Models for discrete longitudinal data / Geert Molenberghs, Geert Verbeke.

Format:

Book

Author/Creator:

Molenberghs, Geert.

Contributor:

Verbeke, Geert.

Bernard W. Freeman Book Fund.

Series:

Springer series in statistics

Language:

English

Subjects (All):

Longitudinal method.

Multivariate analysis.

Physical Description:

690 pages : illustrations ; 24 cm.

Place of Publication:

New York ; London : Springer, 2005.

Summary:

This book provides a comprehensive treatment on modeling approaches for non-Gaussian repeated measures, possibly subject to incompleteness. The authors begin with models for the full marginal distribution of the outcome vector. This allows model fitting to be based on maximum likelihood principles, immediately implying inferential tools for all parameters in the models. At the same time, they formulate computationally less complex alternatives, including generalized estimating equations and pseudo-likelihood methods. They then briefly introduce conditional models and move on to the random-effects family, encompassing the beta-binomial model, the probit model and, in particular the generalized linear mixed model. Several frequently used procedures for model fitting are discussed and differences between marginal models and random-effects models are given attention.

The authors consider a variety of extensions, such as models for multivariate longitudinal measurements, random-effects models with serial correlation, and mixed models with non-Gaussian random effects. They sketch the general principles for how to deal with the commonly encountered issue of incomplete longitudinal data. The authors critique frequently used methods and propose flexible and broadly valid methods instead, and they conclude with key concepts of sensitivity analysis.

Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The text is organized so the reader can skip the software-oriented chapters and sections without breaking the logical flow.

Contents:

I Introductory Material 1

2 Motivating Studies 7

2.2 The Analgesic Trial 8

2.3 The Toenail Data 8

2.4 The Fluvoxamine Trial 12

2.5 The Epilepsy Data 14

2.6 The Project on Preterm and Small for Gestational Age Infants (POPS) Study 14

2.7 National Toxicology Program Data 17

2.8 The Sports Injuries Trial 23

2.9 Age Related Macular Degeneration Trial 24

3 Generalized Linear Models 27

3.2 The Exponential Family 27

3.3 The Generalized Linear Model (GLM) 28

3.5 Maximum Likelihood Estimation and Inference 30

3.6 Logistic Regression for the Toenail Data 31

3.7 Poisson Regression for the Epilepsy Data 32

4 Linear Mixed Models for Gaussian Longitudinal Data 35

4.2 Marginal Multivariate Model 36

4.3 The Linear Mixed Model 36

4.4 Estimation and Inference for the Marginal Model 39

4.5 Inference for the Random Effects 41

5 Model Families 45

5.2 The Gaussian Case 46

5.3 Model Families in General 47

5.4 Inferential Paradigms 52

II Marginal Models 53

6 The Strength of Marginal Models 55

6.2 Marginal Models in Contingency Tables 56

6.3 British Occupational Status Study 62

6.4 The Caithness Data 62

6.5 Analysis of the Fluvoxamine Trial 64

6.6 Extensions 68

6.7 Relation to Latent Continuous Densities 79

7 Likelihood-based Marginal Models 83

7.2 The Bahadur Model 86

7.3 A General Framework for Fully Specified Marginal Models 93

7.4 Maximum Likelihood Estimation 99

7.5 An Influenza Study 99

7.6 The Multivariate Probit Model 102

7.7 The Dale Model 113

7.8 Hybrid Marginal-conditional Specification 122

7.9 A Cross-over Trial: An Example in Primary Dysmenorrhoea 127

7.10 Multivariate Analysis of the POPS Data 131

7.11 Longitudinal Analysis of the Fluvoxamine Study 134

7.12 Appendix: Maximum Likelihood Estimation 136

7.13 Appendix: The Multivariate Plackett Distribution 142

7.14 Appendix: Maximum Likelihood Estimation for the Dale Model 147

8 Generalized Estimating Equations 151

8.2 Standard GEE Theory 153

8.3 Alternative GEE Methods 161

8.4 Prentice's GEE Method 162

8.5 Second-order Generalized Estimating Equations (GEE2) 164

8.6 GEE with Odds Ratios and Alternating Logistic Regression 165

8.7 GEE2 Based on a Hybrid Marginal-conditional Model 168

8.8 A Method Based on Linearization 169

8.9 Analysis of the NTP Data 170

8.10 The Heatshock Study 174

8.11 The Sports Injuries Trial 181

9 Pseudo-Likelihood 189

9.2 Pseudo-Likelihood: Definition and Asymptotic Properties 190

9.3 Pseudo-Likelihood Inference 192

9.4 Marginal Pseudo-Likelihood 195

9.5 Comparison with Generalized Estimating Equations 199

9.6 Analysis of NTP Data 200

10 Fitting Marginal Models with SAS 203

10.2 The Toenail Data 203

10.3 GEE1 with Correlations 204

10.4 Alternating Logistic Regressions 212

10.5 A Method Based on Linearization 215

10.6 Programs for the NTP Data 219

10.7 Alternative Software Tools 221

III Conditional Models 223

11 Conditional Models 225

11.2 Conditional Models 226

11.3 Marginal versus Conditional Models 233

11.4 Analysis of the NTP Data 234

11.5 Transition Models 236

12 Pseudo-Likehood 243

12.2 Pseudo-Likelihood for a Single Repeated Binary Outcome 244

12.3 Pseudo-Likelihood for a Multivariate Repeated Binary Outcome 245

12.4 Analysis of the NTP Data 246

IV Subject-specific Models 255

13 From Subject-specific to Random-effects Models 257

13.2 General Model Formulation 257

13.3 Three Ways to Handle Subject-specific Parameters 258

13.4 Random-effects Models: Special Cases 260

14 The Generalized Linear Mixed Model (GLMM) 265

14.2 Model Formulation and Approaches to Estimation 265

14.3 Estimation: Approximation of the Integrand 268

14.4 Estimation: Approximation of the Data 269

14.5 Estimation: Approximation of the Integral 273

14.6 Inference in Generalized Linear Mixed Models 276

14.7 Analyzing the NTP Data 277

14.8 Analyzing the Toenail Data 278

15 Fitting Generalized Linear Mixed Models with SAS 281

15.2 The GLIMMIX Procedure for Quasi-Likelihood 282

15.3 The GLIMMIX Macro for Quasi-Likelihood 287

15.4 The NLMIXED Procedure for Numerical Quadrature 290

15.5 Alternative Software Tools 296

16 Marginal versus Random-effects Models 297

16.2 Example: The Toenail Data 297

16.3 Parameter Interpretation 298

16.4 Toenail Data: Marginal versus Mixed Models 301

16.5 Analysis of the NTP Data 304

V Case Studies and Extensions 307

17 The Analgesic Trial 309

17.2 Marginal Analyses of the Analgesic Trial 310

17.3 Random-effects Analyses of the Analgesic Trial 314

17.4 Comparing Marginal and Random-effects Analyses 317

17.5 Programs for the Analgesic Trial 318

18 Ordinal Data 325

18.1 Regression Models for Ordinal Data 326

18.2 Marginal Models for Repeated Ordinal Data 329

18.3 Random-effects Models for Repeated Ordinal Data 331

18.4 Ordinal Analysis of the Analgesic Trial 332

18.5 Programs for the Analgesic Trial 334

19 The Epilepsy Data 337

19.2 A Marginal GEE Analysis 337

19.3 A Generalized Linear Mixed Model 340

19.4 Marginalizing the Mixed Model 342

20 Non-linear Models 347

20.2 Univariate Non-linear Models 349

20.3 The Indomethacin Study: Non-hierarchical Analysis 351

20.4 Non-linear Models for Longitudinal Data 355

20.5 Non-linear Mixed Models 357

20.6 The Orange Tree Data 358

20.7 Pharmacokinetic and Pharmacodynamic Models 360

20.8 The Songbird Data 368

20.9 Discrete Outcomes 376

20.10 Hypothesis Testing and Non-linear Models 379

20.11 Flexible Functions 379

20.12 Using SAS for Non-linear Mixed-effects Models 384

21 Pseudo-Likelihood for a Hierarchical Model 393

21.2 Pseudo-Likelihood Estimation 394

21.3 Two Binary Endpoints 397

21.4 A Meta-analysis of Trials in Schizophrenic Subjects 401

22 Random-effects Models with Serial Correlation 405

22.2 A Multilevel Probit Model with Autocorrelation 406

22.3 Parameter Estimation for the Multilevel Probit Model 408

22.4 A Generalized Linear Mixed Model with Autocorrelation 410

22.5 A Meta-analysis of Trials in Schizophrenic Subjects 412

22.6 SAS Code for Random-effects Models with Autocorrelation 415

23 Non-Gaussian Random Effects 419

23.2 The Heterogeneity Model 421

23.3 Estimation and Inference 423

23.4 Empirical Bayes Estimation and Classification 427

23.5 The Verbal Aggression Data 428

24 Joint Continuous and Discrete Responses 437

24.2 A Continuous and a Binary Endpoint 439

24.3 Hierarchical Joint Models 445

24.4 Age Related Macular Degeneration Trial 448

24.5 Joint Models in SAS 455

25 High-dimensional Joint Models 467

25.2 Joint Mixed Model 469

25.3 Model Fitting and Inference 471

25.4 A Study in Psycho-Cognitive Functioning 473

VI Missing Data 479

26 Missing Data Concepts 481

26.2 A Formal Taxonomy 482

27 Simple Methods, Direct Likelihood, and WGEE 489

27.2 Longitudinal Analysis or Not? 490

27.3 Simple Methods 491

27.4 Bias in LOCF, CC, and Ignorable Likelihood 495

27.5 Weighted Generalized Estimating Equations 498

27.6 The Depression Trial 499

27.7 Age Related Macular Degeneration Trial 503

27.8 The Analgesic Trial 507

28 Multiple Imputation and the EM Algorithm 511

28.2 Multiple Imputation 511

28.3 The Expectation-Maximization Algorithm 516

28.4 Which Method to Use? 526

28.5 Age Related Macular Degeneration Study 527

29 Selection Models 531

29.2 An MNAR Dale Model 532

29.3 A Model for Non-monotone Missingness 543

30 Pattern-mixture Models 555

30.2 Pattern-mixture Modeling Approach 556

30.3 Identifying Restriction Strategies 557

30.4 A Unifying Framework for Selection and Pattern-mixture Models 561

30.5 Selection Models versus Pattern-mixture Models 563

30.6 Analysis of

the Fluvoxamine Data 567

31 Sensitivity Analysis 575

31.2 Sensitivity Analysis for Selection Models 576

31.3 A Local Influence Approach for Ordinal Data with Dropout 578

31.4 A Local Influence Approach for Incomplete Binary Data 585

31.5 Interval of Ignorance 590

31.6 Sensitivity Analysis and Pattern-mixture Models 604

32 Incomplete Data and SAS 607

32.2 Complete Case Analysis 607

32.3 Last Observation Carried Forward 609

32.4 Direct Likelihood 611

32.5 Weighted Estimating Equations (WGEE) 613

32.6 Multiple Imputation 618

32.7 The EM Algorithm 633

32.8 MNAR Models and Sensitivity Analysis Tools 635.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Bernard W. Freeman Book Fund.

ISBN:

0387251448

OCLC:

61260822