Wu / Tian Nonparametric Models for Longitudinal Data

With Implementation in R
1. Auflage 2018
ISBN: 978-0-429-93907-5
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 582 Seiten

Reihe: Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data.
This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences.
Features:

• Provides an overview of parametric and semiparametric methods • Shows smoothing methods for unstructured nonparametric models • Covers structured nonparametric models with time-varying coefficients • Discusses nonparametric shared-parameter and mixed-effects models • Presents nonparametric models for conditional distributions and functionals • Illustrates implementations using R software packages • Includes datasets and code in the authors’ website • Contains asymptotic results and theoretical derivations

Autoren/Hrsg.

Wu, Colin O.

Tian, Xin

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Introduction and Review

Introduction

Scientific Objectives of Longitudinal Studies
Data Structures and Examples
Structures of Longitudinal Data
Examples of Longitudinal Studies
Objectives of Longitudinal Analysis
Conditional-Mean Based Regression Models
Parametric Models
Semiparametric Models
Unstructured Nonparametric Models
Structured Nonparametric Models
Conditional-Distribution Based Models
Conditional Distribution Functions and Functionals
Parametric Distribution Models
Semiparametric Distribution Models
Unstructured Nonparametric Distribution Models
Structured Nonparametric Distribution Models
Review of Smoothing Methods
Local Smoothing Methods
Global Smoothing Methods
Introduction to R
Organization of the Book

Parametric and Semiparametric Methods

Linear Marginal and Mixed-Effects Models
Marginal Linear Models
The Linear Mixed-Effects Models
Conditional Maximum Likelihood Estimation
Maximum Likelihood Estimation
Restricted Maximum Likelihood Estimation
Likelihood based Inferences
Nonlinear Marginal and Mixed-Effects Models
Model Formulation and Interpretation
Likelihood-based Estimation and Inferences
Estimation of Subject-Specific Parameters
Semiparametric Partially Linear Models
Marginal Partially Linear Models
Mixed-Effects Partially Linear Models
Iterative Estimation Procedure
Profile Kernel Estimators
Semiparametric Estimation by Splines
R Implementation
The BMACS CD Data
The ENRICHD BDI Data
Remarks and Literature Notes

Unstructured Nonparametric Models

Kernel and Local Polynomial Methods

Least-Squares Kernel Estimators
Least-Squares Local Polynomial Estimators
Cross-Validation Bandwidths
The Leave-One-Subject-Out Cross-Validation
A Computation Procedure for Kernel Estimators
Heuristic Justification of Cross-Validation
Bootstrap Pointwise Confidence Intervals
Resampling-Subject Bootstrap Samples
Two Bootstrap Confidence Intervals
Simultaneous Confidence Bands
R Implementation
The HSCT Data
The BMACS CD Data
Asymptotic Properties of Kernel Estimators
Mean Squared Errors
Assumptions for Asymptotic Derivations
Asymptotic Risk Representations
Useful Special Cases
Remarks and Literature Notes

Basis Approximation Smoothing Methods

Estimation Method
Basis Approximations and Least Squares
Selecting Smoothing Parameters
Bootstrap Inference Procedures
Pointwise Confidence Intervals
Simultaneous Confidence Bands
Hypothesis Testing
R Implementation
The HSCT Data
The BMACS CD Data
Asymptotic Properties
Conditional Biases and Variances
Consistency of Basis Approximation Estimators
Consistency of B-Spline Estimators
Convergence Rates
Consistency of Goodness-of-Fit Test
Remarks and Literature Notes

Penalized Smoothing Spline Methods

Estimation Procedures
Penalized Least Squares Criteria
Penalized Smoothing Spline Estimator
Cross-Validation Smoothing Parameters
Bootstrap Pointwise Confidence Intervals
R Implementation
The HSCT Data
The NGHS BMI Data
Asymptotic Properties
Assumptions and Equivalent Kernel Function
Asymptotic Distributions, Risk and Inferences
Green’s Function for Uniform Density
Theoretical Derivations
Remarks and Literature Notes

