Wu H., Zhang J.-T. Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches

N Y: John Wiley & Sons, 2006. — 402 p. — (Wiley Series in Probality and Statistics). — ISBN: 978-0-471-48350-2.Incorporates mixed-effects modeling techniques for more powerful and efficient methodsThis book presents current and effective nonparametric regression techniques for longitudinal data analysis and systematically investigates the incorporation of mixed-effects modeling techniques into various nonparametric regression models. The authors emphasize modeling ideas and inference methodologies, although some theoretical results for the justification of the proposed methods are presented.With its logical structure and organization, beginning with basic principles, the text develops the foundation needed to master advanced principles and applications. Following a brief overview, data examples from biomedical research studies are presented and point to the need for nonparametric regression analysis approaches. Next, the authors review mixed-effects models and nonparametric regression models, which are the two key building blocks of the proposed modeling techniques.The core section of the book consists of four chapters dedicated to the major nonparametric regression methods: local polynomial, regression spline, smoothing spline, and penalized spline. The next two chapters extend these modeling techniques to semiparametric and time varying coefficient models for longitudinal data analysis. The final chapter examines discrete longitudinal data modeling and analysis.Each chapter concludes with a summary that highlights key points and also provides bibliographic notes that point to additional sources for further study. Examples of data analysis from biomedical research are used to illustrate the methodologies contained throughout the book.Technical proofs are presented in separate appendices.With its focus on solving problems, this is an excellent textbook for upper-level undergraduate and graduate courses in longitudinal data analysis. It is also recommended as a reference for biostatisticians and other theoretical and applied research statisticians with an interest in longitudinal data analysis. Not only do readers gain an understanding of the principles of various nonparametric regression methods, but they also gain a practical understanding of how to use the methods to tackle real-world problems.AcronymsMotivating Longitudinal Data Examples
Progesterone Data
ACTG Data
MACS Data
Parametric Mixed-Effects Models
Nonparametric Regression and Smoothing
Nonparametric Mixed-Effects Models
Building Blocks of the NPME Models
Fundamental Development of the NPME Models
Further Extensions of the NPME Models
Bibliographical NotesModel Specification
Estimation of Fixed and Random-Effects
Bayesian Interpretation
Estimation of Variance Components
The EM-Algorithms
Two-Stage Method
First-Order Linearization Method
Conditional First-Order Linearization Method
Generalized Linear Mixed-Effects Model
Examples of GLME Model
Summary and Bibliographical Notes
Appendix: ProofsGeneral Degree LPK Smoother
Local Constant and Linear Smoothers
Kernel Function
Bandwidth Selection
An Illustrative Example
Regression Splines
Truncated Power Basis
Regression Spline Smoother
Selection of Number and Location of Knots
Smoothing Splines
Cubic Smoothing Splines
General Degree Smoothing Splines
Connection between a Smoothing Spline and a LME Model
Connection between a Smoothing Spline and a State-Space Model
Choice of Smoothing Parameters
Penalized Spline Smoother
Extension
Methods for Smoothing Parameter Selection
Goodness of Fit
Cross-Validation
Generalized Cross-Validation
Akaike Information Criterion
Summary and Bibliographical NotesNonparametric Population Mean Model
Naive Local Polynomial Kernel Method
Local Polynomial Kernel GEE Method
Fan-Zhang 's Two-step Method
Nonparametric Mixed-Effects Model
Local Polynomial Approximation
Local Likelihood Approach
Local Marginal Likelihood Estimation
Local Joint Likelihood Estimation
Component Estimation
A Special Case: Local Constant Mixed-Effects Model
Leave-One-Subject-Out Cross-Validation
Bandwidth Selection Strategies
LPME Backfitting Algorithm
Asymptotical Properties of the LPME Estimators
Finite Sample Properties of the LPME Estimators
Comparison of the LPME Estimators in Section
Comparison of Different Smoothing Methods
Comparisons of BCHB-Based versus Backfitting-Based LPME Estimators
Application to the Progesterone Data
Summary and Bibliographical Notes
Conditions
ProofsNaive Regression Splines
The NRS Smoother
Variability Band Construction
Choice of the Bases
Selection of the Number of Basis Functions
Example and Model Checking
Comparing GCV against SCV
The GRS Smoother
Variability Band Construction
Estimating the Covariance Structure
Mixed-Effects Regression Splines
Fits and Smoother Matrices
Variability Band Construction
No-Effect Test
Choice of the Number of Basis Functions
Example and Model Checking
Comparison via the ACTG Data
Comparison via Simulations
Summary and Bibliographical Notes
Appendix: ProofsNaive Smoothing Splines
Cubic NSS Estimator
Cubic NSS Estimator for Panel Data
Choice of the Smoothing Parameter
NSS Fit as BLUP of a LME Model
Model Checking
Constructing a Cubic GSS Estimator
Choice of the Smoothing Parameter
Subject-Specific Curve Fitting
The ESS Estimators
ESS Fits as BLUPs of a LME Model
Mixed-Effects Smoothing Splines
The Cubic MESS Estimators
Bayesian Interpretation
Variance Components Estimation
Fits and Smoother Matrices
Variability Band Construction
Choice of the Smoothing Parameters
Application to the Conceptive Progesterone Data
General Degree NSS
General Degree ESS
General Degree MESS
Summary and Bibliographical Notes
Appendix: ProofsNaive P-Splines
The NPS Smoother
NPS Fits and Smoother Matrix
Degrees of Freedom
Smoothing Parameter Selection
Choice of the Number of Knots
NPS Fit as BLUP of a LME Model
Degrees of Freedom
GPS Fit as BLUP of a LME Model
Subject-Specific Curve Fitting
EPS Fits as BLUPs of a LME Model
Mixed-Effects P-Splines
The MEPS Smoothers
Bayesian Interpretation
Variance Components Estimation
Variability Band Construction
Choice of the Smoothing Parameters
Choosing the Numbers of Knots
Summary and Bibliographical Notes
Appendix: ProofsModel Specification
Local Polynomial Method
Penalized Spline Method
Smoothing Spline Method
Methods Involving No Smoothing
MACS Data
Model Specification
Local Polynomial Method
Regression Spline Method
Penalized Spline Method
Smoothing Spline Method
ACTG Data Revisited
MACS Data Revisted
ModeI Specification
Wu and Zhang's Approach
Ke and Wang's Approach
Generalizations of Ke and Wang 's Approach
Summary and Bibliographical NotesTime-Varying Coefficient NPM Model
Local Polynomial KerneI Method
Regression Spline Method
Penalized Spline Method
Smoothing Spline Method
Smoothing Parameter Selection
Backfitting Algorithm
Two-Step Method
TVC-NPM Models with Time-Independent Covariates
MACS Data
Progesterone Data
Time-Varying Coefficient SPM Model
Time-Varying Coefficient NPME Model
Local Polynomial Method
Regression Spline Method
Penalized Spline Method
Smoothing Spline Method
Backfitting Algorithms
MACS Data Revisted
Progesterone Data Revisted
Backfitting Algorithm
Summary and Bibliographical NotesGeneralized NPM Model
Generalized SPM Model
Generalized NPME Model
Penalized Local Polynomial Estimation
Bandwidth Selection
Implementation
Asymptotic Theory
Application to an AIDS Clinical Study
Generalized TVC-NPME Model
Generalized SAME Model
Summary and Bibliographical Notes
Appendix: Proofs