Missing Data in Clinical Studies (eBook)

Geert Molenberghs and Michael Kenward are the authors of Missing Data in Clinical Studies, published by Wiley.

Missing Data in Clinical Studies 1
Contents 9
Preface 17
Acknowledgements 21
I Preliminaries 23
1 Introduction 25
1.1 From Imbalance to the Field of Missing Data Research 25
1.2 Incomplete Data in Clinical Studies 27
1.3 MAR, MNAR, and Sensitivity Analysis 30
1.4 Outline of the Book 31
2 Key Examples 33
2.1 Introduction 33
2.2 The Vorozole Study 34
2.3 The Orthodontic Growth Data 34
2.4 Mastitis in Dairy Cattle 36
2.5 The Depression Trials 36
2.6 The Fluvoxamine Trial 39
2.7 The Toenail Data 40
2.8 Age-Related Macular Degeneration Trial 42
2.9 The Analgesic Trial 44
2.10 The Slovenian Public Opinion Survey 46
3 Terminology and Framework 49
3.1 Modelling Incompleteness 49
3.2 Terminology 51
3.3 Missing Data Frameworks 52
3.4 Missing Data Mechanisms 53
3.5 Ignorability 55
3.6 Pattern-Mixture Models 56
Part II Classical Techniques and the Need for Modelling 61
4 A Perspective on Simple Methods 63
4.1 Introduction 63
4.1.1 Measurement model 63
4.1.2 Method for handling missingness 64
4.2 Simple Methods 64
4.2.1 Complete case analysis 64
4.2.2 Imputation methods 65
4.2.3 Last observation carried forward 67
4.3 Problems with Complete Case Analysis and Last Observation Carried Forward 69
4.4 Using the Available Cases: a Frequentist versus a Likelihood Perspective 72
4.4.1 A bivariate normal population 72
4.4.2 An incomplete contingency table 74
4.5 Intention to Treat 75
4.6 Concluding Remarks 76
5 Analysis of the Orthodontic Growth Data 77
5.1 Introduction and Models 77
5.2 The Original, Complete Data 78
5.3 Direct Likelihood 79
5.4 Comparison of Analyses 81
5.5 Example SAS Code for Multivariate Linear Models 84
5.6 Comparative Power under Different Covariance Structures 85
5.7 Concluding Remarks 87
6 Analysis of the Depression Trials 89
6.1 View 1: Longitudinal Analysis 90
6.2 Views 2a and 2b and All versus Two Treatment Arms 94
III Missing at Random and Ignorability 97
7 The Direct Likelihood Method 99
7.1 Introduction 99
7.2 Ignorable Analyses in Practice 100
7.3 The Linear Mixed Model 101
7.4 Analysis of the Toenail Data 104
7.5 The Generalized Linear Mixed Model 107
7.6 The Depression Trials 112
7.7 The Analgesic Trial 113
8 The Expectation–Maximization Algorithm 115
8.1 Introduction 115
8.2 The Algorithm 116
8.2.1 The initial step 116
8.2.2 The E step 117
8.2.3 The M step 117
8.3 Missing Information 117
8.4 Rate of Convergence 118
8.5 EM Acceleration 119
8.6 Calculation of Precision Estimates 120
8.7 A Simple Illustration 120
8.8 Concluding Remarks 125
9 Multiple Imputation 127
9.1 Introduction 127
9.2 The Basic Procedure 127
9.3 Theoretical Justification 129
9.4 Inference under Multiple Imputation 130
9.5 Efficiency 131
9.6 Making Proper Imputations 132
9.7 Some Roles for Multiple Imputation 137
9.8 Concluding Remarks 139
10 Weighted Estimating Equations 141
10.1 Introduction 141
10.2 Inverse Probability Weighting 142
10.3 Generalized Estimating Equations for Marginal Models 145
10.3.1 Marginal models for non-normal data 145
10.3.2 Generalized estimating equations 145
10.3.3 A method based on linearization 146
10.4 Weighted Generalized Estimating Equations 148
10.5 The Depression Trials 148
10.6 The Analgesic Trial 150
10.7 Double Robustness 152
10.8 Concluding Remarks 155
11 Combining GEE and MI 157
11.1 Introduction 157
11.2 Data Generation and Fitting 158
11.2.1 The Bahadur model 158
11.2.2 A transition model 159
11.3 MI-GEE and MI-Transition 159
11.4 An Asymptotic Simulation Study 159
11.4.1 Design 160
11.4.2 Results 161
11.5 Concluding Remarks 164
12 Likelihood-Based Frequentist Inference 167
12.1 Introduction 167
12.2 Information and Sampling Distributions 169
12.3 Bivariate Normal Data 171
12.4 Bivariate Binary Data 175
