Measurement error in nonlinear models: a modern perspective

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 ssx and ssz Efficient Score Tests of H0 : ssx = 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