Raymond J. Carroll, David Ruppert, Leonard A. Stefanski, Ciprian M. Crainiceanu9781584886334, 1584886331
What’s new in the Second Edition?
· Greatly expanded discussion and applications of Bayesian computation via Markov Chain Monte Carlo techniques
· A new chapter on longitudinal data and mixed models
· A thoroughly revised chapter on nonparametric regression and density estimation
· A totally new chapter on semiparametric regression
· Survival analysis expanded into its own separate chapter
· Completely rewritten chapter on score functions
· Many more examples and illustrative graphs
· Unique data sets compiled and made available online
In addition, the authors expanded the background material in Appendix A and integrated the technical material from chapter appendices into a new Appendix B for convenient navigation. Regardless of your field, if you’re looking for the most extensive discussion and review of measurement error models, then Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition is your ideal source.
Table of contents :
Contents……Page 0
Measurement Error in Nonlinear Models……Page 5
Preface to the First Edition……Page 8
Preface to the Second Edition……Page 12
Guide to Notation……Page 14
Contents……Page 17
1.1 The Double/Triple Whammy of Measurement Error……Page 27
1.2 Classical Measurement Error: A Nutrition Example……Page 28
1.3 Measurement Error Examples……Page 29
1.4 Radiation Epidemiology and Berkson Errors……Page 30
1.4.1 The Difference Between Berkson and Classical Errors: How to Gain More Power Without Really Trying……Page 31
1.5 Classical Measurement Error Model Extensions……Page 33
1.6.1 NHANES……Page 35
1.6.2 Nurses’ Health Study……Page 36
1.6.4 Bioassay in a Herbicide Study……Page 37
1.6.6 Coronary Heart Disease and Blood Pressure……Page 38
1.6.8 Blood Pressure and Urinary Sodium Chloride……Page 39
1.7 Checking the Classical Error Model……Page 40
1.8.1 Linear Regression Example……Page 44
1.8.2 Radiation Epidemiology Example……Page 46
Bibliographic Notes……Page 49
2.1 Functional and Structural Models……Page 51
2.2.1 General Approaches: Berkson and Classical Models……Page 52
2.2.2 Is It Berkson or Classical?……Page 53
2.2.3 Berkson Models from Classical……Page 54
2.2.4 Transportability of Models……Page 55
2.2.5 Potential Dangers of Transporting Models……Page 56
2.3 Sources of Data……Page 58
2.4 Is There an Exact” Predictor? What Is Truth?……Page 59
2.5 Differential and Nondifferential Error……Page 62
2.6 Prediction……Page 64
Bibliographic Notes……Page 65
3.2 Bias Caused by Measurement Error……Page 66
3.2.1 Simple Linear Regression with Additive Error……Page 67
3.2.2 Regression Calibration: Classical Error as Berkson Error……Page 69
3.2.3 Simple Linear Regression with Berkson Error……Page 70
3.2.4 Simple Linear Regression, More Complex Error Structure……Page 71
3.2.5 Summary of Simple Linear Regression……Page 74
3.3.1 Multiple Regression: Single Covariate Measured with Error……Page 77
3.3.2 Multiple Covariates Measured with Error……Page 78
3.4.1 Method of Moments……Page 80
3.4.2 Orthogonal Regression……Page 82
3.5 Bias Versus Variance……Page 85
3.5.1 Theoretical Bias-Variance Tradeoff Calculations……Page 86
3.6 Attenuation in General Problems……Page 88
Bibliographic Notes……Page 89
4.1 Overview……Page 90
4.3 NHANES Example……Page 91
4.4.2 Best Linear Approximations Using Replicate Data……Page 95