Time-Varying Coefficient Models

Smoothing with Time-Invariant Covariates

Data Structure and Model Formulation
Data Structure
The Time-Varying Coefficient Model
A Useful Componentwise Representation
Componentwise Kernel Estimators
Construction of Estimators through Least Squares
Cross-Validation Bandwidth Choices
Componentwise Penalized Smoothing Splines
Estimators by Componentwise Roughness Penalty
Estimators by Combined Roughness Penalty
Cross-Validation Smoothing Parameters
Bootstrap Confidence Intervals
R Implementation
The BMACS CD Data
A Simulation Study
Asymptotic Properties for Kernel Estimators
Mean Squared Errors
Asymptotic Assumptions
Asymptotic Risk Representations
Remarks and Implications
Useful Special Cases
Theoretical Derivations
Asymptotic Properties for Smoothing Splines
Assumptions and Equivalent Kernel Functions
Asymptotic Distributions and Mean Squared Errors
Theoretical Derivations
Remarks and Literature Notes

The One-Step Local Smoothing Methods

Data Structure and Model Interpretations
Data Structure
Model Formulation
Model Interpretations
Remarks on Estimation Methods
Smoothing Based on Local Least Squares Criteria
General Formulation
Least Squares Kernel Estimators
Least Squares Local Linear Estimators
Smoothing with Centered Covariates
Cross-Validation Bandwidth Choice
Pointwise and Simultaneous Confidence Bands
Pointwise Confidence Intervals by Bootstrap
Simultaneous Confidence Bands
R Implementation
The NGHS BP Data
The BMACS CD Data
Asymptotic Properties for Kernel Estimators
Asymptotic Assumptions
Mean Squared Errors
Asymptotic Risk Representations
Asymptotic Distributions
Asymptotic Pointwise Confidence Intervals
Remarks and Literature Notes

The Two-Step Local Smoothing Methods

Overview and Justifications
Raw Estimators
General Expression and Properties
Component Expressions and Properties
Variance and Covariance Estimators
Refining the Raw Estimates by Smoothing
Rationales for Refining by Smoothing
The Smoothing Estimation Step
Bandwidth Choices
Pointwise and Simultaneous Confidence Bands
Pointwise Confidence Intervals by Bootstrap
Simultaneous Confidence Bands
R Implementation
The NGHS BP Data
Remark on the Asymptotic Properties
Remarks and Literature Notes

Global Smoothing Methods

Basis Approximation Model and Interpretations
Data Structure and Model Formulation
Basis Approximation
Remarks on Estimation Methods
Estimation Method
Approximate Least Squares
Remarks on Basis and Weight Choices
Least Squares B-Spline Estimators
Cross-Validation Smoothing Parameters
Conditional Biases and Variances
Estimation of Variance and Covariance Structures
Resampling-Subject Bootstrap Inferences
Pointwise Confidence Intervals
Simultaneous Confidence Bands
Hypothesis Testing for Constant Coefficients
R Implementation with the NGHS BP Data
Estimation by B-Splines
Testing Constant Coefficients
Asymptotic Properties
Integrated Squared Errors
Asymptotic Assumptions
Convergence Rates for Integrated Squared Errors
Theoretical Derivations
Consistent Hypothesis Tests
Remarks and Literature Notes

Shared-Parameter and Mixed-Effects Models

Models for Concomitant Interventions

Concomitant Interventions
Motivation for Outcome-Adaptive Covariate
Two Modeling Approaches
Data Structure with a Single Intervention
Naive Mixed-Effects Change-Point Models
Justifications for Chang-Point Models
Model Formulation and Interpretation
Biases of Naive Mixed-Effects Models
General Structure for Shared-Parameters
The Varying-Coefficient Mixed-Effects Models
Model Formulation and Interpretation
Special Cases of Conditional Mean Effects
Likelihood-Based Estimation
Least Squares Estimation
Estimation of the Covariances
The Shared-Parameter Change-Point Models
Model Formulation and Justifications
The Linear Shared-Parameter Change-Point Model
The Additive Shared-Parameter Change-Point Model
Likelihood-Based Estimation
Gaussian Shared-Parameter Change-Point Models
A Two-Stage Estimation Procedure
Confidence Intervals for Parameter Estimators
Asymptotic Confidence Intervals
Bootstrap Confidence Intervals
R Implementation to the ENRICHD Data
Varying-Coefficient Mixed-Effects Models
Shared-Parameter Change-Point Models
Asymptotic Consistency
The Varying-Coefficient Mixed-Effects Models
Maximum Likelihood Estimators
The Additive Shared-Parameter Models
Remarks and Literature Notes

