Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition,9781584886334

Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition

by ;
Edition: 2nd
ISBN13: 9781584886334
ISBN10: 1584886331
Format: Hardcover
Pub. Date: 2006-06-21
Publisher(s): Chapman & Hall/
List Price: $147.00

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Summary

It's been over a decade since the first edition of Measurement Error in Nonlinear Modelssplashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Editionhas been revamped and extensively updated to offer the most comprehensive and up-to-date survey of measurement error models currently available.What's new in the Second Edition?· Greatly expandeddiscussion and applications of Bayesian computation via Markov Chain Monte Carlo techniques· A new chapteron longitudinal data and mixed models· Athoroughly revisedchapter on nonparametric regression and density estimation· A totally newchapter on semiparametric regression· Survival analysis expandedinto its own separate chapter· Completely rewrittenchapter on score functions· Many moreexamples and illustrative graphs· Unique data setscompiled and made available onlineIn 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 Editionis your ideal source.

Table of Contents

1 INTRODUCTION
1(24)
1.1 The Double/Triple Whammy of Measurement Error
1(1)
1.2 Classical Measurement Error: A Nutrition Example
2(1)
1.3 Measurement Error Examples
3(1)
1.4 Radiation Epidemiology and Berkson Errors
4(3)
1.4.1 The Difference Between Berkson and Classical Errors: How to Gain More Power Without Really Trying
5(2)
1.5 Classical Measurement Error Model Extensions
7(2)
1.6 Other Examples of Measurement Error Models
9(5)
1.6.1 NHANES
9(1)
1.6.2 Nurses' Health Study
10(1)
1.6.3 The Atherosclerosis Risk in Communities Study
11(1)
1.6.4 Bioassay in a Herbicide Study
11(1)
1.6.5 Lung Function in Children
12(1)
1.6.6 Coronary Heart Disease and Blood Pressure
12(1)
1.6.7 A-Bomb Survivors Data
13(1)
1.6.8 Blood Pressure and Urinary Sodium Chloride
13(1)
1.6.9 Multiplicative Error for Confidentiality
14(1)
1.6.10 Cervical Cancer and Herpes Simplex Virus
14(1)
1.7 Checking the Classical Error Model
14(4)
1.8 Loss of Power
18(5)
1.8.1 Linear Regression Example
18(2)
1.8.2 Radiation Epidemiology Example
20(3)
1.9 A Brief Tour
23(1)
Bibliographic Notes
23(2)
2 IMPORTANT CONCEPTS
25(16)
2.1 Functional and Structural Models
25(1)
2.2 Models for Measurement Error
26(6)
2.2.1 General Approaches: Berkson and Classical Models
26(1)
2.2.2 Is It Berkson or Classical?
27(1)
2.2.3 Berkson Models from Classical
28(1)
2.2.4 Transportability of Models
29(1)
2.2.5 Potential Dangers of Transporting Models
30(2)
2.2.6 Semicontinuous Variables
32(1)
2.2.7 Misclassification of a Discrete Covariate
32(1)
2.3 Sources of Data
32(1)
2.4 Is There an "Exact" Predictor? What Is Truth?
33(3)
2.5 Differential and Nondifferential Error
36(2)
2.6 Prediction
38(1)
Bibliographic Notes
39(2)
3 LINEAR REGRESSION AND ATTENUATION
41(24)
3.1 introduction
41(1)
3.2 Bias Caused by Measurement Error
41(11)
3.2.1 Simple Linear Regression with Additive Error
42(2)
3.2.2 Regression Calibration: Classical Error as Berkson Error
44(1)
3.2.3 Simple Linear Regression with Berkson Error
45(1)
3.2.4 Simple Linear Regression, More Complex Error Structure
46(3)
3.2.5 Summary of Simple Linear Regression
49(3)
3.3 Multiple and Orthogonal Regression
52(3)
3.3.1 Multiple Regression: Single Covariate Measured with Error
52(1)
3.3.2 Multiple Covariates Measured with Error
53(2)
3.4 Correcting for Bias
55(5)
3.4.1 Method of Moments
55(2)
3.4.2 Orthogonal Regressions
57(3)
3.5 Bias Versus Variance
60(3)
3.5.1 Theoretical Bias Variance Tradeoff Calculations
61(2)
3.6 Attenuation in General Problems
63(1)
Bibliographic Notes
64(1)
4 REGRESSION CALIBRATION
65(32)
4.1 Overview
65(1)
4.2 The Regression Calibration Algorithm
66(1)
4.3 NHANES Example
66(4)
4.4 Estimating the Calibration Function Parameters
70(2)
4.4.1 Overview and First 'Methods
70(1)
4.4.2 Best Linear Approximations Using Replicate Data
70(2)
4.4.3 Alternatives When Using Partial Replicates
72(1)
4.4.4 James-Stein Calibration
72(1)
4.5 Multiplicative Measurement Error
72(7)