4.5 Multiplicative Measurement Error……Page 97
4.5.1 Should Predictors Be Transformed?……Page 98
4.5.2 Lognormal X and U……Page 99
4.5.3 Linear Regression……Page 102
4.5.4 Additive and Multiplicative Error……Page 103
4.7 Expanded Regression Calibration Models……Page 104
4.7.1 The Expanded Approximation Defined……Page 106
4.7.2 Implementation……Page 108
4.7.3 Bioassay Data……Page 110
4.8.2 Logistic Regression……Page 115
4.8.3 Loglinear Mean Models……Page 118
4.9.2 Quadratic Regression with Homoscedastic Regression Calibration……Page 119
Bibliographic Notes and Software……Page 120
5.1 Overview……Page 122
5.2.1 SIMEX in Simple Linear Regression……Page 123
5.3.1 Simulation and Extrapolation Steps……Page 125
5.3.2 Extrapolant Function Considerations……Page 133
5.3.3 SIMEX Standard Errors……Page 135
5.3.4 Extensions and Refinements……Page 136
5.4.1 Framingham Heart Study……Page 137
5.4.2 Single Covariate Measured with Error……Page 138
5.4.3 Multiple Covariates Measured with Error……Page 143
5.5.1 Multiple Linear Regression……Page 145
5.5.3 Quadratic Mean Models……Page 147
5.6.1 Mixture of Berkson and Classical Error……Page 148
5.6.2 Misclassi¯cation SIMEX……Page 150
5.6.3 Checking Structural Model Robustness via Remeasurement……Page 151
Bibliographic Notes……Page 153
6.1 Overview……Page 154
6.1.1 A Note on Notation……Page 155
6.2.1 Instrumental Variables via Differentiation……Page 156
6.2.2 Simple Linear Regression with One Instrument……Page 157
6.2.3 Linear Regression with Multiple Instruments……Page 159
6.3.1 IV Assumptions……Page 162
6.3.2 Mean and Variance Function Models……Page 163
6.3.3 First Regression Calibration IV Algorithm……Page 164
6.4 Adjusted Score Method……Page 165
6.5.1 Framingham Data……Page 168
6.6.1 Hybrid Classical and Regression Calibration……Page 170
6.6.2 Error Model Approaches……Page 172
Bibliographic Notes……Page 173
7.1 Overview……Page 175
7.2.1 Linear Regression Corrected and Conditional Scores……Page 176
7.2.2 Logistic Regression Corrected and Conditional Scores……Page 181
7.2.3 Framingham Data Example……Page 183
7.3.1 Conditional Score Basic Theory……Page 186
7.3.2 Conditional Scores for Basic Models……Page 188
7.3.3 Conditional Scores for More Complicated Models……Page 190
7.4 Corrected Score Functions……Page 193
7.4.2 Monte Carlo Corrected Scores……Page 194
7.4.3 Some Exact Corrected Scores……Page 196
7.4.5 Corrected Scores with Replicate Measurements……Page 197
7.5 Computation and Asymptotic Approximations……Page 198
7.5.1 Known Measurement Error Variance……Page 199
7.5.2 Estimated Measurement Error Variance……Page 200
7.6 Comparison of Conditional and Corrected Scores……Page 201
7.7 Bibliographic Notes……Page 202
8.1 Introduction……Page 204
8.1.1 Step 1: The Likelihood If X Were Observable……Page 206
8.2 Steps 2 and 3: Constructing Likelihoods……Page 207
8.2.1 The Discrete Case……Page 208
8.2.2 Likelihood Construction for General Error Models……Page 209
8.2.3 The Berkson Model……Page 211
8.2.4 Error Model Choice……Page 212
8.4 Cervical Cancer and Herpes……Page 213
8.5 Framingham Data……Page 215
8.6 Nevada Test Site Reanalysis……Page 216
8.6.1 Regression Calibration Implementation……Page 218
8.6.2 Maximum Likelihood Implementation……Page 219
8.7 Bronchitis Example……Page 220
8.7.1 Calculating the Likelihood……Page 221
8.7.3 Simulation Study and Maximum Likelihood……Page 222
