Measurement Error in Nonlinear Models

Guide to Notation

Introduction
-The Double/Triple-Whammy of Measurement Error
-Classical Measurement Error A Nutrition Example
-Measurement Error Examples
-Radiation Epidemiology and Berkson Errors
-Classical Measurement Error Model Extensions
-Other Examples of Measurement Error Models
-Checking The Classical Error Model
-Loss of Power
-A Brief Tour
-Bibliographic Notes

Important Concepts
-Functional and Structural Models
-Models for Measurement Error
-Sources of Data
-Is There an “Exact" Predictor? What is Truth?
-Differential and Nondifferential Error
-Prediction
-Bibliographic Notes

Linear Regression and Attenuation
-Introduction
-Bias Caused by Measurement Error
-Multiple and Orthogonal Regression
-Correcting for Bias
-Bias Versus Variance
-Attenuation in General Problems
-Bibliographic Notes

Regression Calibration
-Overview
-The Regression Calibration Algorithm
-NHANES Example
-Estimating the Calibration Function Parameters
-Multiplicative Measurement Error
-Standard Errors
-Expanded Regression Calibration Models
-Examples of the Approximations
-Theoretical Examples
-Bibliographic Notes and Software

Simulation Extrapolation
-Overview
-Simulation Extrapolation Heuristics
-The SIMEX Algorithm
-Applications
-SIMEX in Some Important Special Cases
-Extensions and Related Methods
-Bibliographic Notes

Instrumental Variables
-Overview
-Instrumental Variables in Linear Models
-Approximate Instrumental Variable Estimation
-Adjusted Score Method
-Examples
-Other Methodologies
-Bibliographic Notes

Score Function Methods
-Overview
-Linear and Logistic Regression
-Conditional Score Functions
-Corrected Score Functions
-Computation and Asymptotic Approximations
-Comparison of Conditional and Corrected Scores
-Bibliographic Notes

Likelihood and Quasilikelihood
-Introduction
-Steps 2 and 3: Constructing Likelihoods
-Step 4: Numerical Computation of Likelihoods
-Cervical Cancer and Herpes
-Framingham Data
-Nevada Test Site Reanalysis
-Bronchitis Example
-Quasilikelihood and Variance Function Models
-Bibliographic Notes

Bayesian Methods
-Overview
-The Gibbs Sampler
-Metropolis-Hastings Algorithm
-Linear Regression
-Nonlinear Models
-Logistic Regression
-Berkson Errors
-Automatic implementation
-Cervical Cancer and Herpes
-Framingham Data
-OPEN Data: A Variance Components Model
-Bibliographic Notes

Hypothesis Testing
-Overview
-The Regression Calibration Approximation
-Illustration: OPEN Data
-Hypotheses about Sub-Vectors of βx and βz
-Efficient Score Tests of H0 : βx = 0
-Bibliographic Notes

Longitudinal Data and Mixed Models
-Mixed Models for Longitudinal Data
-Mixed Measurement Error Models
-A Bias Corrected Estimator
-SIMEX for GLMMEMs
-Regression Calibration for GLMMs
-Maximum Likelihood Estimation
-Joint Modeling
-Other Models and Applications
-Example: The CHOICE Study
-Bibliographic Notes

Nonparametric Estimation
-Deconvolution
-Nonparametric Regression
-Baseline Change Example
-Bibliographic Notes

Semiparametric Regression
-Overview
-Additive Models
-MCMC for Additive Spline Models
-Monte-Carlo EM-Algorithm
-Simulation with Classical Errors
-Simulation with Berkson Errors
-Semiparametrics: X Modeled Parametrically
-Parametric Models: No Assumptions on X
-Bibliographic Notes

Survival Data
-Notation and Assumptions
-Induced Hazard Function
-Regression Calibration for Survival Analysis
-SIMEX for Survival Analysis
-Chronic Kidney Disease Progression
-Semi and Nonparametric Methods
-Likelihood Inference for Frailty Models
-Bibliographic Notes

Response Variable Error
-Response Error and Linear Regression
-Other Forms of Additive Response Error
-Logistic Regression with Response Error
-Likelihood Methods
-Use of Complete Data Only
-Semiparametric Methods for Validation Data
-Bibliographic Notes

Appendix A: Background Material
-Overview
-Normal and Lognormal Distributions
-Gamma and Inverse Gamma Distributions
-Best and Best Linear Prediction and Regression
-Likelihood Methods
-Unbiased Estimating Equations
-Quasilikelihood and Variance Function Models (QVF)
-Generalized Linear Models
-Bootstrap Methods

Appendix B: Technical Details
-Appendix to Chapter 1: Power in Berkson and Classical Error Models
-Appendix to Chapter 3: Linear Regression and Attenuation
-Regression Calibration
-SIMEX
-Instrumental Variables
-Score Function Methods
-Likelihood and Quasilikelihood
-Bayesian Methods

References
Applications and Examples Index

Index