Nonparametric Mixed-Effects Models

Objectives of Nonparametric Mixed-Effects Models
Data Structure and Model Formulation
Data Structure
Mixed-Effects Models without Covariates
Mixed-Effects Models with a Single Covariate
Extensions to Multiple Covariates
Estimation and Prediction without Covariates
Estimation with Known Covariance Matrix
Estimation with Unknown Covariance Matrix
Individual Trajectories
Cross-Validation Smoothing Parameters
Functional Principal Components Analysis
The Reduced Rank Model
Estimation of Eigenfunctions and Eigenvalues
Model Selection of Reduced Ranks
Estimation and Prediction with Covariates
Models without Covariate Measurement Error
Models with Covariate Measurement Error
R Implementation
The BMACS CD Data
The NGHS BP Data
Remarks and Literature Notes

Nonparametric Models for Distributions

Unstructured Models for Distributions

Objectives and General Setup
Objectives
Applications
Estimation of Conditional Distributions
Rank-Tracking Probability
Data Structure and Conditional Distributions
Data Structure
Conditional Distribution Functions
Conditional Quantiles
Rank-Tracking Probabilities
Rank-Tracking Probability Ratios
Continuous and Time-Varying Covariates
Estimation Methods
Conditional Distribution Functions
Conditional Cumulative Distribution Functions
Conditional Quantiles and Functionals
Rank-Tracking Probabilities
Cross-Validation Bandwidth Choices
Bootstrap Pointwise Confidence Intervals
R Implementation
The NGHS BMI Data
Asymptotic Properties
Asymptotic Assumptions
Asymptotic Mean Squared Errors
Theoretical Derivations
Remarks and Literature Notes

Time-Varying Transformation Models - I

Overview and Motivation
Data Structure and Model Formulation
Data Structure
The Time-Varying Transformation Models
Two-Step Estimation Method
Raw Estimates of Coefficients
Bias, Variance and Covariance of Raw Estimates
Smoothing Estimators
Bandwidth Choices
Bootstrap Confidence Intervals
Implementation and Numerical Results
The NGHS Data
Asymptotic Properties
Conditional Mean Squared Errors
Asymptotic Assumptions
Asymptotic Risk Expressions
Theoretical Derivations
Remarks and Literature Notes

Time-Varying Transformation Models -

Overview and Motivation
Data Structure and Distribution Functionals
Data Structure
Conditional Distribution Functions
Conditional Quantiles
Rank-Tracking Probabilities
Rank-Tracking Probability Ratios
The Time-Varying Transformation Models
Two-Step Estimation and Prediction Methods
Raw Estimators of Distribution Functions
Smoothing Estimators for Conditional CDFs
Smoothing Estimators for Quantiles
Estimation of Rank-Tracking Probabilities
Estimation of Rank-Tracking Probability Ratios
Bandwidth Choices
R Implementation
Conditional CDF for the NGHS SBP Data
RTP and RTPR for the NGHS SBP Data
Asymptotic Properties
Asymptotic Assumptions
Raw Baseline and Distribution Function Estimators
Local Polynomial Smoothing Estimators
Theoretical Derivations
Remarks and Literature Notes

Tracking with Mixed-Effects Models

Data Structure and Models
Data Structure
The Nonparametric Mixed-Effects Models
Conditional Distributions and Tracking Indices
Prediction and Estimation Methods
B-spline Prediction of Trajectories
Estimation with Predicted Outcome Trajectories
Estimation based on Split Samples
Bootstrap Pointwise Confidence Intervals
R Implementation with the NGHS Data
Rank-Tracking for BMI
Rank-Tracking for SBP
Remarks and Literature Notes

Bibliography

Index

Über Autor(innen)

Both authors are mathematical statisticians at the National Institutes of Health (NIH) and have published extensively in statistical and biomedical journals.
Colin O. Wu earned his Ph.D. in statistics from the University of California, Berkeley (1990), and is also Adjunct Professor at the Georgetown University School of Medicine. He served as Associate Editor for Biometrics and Statistics in Medicine, and reviewer for National Science Foundation, NIH, and the U.S. Department of Veterans Affairs.
Xin Tian earned her Ph.D. in statistics from Rutgers, the State University of New Jersey (2003). She has served on various NIH committees and collaborated extensively with clinical researchers.