4.5.1 Should Predictors Be Transformed?
73(1)
4.5.2 Lognormal X and U
74(3)
4.5.3 Linear Regression
77(1)
4.5.4 Additive and Multiplicative Error
78(1)
4.6 Standard Errors
79(1)
4.7 Expanded Regression Calibration Models
79(11)
4.7.1 The Expanded Approximation Defined
81(2)
4.7.2 Implementation
83(2)
4.7.3 Bioassay Data
85(5)
4.8 Examples of the Approximations
90(4)
4.8.1 Linear Regression
90(1)
4.8.2 Logistic Regression
90(3)
4.8.3 Loglinear Mean Models
93(1)
4.9 Theoretical Examples
94(1)
4.9.1 Homoscedastic Regression
94(1)
4.9.2 Quadratic Regression with Homoscedastic Regression Calibration
94(1)
4.9.3 Loglinear Mean Model
95(1)
Bibliographic Notes and Software
95(2)
5 SIMULATION EXTRAPOLATION
97(32)
5.1 Overview
97(1)
5.2 Simulation Extrapolation Heuristics
98(2)
5.2.1 SIMEX in Simple Linear Regression
98(2)
5.3 The SIMEX Algorithm
100(12)
5.3.1 Simulation and Extrapolation Steps
100(8)
5.3.2 Extrapolant Function Considerations
108(2)
5.3.3 SIMEX Standard Errors
110(1)
5.3.4 Extensions and Refinements
111(1)
5.3.5 Multiple Covariates with Measurement Error
112(1)
5.4 Applications
112(8)
5.4.1 Framingham Heart Study
112(1)
5.4.2 Single Covariate Measured with Error
113(5)
5.4.3 Multiple Covariates Measured with Error
118(2)
5.5 SIMEX in Some Important Special Cases
120(3)
5.5.1 Multiple Linear Regression
120(2)
5.5.2 Loglinear Mean Models
122(1)
5.5.3 Quadratic Mean Models
122(1)
5.6 Extensions and Related Methods
123(5)
5.6.1 Mixture of Berkson arid Classical Error
123(2)
5.6.2 Misclassification SIMEX
125(1)
5.6.3 Checking Structural Model Robustness via Remeasurement
126(2)
Bibliographic Notes
128(1)
6 INSTRUMENTAL VARIABLES
129(22)
6.1 Overview
129(2)
6.1.1 A Note on Notation
130(1)
6.2 Instrumental Variables in Linear Models
131(6)
6.2.1 Instrumental Variables via Differentiation
131(1)
6.2.2 Simple Linear Regression with One Instrument
132(2)
6.2.3 Linear Regression with Multiple Instruments
134(3)
6.3 Approximate Instrumental Variable Estimation
137(3)
6.3.1 IV Assumptions
137(1)
6.3.2 Mean and Variance Function Models
138(1)
6.3.3 First Regression Calibration IV Algorithm
139(1)
6.3.4 Second Regression Calibration IV Algorithm
140(1)
6.4 Adjusted Score Method
140(3)
6.5 Examples
143(2)
6.5.1 Framingham Data
143(2)
6.5.2 Simulated Data
145(1)
6.6 Other Methodologies
145(3)
6.6.1 Hybrid Classical and Regression Calibration
145(2)
6.6.2 Error Model Approaches
147(1)
Bibliographic Notes
148(3)
7 SCORE FUNCTION METHODS
151(30)
7.1 Overview
151(1)
7.2 Linear and Logistic Regression
152(10)
7.2.1 Linear Regression Corrected and Conditional Scores
152(5)
7.2.2 Logistic Regression Corrected and Conditional Scores
157(2)
7.2.3 Framingham Data Example
159(3)
7.3 Conditional Score Functions
162(7)
7.3.1 Conditional Score Basic. Theory
