aggression Datap. 428
23.6 Concluding Remarksp. 435
24 Joint Continuous and Discrete Responsesp. 437
24.1 Introductionp. 437
24.2 A Continuous and a Binary Endpointp. 439
24.3 Hierarchical Joint Modelsp. 445
24.4 Age Related Macular Degeneration Trialp. 448
24.5 Joint Models in SASp. 455
24.6 Concluding Remarksp. 464
25 High-dimensional Joint Modelsp. 467
25.1 Introductionp. 467
25.2 Joint Mixed Modelp. 469
25.3 Model Fitting and Inferencep. 471
25.4 A Study in Psycho-Cognitive Functioningp. 473
VI Missing Datap. 479
26 Missing Data Conceptsp. 481
26.1 Introductionp. 481
26.2 A Formal Taxonomyp. 482
27 Simple Methods, Direct Likelihood, and WGEEp. 489
27.1 Introductionp. 489
27.2 Longitudinal Analysis or Not?p. 490
27.3 Simple Methodsp. 491
27.4 Bias in LOCF, CC, and Ignorable Likelihoodp. 495
27.5 Weighted Generalized Estimating Equationsp. 498
27.6 The Depression Trialp. 499
27.7 Age Related Macular Degeneration Trialp. 503
27.8 The Analgesic Trialp. 507
28 Multiple Imputation and the EM Algorithmp. 511
28.1 Introductionp. 511
28.2 Multiple Imputationp. 511
28.3 The Expectation-Maximization Algorithmp. 516
28.4 Which Method to Use?p. 526
28.5 Age Related Macular Degeneration Studyp. 527
28.6 Concluding Remarksp. 529
29 Selection Modelsp. 531
29.1 Introductionp. 531
29.2 An MNAR Dale Modelp. 532
29.3 A Model for Non-monotone Missingnessp. 543
29.4 Concluding Remarksp. 552
30 Pattern-mixture Modelsp. 555
30.1 Introductionp. 555
30.2 Pattern-mixture Modeling Approachp. 556
30.3 Identifying Restriction Strategiesp. 557
30.4 A Unifying Framework for Selection and Pattern-mixture Modelsp. 561
30.5 Selection Models versus Pattern-mixture Modelsp. 563
30.6 Analysis of the Fluvoxamine Datap. 567
30.7 Concluding Remarksp. 572
31 Sensitivity Analysisp. 575
31.1 Introductionp. 575
31.2 Sensitivity Analysis for Selection Modelsp. 576
31.3 A Local Influence Approach for Ordinal Data with Dropoutp. 578
31.4 A Local Influence Approach for Incomplete Binary Datap. 585
31.5 Interval of Ignorancep. 590
31.6 Sensitivity Analysis and Pattern-mixture Modelsp. 604
31.7 Concluding Remarksp. 605
32 Incomplete Data and SASp. 607
32.1 Introductionp. 607
32.2 Complete Case Analysisp. 607
32.3 Last Observation Carried Forwardp. 609
32.4 Direct Likelihoodp. 611
32.5 Weighted Estimating Equations (WGEE)p. 613
32.6 Multiple Imputationp. 618
32.7 The EM Algorithmp. 633
32.8 MNAR Models and Sensitivity Analysis Toolsp. 635
Referencesp. 637
Indexp. 671
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