8.8 Quasilikelihood and Variance Function Models……Page 224
8.8.1 Details of Step 3 for QVF Models……Page 225
Bibliographic Notes……Page 226
9.1.1 Problem Formulation……Page 227
9.1.2 Posterior Inference……Page 229
9.1.3 Bayesian Functional and Structural Models……Page 230
9.2 The Gibbs Sampler……Page 231
9.3 Metropolis{Hastings Algorithm……Page 233
9.4 Linear Regression……Page 235
9.4.1 Example……Page 238
9.5.1 A General Model……Page 241
9.5.2 Polynomial Regression……Page 242
9.5.3 Multiplicative Error……Page 243
9.5.4 Segmented Regression……Page 244
9.6 Logistic Regression……Page 245
9.7.1 Nonlinear Regression with Berkson Errors……Page 247
9.7.2 Logistic Regression with Berkson Errors……Page 249
9.7.3 Bronchitis Data……Page 250
9.8 Automatic Implementation……Page 252
9.8.1 Implementation and Simulations in WinBUGS……Page 253
9.8.2 More Complex Models……Page 256
9.9 Cervical Cancer and Herpes……Page 257
9.10 Framingham Data……Page 259
9.11 OPEN Data: A Variance Components Model……Page 260
Bibliographic Notes……Page 262
10.1.1 Simple Linear Regression, Normally Distributed X……Page 264
10.1.2 Analysis of Covariance……Page 267
10.1.4 Summary of Major Results……Page 269
10.2 The Regression Calibration Approximation……Page 270
10.2.3 Testing H0 : Btx, Bt z)t = 0……Page 271
10.4 Hypotheses about Subvectors of Bx and Bz……Page 272
10.4.1 Illustration: Framingham Data……Page 273
10.5 Efficient Score Tests of H0 : Bx = 0……Page 274
10.5.1 Generalized Score Tests……Page 275
Bibliographic Notes……Page 278
11.1.1 Simple Linear Mixed Models……Page 279
11.1.2 The General Linear Mixed Model……Page 280
11.1.4 The Generalized Linear Mixed Model……Page 281
11.2.1 The Variance Components Model Revisited……Page 282
11.2.3 Some Simple Examples……Page 283
11.3 A Bias-Corrected Estimator……Page 285
11.5 Regression Calibration for GLMMs……Page 287
11.7 Joint Modeling……Page 288
11.8.1 Models with Random E®ects Multiplied by X……Page 289
11.8.3 Inducing a True-Data Model from a Standard Observed Data Model……Page 290
11.8.4 Autoregressive Models in Longitudinal Data……Page 291
11.9 Example: The CHOICE Study……Page 292
11.9.2 Naive Replication and Sensitivity……Page 293
11.9.3 Accounting for Biological Variability……Page 294
Bibliographic Notes……Page 296
12.1.1 The Problem……Page 298
12.1.3 Methodology……Page 299
12.1.4 Properties of Deconvolution Methods……Page 300
12.1.5 Is It Possible to Estimate the Bandwidth?……Page 301
12.1.6 Parametric Deconvolution……Page 303
12.1.7 Estimating Distribution Functions……Page 306
12.1.8 Optimal Score Tests……Page 307
12.1.9 Framingham Data……Page 308
12.1.10 NHANES Data……Page 309
12.1.11 Bayesian Density Estimation by Normal Mixtures……Page 310
12.2.1 Local-Polynomial, Kernel-Weighted Regression……Page 312
12.2.2 Splines……Page 313
12.2.3 QVF and Likelihood Models……Page 314
12.2.4 SIMEX for Nonparametric Regression……Page 315
12.2.6 Structural Splines……Page 316
12.2.7 Taylex and Other Methods……Page 317
12.3 Baseline Change Example……Page 318
12.3.1 Discussion of the Baseline Change Controls Data……Page 320
Bibliographic Notes……Page 321
13.2 Additive Models……Page 322
13.3 MCMC for Additive Spline Models……Page 323
13.4 Monte Carlo EM-Algorithm……Page 324
13.4.3 The Algorithm……Page 325
13.5 Simulation with Classical Errors……Page 328
13.6 Simulation with Berkson Errors……Page 330