162(2)
7.3.2 Conditional Scores for Basic Models
164(2)
7.3.3 Conditional Scores for More Complicated Models
166(3)
7.4 Corrected Score Functions
169(2)
7.4.1 Corrected Score Basic Theory
170(1)
7.4.2 Monte Carlo Corrected Scores
170(2)
7.4.3 Some Exact Corrected Scores
172(1)
7.4.4 SIMEX Connection
173(1)
7.4.5 Corrected Scores with Replicate Measurements
173
7.5 Computation and Asymptotic Approximations
171(6)
7.5.1 Known Measurement Error Variance
175(1)
7.5.2 Estimated Measurement Error Variance
176(1)
7.6 Comparison of Conditional and Corrected Scores
177(1)
7.7 Bibliographic Notes
178(1)
Bibliographic Notes
178(3)
8 LIKELIHOOD AND QUASILIKELIHOOD
181(24)
8.1 Introduction
181(3)
8.1.1 Step 1: The Likelihood If X Were Observable
183(1)
8.1.2 A General Concern: Identifiable Models
184(1)
8.2 Steps 2 and 3: Constructing Likelihoods
184(6)
8.2.1 The Discrete Case
185(1)
8.2.2 Likelihood Construction for General Error Models
186(2)
8.2.3 The Berkson Model
188(1)
8.2.4 Error Model Choice
189(1)
8.3 Step 4: Numerical Computation of Likelihoods
190(1)
8.4 Cervical Cancer and Herpes
190(2)
8.5 Framingham Data
192(1)
8.6 Nevada Test Site Reanalysis
193(4)
8.6.1 Regression Calibration Implementation
195(1)
8.6.2 Maximum Likelihood Implementation
196(1)
8.7 Bronchitis Example
197(4)
8.7.1 Calculating the Likelihood
198(1)
8.7.2 Effects of Measurement Error on Threshold Models
199(1)
8.7.3 Simulation Study and Maximum Likelihood
199(2)
8.7.4 Berkson Analysis of the Data
201(1)
8.8 Quasilikelihood and Variance Function Models
201(2)
8.8.1 Details of Step 3 for QVF Models
202(1)
8.8.2 Details of Step 4 for QVF Models
203(1)
Bibliographic Notes
203(2)
9 BAYESIAN METHODS 205(38)
9.1 Overview
205(4)
9.1.1 Problem Formulation
205(2)
9.1.2 Posterior Inference
207(1)
9.1.3 Bayesian Functional and Structural Models
208(1)
9.1.4 Modularity of Bayesian MCMC
209(1)
9.2 The Gibbs Sampler
209(2)
9.3 Metropolis—Hastings Algorithm
211(2)
9.4 Linear Regression
213(6)
9.4.1 Example
216(3)
9.5 Nonlinear Models
219(4)
9.5.1 A General Model
219(1)
9.5.2 Polynomial Regression
220(1)
9.5.3 Multiplicative Error
221(1)
9.5.4 Segmented Regression
222(1)
9.6 Logistic Regression
223(2)
9.7 Berkson Errors
225(5)
9.7.1 Nonlinear Regression with Berkson Errors
225(2)
9.7.2 Logistic Regression with Berkson Errors
227(1)
9.7.3 Bronchitis Data
228(2)
9.8 Automatic Implementation
230(5)
9.8.1 Implementation and Simulations in WinBUGS
231(3)
9.8.2 More Complex Models
234(1)
9.9 Cervical Cancer and Herpes
235(2)
9.10 Framingham Data
237(1)
9.11 OPEN Data: A Variance Components Model
238(2)
Bibliographic Notes
240(3)
10 HYPOTHESIS TESTING 243(16)
10.1 Overview
243(6)
10.1.1 Simple Linear Regression, Normally Distributed X
243(3)
10.1.2 Analysis of Covariance
246(2)