12.5 Implications for Standard Software 178
12.6 Analysis of the Fluvoxamine Trial 180
12.7 The Muscatine Coronary Risk Factor Study 182
12.8 The Crépeau Data 183
12.9 Concluding Remarks 183
13 Analysis of the Age-Related Macular Degeneration Trial 185
13.1 Introduction 185
13.2 Direct Likelihood Analysis of the Continuous Outcome 186
13.3 Weighted Generalized Estimating Equations 187
13.4 Direct Likelihood Analysis of the Binary Outcome 189
13.5 Multiple Imputation 190
13.6 Concluding Remarks 192
14 Incomplete Data and SAS 193
14.1 Introduction 193
14.2 Complete Case Analysis 193
14.3 Last Observation Carried Forward 195
14.4 Direct Likelihood 196
14.5 Weighted Estimating Equations 197
14.6 Multiple Imputation 198
14.6.1 The MI procedure for the imputation task 199
14.6.2 The analysis task 200
14.6.3 The inference task 203
14.6.4 The MI procedure to create monotone missingness 204
IV Missing Not at Random 205
15 Selection Models 207
15.1 Introduction 207
15.2 The Diggle–Kenward Model for Continuous Outcomes 208
15.3 Illustration and SAS Implementation 210
15.4 An MNAR Dale Model 216
15.4.1 Likelihood function 216
15.4.2 Analysis of the fluvoxamine trial 219
15.4.3 The tinea pedis study 224
15.5 A Model for Non-monotone Missingness 226
15.5.1 Analysis of the fluvoxamine trial 229
15.6 Concluding Remarks 234
16 Pattern-Mixture Models 237
16.1 Introduction 237
16.2 A Simple Gaussian Illustration 238
16.3 A Paradox 241
16.4 Strategies to Fit Pattern-Mixture Models 242
16.5 Applying Identifying Restrictions 243
16.6 Pattern-Mixture Analysis of the Vorozole Study 244
16.6.1 Derivations 245
16.6.2 Application to the vorozole study 246
16.7 A Clinical Trial in Alzheimer’s Disease 259
16.8 Analysis of the Fluvoxamine Trial 264
16.8.1 Selection modelling 264
16.8.2 Pattern-mixture modelling 265
16.8.3 Comparison 268
16.9 Concluding Remarks 268
17 Shared-Parameter Models 271
18 Protective Estimation 275
18.1 Introduction 275
18.2 Brown’s Protective Estimator for Gaussian Data 276
18.3 A Protective Estimator for Categorical Data 278
18.3.1 Likelihood estimation 282
18.3.2 Pseudo-likelihood estimation 285
18.3.3 Variance estimation 286
18.3.4 Analysis of artificial data 291
18.3.5 Analysis of the fluvoxamine trial 292
18.3.6 Presence or absence of colds 296
18.4 A Protective Estimator for Gaussian Data 297
18.4.1 Notation and maximum likelihood 297
18.4.2 Protective estimator 299
18.4.3 The six cities study 301
18.5 Concluding Remarks 304
V Sensitivity Analysis 305
19 MNAR, MAR, and the Nature of Sensitivity 307
19.1 Introduction 307
19.2 Every MNAR Model Has an MAR Bodyguard 308
19.2.1 A bivariate outcome with dropout 311
19.2.2 A trivariate outcome with dropout 312
19.2.3 A bivariate outcome with non-monotone missingness 313
19.3 The General Case of Incomplete Contingency Tables 314
19.3.1 A bivariate contingency table with dropout 315
19.3.2 A bivariate contingency table with non-monotone missingness 316
19.4 The Slovenian Public Opinion Survey 317
19.4.1 The BRD models 318
19.4.2 Initial analysis 318
19.4.3 BRD analysis 321
19.5 Implications for Formal and Informal Model Selection 324
19.6 Behaviour of the Likelihood Ratio Test for MAR versus MNAR 327
19.6.1 Simulated null distributions 328
19.6.2 Performance of bootstrap approaches 329
19.7 Concluding Remarks 333
20 Sensitivity Happens 335
20.1 Introduction 335
20.2 A Range of MNAR Models 336
20.3 Identifiability Problems 342
20.4 Analysis of the Fluvoxamine Trial 344
20.5 Concluding Remarks 349
21 Regions of Ignorance and Uncertainty 351
21.1 Introduction 351
21.2 Prevalence of HIV in Kenya 352
21.3 Uncertainty and Sensitivity 352
21.4 Models for Monotone Patterns 353
21.5 Models for Non-monotone Patterns 354
21.6 Formalizing Ignorance and Uncertainty 355
21.7 Analysis of the Fluvoxamine Trial 360
21.7.1 Identified models 361
21.7.2 Sensitivity analysis 363
