Nonparametric Models for Longitudinal Data : With Implementation in R

✍ Scribed by Tian, Xin; Wu, Colin O.

• Publisher: CRC Press
• Year: 2018
• Tongue: English
• Leaves: 583
• Series: Monographs on statistics and applied probability (Series) 159.
• Category: Library

✦ Synopsis

"This book covers the recent advancement of statistical methods for the analysis of longitudinal data. Real datasets from four large NIH-supported longitudinal clinical trials and epidemiological studies illustrate the practical applications of the statistical methods. This book focuses on the nonparametric approaches, which have gained tremendous popularity in biomedical studies. These approaches have the flexibility to answer many scientific questions that cannot be properly addressed by the existing parametric approaches, such as the linear and nonlinear mixed effects models."--Provided by publisher.  Read more...

✦ Table of Contents

Cover
Half title
MONOGRAPHS ON STATISTICS ANDAPPLIED PROBABILITY
Title
copyright
Dedication
Contents
List of Figures
List of Tables
Preface
About the Authors
I Introduction and Review
1 Introduction
1.1 Scientific Objectives of Longitudinal Studies
1.2 Data Structures and Examples
1.2.1 Structures of Longitudinal Data
1.2.2 Examples of Longitudinal Studies
1.2.3 Objectives of Longitudinal Analysis
1.3 Conditional-Mean Based Regression Models
1.3.1 Parametric Models
1.3.2 Semiparametric Models
1.3.3 Unstructured Nonparametric Models
1.3.4 Structured Nonparametric Models. 1.4 Conditional-Distribution Based Models1.4.1 Conditional Distribution Functions and Functionals
1.4.2 Parametric Distribution Models
1.4.3 Semiparametric Distribution Models
1.4.4 Unstructured Nonparametric Distribution Models
1.4.5 Structured Nonparametric Distribution Models
1.5 Review of Smoothing Methods
1.5.1 Local Smoothing Methods
1.5.2 Global Smoothing Methods
1.6 Introduction to R
1.7 Organization of the Book
2 Parametric and Semiparametric Methods
2.1 Linear Marginal and Mixed-Effects Models
2.1.1 Marginal Linear Models
2.1.2 The Linear Mixed-Effects Models. 2.1.3 Conditional Maximum Likelihood Estimation2.1.4 Maximum Likelihood Estimation
2.1.5 Restricted Maximum Likelihood Estimation
2.1.6 Likelihood-Based Inferences
2.2 Nonlinear Marginal and Mixed-Effects Models
2.2.1 Model Formulation and Interpretation
2.2.2 Likelihood-Based Estimation and Inferences
2.2.3 Estimation of Subject-Specific Parameters
2.3 Semiparametric Partially Linear Models
2.3.1 Marginal Partially Linear Models
2.3.2 Mixed-Effects Partially Linear Models
2.3.3 Iterative Estimation Procedure
2.3.4 Profile Kernel Estimators. 2.3.5 Semiparametric Estimation by Splines2.4 R Implementation
2.4.1 The BMACS CD4 Data
2.4.2 The ENRICHD BDI Data
2.5 Remarks and Literature Notes
II Unstructured Nonparametric Models
3 Kernel and Local Polynomial Methods
3.1 Least Squares Kernel Estimators
3.2 Least Squares Local Polynomial Estimators
3.3 Cross-Validation Bandwidths
3.3.1 The Leave-One-Subject-Out Cross-Validation
3.3.2 A Computation Procedure for Kernel Estimators
3.3.3 Heuristic Justification of Cross-Validation
3.4 Bootstrap Pointwise Confidence Intervals
3.4.1 Resampling-Subject Bootstrap Samples. 3.4.2 Two Bootstrap Confidence Intervals3.4.3 Simultaneous Confidence Bands
3.5 R Implementation
3.5.1 The HSCT Data
3.5.2 The BMACS CD4 Data
3.6 Asymptotic Properties of Kernel Estimators
3.6.1 Mean Squared Errors
3.6.2 Assumptions for Asymptotic Derivations
3.6.3 Asymptotic Risk Representations
3.6.4 Useful Special Cases
3.7 Remarks and Literature Notes
4 Basis Approximation Smoothing Methods
4.1 Estimation Method
4.1.1 Basis Approximations and Least Squares
4.1.2 Selecting Smoothing Parameters
4.2 Bootstrap Inference Procedures
4.2.1 Pointwise Confidence Intervals.

✦ Subjects

Psychology -- Methodology;Psychology -- Statistics;Biology -- Statistics;Mathematical statistics;MATHEMATICS -- Applied;MATHEMATICS -- Probability & Statistics -- General;Biology;Psychology