10.1.3 General Considerations: What Is a Valid Test?
248(1)
10.1.4 Summary of Major Results
248(1)
10.2 The Regression Calibration Approximation
249(2)
10.2.1 Testing H0 : βx = 0
250(1)
10.2.2 Testing H0 : βz = 0
250(1)
10.2.3 Testing H0 : (βtx,βtz)t = 0
250(1)
10.3 Illustration: OPEN Data
251(1)
10.4 Hypotheses about Subvectors of βx and βz
251(2)
10.4.1 Illustration: Framingham Data
252(1)
10.5 Efficient Score Tests of Ho : βx = 0
253(4)
10.5.1 Generalized Score Tests
254(3)
Bibliographic Notes
257(2)
11 LONGITUDINAL DATA AND MIXED MODELS 259(20)
11.1 Mixed Models for Longitudinal Data
259(3)
11.1.1 Simple Linear Mixed Models
259(1)
11.1.2 The General Linear Mixed Model
260(1)
11.1.3 The Linear Logistic Mixed Model
261(1)
11.1.4 The Generalized Linear Mixed Model
261(1)
11.2 Mixed Measurement Error Models
262(3)
11.2.1 The Variance Components Model Revisited
262(1)
11.2.2 General Considerations
263(1)
11.2.3 Some Simple Examples
263(2)
11.2.4 Models for Within-Subject X-Correlation
265(1)
11.3 A Bias-Corrected Estimator
265(2)
11.4 SIMEX for GLMMEMs
267(1)
11.5 Regression Calibration for GLMMs
267(1)
11.6 Maximum Likelihood Estimation
268(1)
11.7 Joint Modeling
268(1)
11.8 Other Models and Applications
269(3)
11.8.1 Models with Random Effects Multiplied by X
269(1)
11.8.2 Models with Random Effects Depending Nonlinearly on X
270(1)
11.8.3 Inducing a True-Data Model from a Standard Observed Data Model
270(1)
11.8.4 Autoregressive Models in Longitudinal Data
271(1)
11.9 Example: The CHOICE Study
272(4)
11.9.1 Basic Model
273(1)
11.9.2 Naive Replication and Sensitivity
273(1)
11.9.3 Accounting for Biological Variability
274(2)
Bibliographic Notes
276(3)
12 NONPARAMETRIC ESTIMATION 279(24)
12.1 Deconvolution
279(14)
12.1.1 The Problem
279(1)
12.1.2 Fourier Inversion
280(1)
12.1.3 Methodology
280(1)
12.1.4 Properties of Deconvolution Methods
281(1)
12.1.5 Is It Possible to Estimate the Bandwidth?
282(2)
12.1.6 Parametric Deconvolution
284(3)
12.1.7 Estimating Distribution Functions
287(1)
12.1.8 Optimal Score Tests
288(1)
12.1.9 Framingham Data
289(1)
12.1.10 N0NHANES Data
290(1)
12.1.11 Bayesian Density Estimation by Normal Mixtures
291(2)
12.2 Nonparametric Regression
293(6)
12.2.1 Local-Polynomial, Kernel-Weighted Regression
293(1)
12.2.2 Splines
294(1)
12.2.3 QVF and Likelihood Models
295(1)
12.2.4 SIMEX for Nonparametric Regression
296(1)
12.2.5 Regression Calibration
297(1)
12.2.6 Structural Splines
297(1)
12.2.7 Taylex and Other Methods
298(1)
12.3 Baseline Change Example
299(3)
12.3.1 Discussion of the Baseline Change Controls Data
301(1)
Bibliographic Notes
302(1)
13 SEMIPARAMETRIC REGRESSION 303(16)
13.1 Overview
303(1)
13.2 Additive Models
303(1)
13.3 MCMC for Additive Spline Models
304(1)
13.4 Monte Carlo EM-Algorithm
305(4)
13.4.1 Starting Values
306(1)
13.4.2 Metropolis Hastings Fact
306(1)
13.4.3 The Algorithm
306(3)
13.5 Simulation with Classical Errors
309(2)
13.6 Simulation with Berkson Errors
311(1)
13.7 Semiparametrics: X Modeled Parametrically
312(2)
13.8 Parametric Models: No Assumptions on X
314(4)
13.8.1 Deconvolution Methods
314(1)
13.8.2 Models Linear in Functions of X
315(1)
13.8.3 Linear Logistic Regression with Replicates
316(1)
13.8.4 Doubly Robust Parametric Modeling
317(1)
Bibliographic Notes
318(1)
14 SURVIVAL DATA 319(20)
14.1 Notation and Assumptions
319(1)
14.2 Induced Hazard Function
320(1)
14.3 Regression Calibration for Survival Analysis
321(2)
14.3.1 Methodology and Asymptotic Properties
321(1)
14.3.2 Risk Set Calibration
322(1)
14.4 SIMEX for Survival Analysis
323(1)
14.5 Chronic Kidney Disease Progression
324(5)
14.5.1 Regression Calibration: for CKD Progression
325(1)
14.5.2 SIMEX for CND Progression
326(3)
14.6 Semi and Nonparametric Methods
329(1)
14.6.1 Nonparametric Estimation with Validation Data
330(2)