13.7 Semiparametrics: X Modeled Parametrically……Page 331
13.8.1 Deconvolution Methods……Page 333
13.8.2 Models Linear in Functions of X……Page 334
13.8.3 Linear Logistic Regression with Replicates……Page 335
13.8.4 Doubly Robust Parametric Modeling……Page 336
Bibliographic Notes……Page 337
14.1 Notation and Assumptions……Page 338
14.2 Induced Hazard Function……Page 339
14.3.1 Methodology and Asymptotic Properties……Page 340
14.3.2 Risk Set Calibration……Page 341
14.4 SIMEX for Survival Analysis……Page 342
14.5 Chronic Kidney Disease Progression……Page 343
14.5.1 Regression Calibration for CKD Progression……Page 344
14.5.2 SIMEX for CKD Progression……Page 345
14.6 Semi and Nonparametric Methods……Page 348
14.6.1 Nonparametric Estimation with Validation Data……Page 349
14.6.2 Nonparametric Estimation with Replicated Data……Page 351
14.6.3 Likelihood Estimation……Page 352
14.7 Likelihood Inference for Frailty Models……Page 355
Bibliographic Notes……Page 356
15.1 Response Error and Linear Regression……Page 358
15.2.1 Biased Responses……Page 362
15.2.2 Response Error in Heteroscedastic Regression……Page 363
15.3.1 The Impact of Response Misclassification……Page 364
15.3.2 Correcting for Response Misclassification……Page 366
15.4.1 General Likelihood Theory and Surrogates……Page 372
15.4.2 Validation Data……Page 373
15.5.1 Likelihood of the Validation Data……Page 374
15.6.1 Simple Random Sampling……Page 375
15.6.2 Other Types of Sampling……Page 376
Bibliographic Notes……Page 377
A.2 Normal and Lognormal Distributions……Page 378
A.3 Gamma and Inverse-Gamma Distributions……Page 379
A.4.1 Linear Prediction……Page 380
A.4.3 Nonlinear Prediction……Page 382
A.5.2 Maximum Likelihood Estimation……Page 383
A.5.4 Pro¯le Likelihood and Likelihood Ratio Con¯dence Intervals……Page 384
A.5.5 E±cient Score Tests……Page 385
A.6.1 Introduction and Basic Large Sample Theory……Page 386
A.6.2 Sandwich Formula Example: Linear Regression without Measurement Error……Page 388
A.6.3 Sandwich Method and Likelihood-Type Inference……Page 389
A.6.6 Stacking Estimating Equations: Using Prior Estimates of Some Parameters……Page 391
A.7.1 General Ideas……Page 393
A.7.2 Estimation and Inference for QVF Models……Page 394
A.9.1 Introduction……Page 396
A.9.2 Nonlinear Regression without Measurement Error……Page 397
A.9.4 Bootstrapping Logistic Regression Models……Page 399
A.9.5 Bootstrapping Measurement Error Models……Page 400
A.9.6 Bootstrap Con¯dence Intervals……Page 401
B.1 Appendix to Chapter 1: Power in Berkson and Classical Error Models……Page 403
B.2 Appendix to Chapter 3: Linear Regression and Attenuation……Page 404
B.3.1 Standard Errors and Replication……Page 405
B.3.3 Heuristics and Accuracy of the Approximations……Page 409
B.4 Appendix to Chapter 5: SIMEX……Page 410
B.4.1 Simulation Extrapolation Variance Estimation……Page 411
B.4.2 Estimating Equation Approach to Variance Estimation……Page 413
B.5.1 Derivation of the Estimators……Page 417
B.5.2 Asymptotic Distribution Approximations……Page 419
B.6.2 Technical Complements to Distribution Theory for Estimated §uu……Page 424
B.7.1 Monte Carlo Computation of Integrals……Page 425
B.7.2 Linear, Probit, and Logistic Regression……Page 426
B.8.1 Code for Section 9.8.1……Page 427
B.8.2 Code for Section 9.11……Page 428
References……Page 430
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