21.8 Artificial Examples 367
21.9 The Slovenian Public Opinion Survey 370
21.10 Some Theoretical Considerations 373
21.11 Concluding Remarks 373
22 Local and Global Influence Methods 375
22.1 Introduction 375
22.2 Gaussian Outcomes 376
22.2.1 Application to the Diggle–Kenward model 378
22.2.2 The special case of three measurements 381
22.3 Mastitis in Dairy Cattle 382
22.3.1 Informal sensitivity analysis 383
22.3.2 Local influence approach 389
22.4 Alternative Local Influence Approaches 395
22.5 The Milk Protein Content Trial 397
22.5.1 Informal sensitivity analysis 399
22.5.2 Formal sensitivity analysis 408
22.6 Analysis of the Depression Trials 420
22.7 A Local Influence Approach for Ordinal Data with Dropout 427
22.8 Analysis of the Fluvoxamine Data 428
22.9 A Local Influence Approach for Incomplete Binary Data 432
22.10 Analysis of the Fluvoxamine Data 433
22.11 Concluding Remarks 437
23 The Nature of Local Influence 439
23.1 Introduction 439
23.2 The Rats Data 440
23.3 Analysis and Sensitivity Analysis of the Rats Data 441
23.4 Local Influence Methods and Their Behaviour 444
23.4.1 Effect of sample size 445
23.4.2 Pointwise confidence limits and simultaneous confidence bounds for the local influence measure 446
23.4.3 Anomalies in the missingness mechanism 447
23.4.4 Anomalies in the measurement model 450
23.5 Concluding Remarks 452
24 A Latent-Class Mixture Model for Incomplete Longitudinal Gaussian Data 453
24.1 Introduction 453
24.2 Latent-Class Mixture Models 453
24.3 The Likelihood Function and Estimation 456
24.3.1 Likelihood function 456
24.3.2 Estimation using the EM algorithm 458
24.3.3 The E step 459
24.3.4 The M step 460
24.3.5 Some remarks regarding the EM algorithm 461
24.4 Classification 462
24.5 Simulation Study 463
24.5.1 A simplification of the latent-class mixture model 463
24.5.2 Design 464
24.5.3 Results 465
24.6 Analysis of the Depression Trials 468
24.6.1 Formulating a latent-class mixture model 468
24.6.2 A sensitivity analysis 471
24.7 Concluding Remarks 472
VI Case Studies 473
25 The Age-Related Macular Degeneration Trial 475
25.1 Selection Models and Local Influence 475
25.2 Local Influence Analysis 477
25.3 Pattern-Mixture Models 480
25.4 Concluding Remarks 481
26 The Vorozole Study 483
26.1 Introduction 483
26.2 Exploring the Vorozole Data 483
26.2.1 Average evolution 483
26.2.2 Variance structure 486
26.2.3 Correlation structure 487
26.2.4 Missing data aspects 488
26.3 A Selection Model for the Vorozole Study 493
26.4 A Pattern-Mixture Model for the Vorozole Study 497
26.5 Concluding Remarks 503
References 505
Index 519
Statistics in Practice 527

?Overall, this is an excellent text on missing data that is
engaging for practitioners while being rigorous enoughfor use in
the graduate biostatistics courses.?(Biometrics , September
2009)" "Missing Data in Clinical Studies does an excellent
job of presenting essential ideas on modern concepts and techniques
relevant to missing data in clinical studies." (Journal of the
American Statistician, December 2008)

"?this book is reasonably well organized and covers all the
relevant theory and much of the practical applications of the
field." (Journal of the American Chemical Association,
August 6, 2008)

"Missing Data in Clinical Studies does an excellent job of
presenting essential ideas on modern concepts and techniques
relevant to missing data in clinical studies." (Journal of
the American Statistician, December 2008)

"Clear, generally accessible and well written, and the content
is rich. This text is a highly recommendable addition to the
shelves of practicing statisticians." (Journal of Applied
Statistics, August 2008)

"The authors give key examples in the form of several clinical
trials and their analyses using the appropriate remedial
techniques." (Journal of Tropical Pediatrics, August
2007)