14.6.2 Nonparametric Estimation with Replicated Data
332(1)
14.6.3 Likelihood Estimation
333
14.7 Likelihood Inference for Frailty Models
330(7)
Bibliographic Notes
337(2)
15 RESPONSE VARIABLE ERROR 339(20)
15.1 Response Error and Linear Regression
339(4)
15.2 Other Forms of Additive Response terror
343(2)
15.2.1 Biased Responses
343(1)
15.2.2 Response Error in Heteroscedastic Regression
344(1)
15.3 Logistic Regression with Response Error
345(8)
15.3.1 The Impact of Response Misclassification
345(2)
15.3.2 Correcting for Response Misclassification
347(6)
15.1 Likelihood Methods
353(2)
15.4.1 General Likelihood Theory and Surrogates
353(1)
15.4.2 Validation Data
354(1)
15.5 Use of Complete Data Only
355(1)
15.5.1 Likelihood of the Validation Data
355(1)
15.5.2 Other Methods
356(1)
15.6 Semiparametric Methods for Validation Data
356(2)
15.6.1 Simple Random Sampling
356(1)
15.6.2 Other Types of Sampling
357(1)
Bibliographic Notes
358(1)
A BACKGROUND MATERIAL 359(26)
A.1 Overview
359(1)
A.2 Normal and Lognormal Distributions
359(1)
A.3 Gamma and Inverse-Gamma Distributions
360(1)
A.4 Best and Best Linear Prediction and Regression
361(3)
A.4.1 Linear Prediction
361(2)
A.4.2 Best Linear Prediction without an Intercept
363(1)
A.4.3 Nonlinear Prediction
363(1)
A.5 Likelihood Methods
364(3)
A.5.1 Notation
364(1)
A.5.2 Maximum Likelihood Estimation
364(1)
A.5.3 Likelihood Ratio Tests
365(1)
A.5.4 Profile Likelihood and Likelihood Ratio Confidence Intervals
365(1)
A.5.5 Efficient Score Tests
366(1)
A.6 Unbiased Estimating Equations
367(7)
A.6.1 Introduction and Basic Large Sample Theory
367(2)
A.6.2 Sandwich Formula Example: Linear Regression without Measurement Error
369(1)
A.6.3 Sandwich Method and Likelihood-Type Inference
370(2)
A.6.4 Unbiased, but Conditionally Biased, Estimating Equations
372(1)
A.6.5 Biased Estimating Equations
372(1)
A.6.6 Stacking Estimating Equations: Using Prior Estimates of Some Parameters
372(2)
A.7 Quasilikelihood and Variance Function Models (QVF)
374(3)
A.7.1 General Ideas
374(1)
A.7.2 Estimation and Inference for QVF Models
375(2)
A.8 Generalized Linear Models
377(1)
A.9 Bootstrap Methods
377(8)
A.9.1 Introduction
377(1)
A.9.2 Nonlinear Regression without Measurement Error
378(2)
A.9.3 Bootstrapping Heteroscedastic Regression Models
380(1)
A.9.4 Bootstrapping Logistic Regression Models
380(1)
A.9.5 Bootstrapping Measurement Error Models
381(1)
A.9.6 Bootstrap Confidence Intervals
382(3)
B TECHNICAL DETAILS 385(28)
B.1 Appendix to Chapter 1: Power in Berkson and Classical Error Models
385(1)
B.2 Appendix to Chapter 3: Linear Regression and Attenuation
386(1)
B.3 Appendix to Chapter 4: Regression Calibration
387(5)
B.3.1 Standard Errors and Replication
387(4)
B.3.2 Quadratic Regression: Details of the Expanded Calibration Model
391(1)
B.3.3 Heuristics and Accuracy of the Approximations
391(1)
B.4 Appendix to Chapter 5: SIMEX
392(7)
B.4.1 Simulation Extrapolation Variance Estimation
393(2)
B.4.2 Estimating Equation Approach to Variance Estimation
395(4)
B.5 Appendix to Chapter 6: Instrumental Variables
399(7)
B.5.1 Derivation of the Estimators
399(2)
B.5.2 Asymptotic Distribution Approximations
401(5)
B.6 Appendix to Chapter 7: Score Function Methods
406(1)
B.6.1 Technical Complements to Conditional Score Theory
406(1)
B.6.2 Technical Complements to Distribution Theory for Estimated Σuu
406(1)
B.7 Appendix to Chapter 8: Likelihood and Quasilikelihood
407(2)
B.7.1 Monte Carlo Computation of Integrals
407(1)
B.7.2 Linear, Probit, and Logistic Regression
408(1)
B.8 Appendix to Chapter 9: Bayesian Methods
409(4)
B.8.1 Code for Section 9.8.1
409(1)
B.8.2 Code for Section 9.11
410(3)
References 413(26)
Applications and Examples Index 439(2)
Author Index 441(6)
Subject Index 447

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