Analysis of Longitudinal Data with Example

✍ Scribed by You-Gan Wang, Liya Fu, Sudhir Paul

• Publisher: CRC Press
• Year: 2022
• Tongue: English
• Leaves: 253
• Category: Library

✦ Synopsis

Development in methodology on longitudinal data is fast. Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. This book will present a discussion of the modern approaches to inference, including the links between the theories of estimators and various types of efficient statistical models including likelihood-based approaches. The theory will be supported with practical examples of R-codes and R-packages applied to interesting case-studies from a number of different areas.

Key Features:

•Includes the most up-to-date methods

•Use simple examples to demonstrate complex methods

•Uses real data from a number of areas

•Examples utilize R code

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
List of Figures
List of Tables
Preface
Author Bios
Contributors
Acknowledgment
1. Introduction
1.1. Longitudinal Studies
1.2. Notation
2. Examples and Organization of The Book
2.1. Examples for Longitudinal Studies
2.1.1. HIV Study
2.1.2. Progabide Study
2.1.3. Hormone Study
2.1.4. Teratology Studies
2.1.5. Schizophrenia Study
2.1.6. Labor Pain Study
2.1.7. Labor Market Experience
2.1.8. Water Quality Data
2.2. Organization of the Book
3. Model Framework and Its Components
3.1. Distributional Theory
3.1.1. Linear Exponential Distribution Family
3.1.2. Quadratic Exponential Distribution Family
3.1.3. Tilted Exponential Family
3.2. Quasi-Likelihood
3.3. Gaussian Likelihood
3.4. GLM and Mean Functions
3.5. Marginal Models
3.6. Modeling the Variance
3.7. Modeling the Correlation
3.8. Random Effects Models
4. Parameter Estimation
4.1. Likelihood Approach
4.2. Quasi-likelihood Approach
4.3. Gaussian Approach
4.4. Generalized Estimating Equations (GEE)
4.4.1. Estimation of Mean Parameters ß
4.4.2. Estimation of Variance Parameters τ
4.4.2.1. Gaussian Estimation
4.4.2.2. Extended Quasi-likelihood
4.4.2.3. Nonlinear Regression
4.4.2.4. Estimation of Scale Parameter ϕ
4.4.3. Estimation of Correlation Parameters
4.4.3.1. Stationary Correlation Structures
4.4.3.2. Generalized Markov Correlation Structure
4.4.3.3. Second Moment Method
4.4.3.4. Gaussian Estimation
4.4.3.5. Quasi Least-squares
4.4.3.6. Conditional Residual Method
4.4.3.7. Cholesky Decomposition
4.4.4. Covariance Matrix of ß
4.4.5. Example: Epileptic Data
4.4.6. Infeasibility
4.5. Quadratic Inference Function
5. Model Selection
5.1. Introduction
5.2. Selecting Covariates
5.2.1. Quasi-likelihood Criterion
5.2.2. Gaussian Likelihood Criterion
5.3. Selecting Correlation Structure
5.3.1. CIC Criterion
5.3.2. C(R) Criterion
5.3.3. Empirical Likelihood Criteria
5.4. Examples
5.4.1. Examples for Variable Selection
5.4.2. Examples for Correlation Structure Selection
6. Robust Approaches
6.1. Introduction
6.2. Rank-based Method
6.2.1. An Independence Working Model
6.2.2. A Weighted Method
6.2.3. Combined Method
6.2.4. A Method Based on GEE
6.2.5. Pediatric Pain Tolerance Study
6.3. Quantile Regression
6.3.1. An Independence Working Model
6.3.2. A Weighted Method Based on GEE
6.3.3. Modeling Correlation Matrix via Gaussian Copulas
6.3.3.1. Constructing Estimating Functions
6.3.3.2. Parameter and Covariance Matrix Estimation
6.3.4. Working Correlation Structure Selection
6.3.5. Analysis of Dental Data
6.4. Other Robust Methods
6.4.1. Score Function and Weighted Function
6.4.2. Main Algorithm
6.4.3. Choice of Tuning Parameters
7. Clustered Data Analysis
7.1. Introduction
7.1.1. Clustered Data
7.1.2. Intracluster Correlation
7.2. Analysis of Clustered Data: Continuous Responses
7.2.1. Inference for Intraclass Correlation from One-way Analysis of Variance
7.2.2. Inference for Intracluster Correlation from More General Settings
7.2.3. Maximum Likelihood Estimation of the Parameters
7.2.4. Asymptotic Variance
7.2.5. Inference for Intracluster Correlation Coefficient
7.2.6. Analysis of Clustered or Intralitter Data: Discrete Responses
7.2.7. The Models
7.2.8. Estimation
7.2.9. Inference
7.3. Some Examples
7.4. Regression Models for Multilevel Clustered Data
7.5. Two-Level Linear Models
7.6. An Example: Developmental Toxicity Study of Ethylene Glycol
7.7. Two-Level Generalized Linear Model
7.8. Rank Regression
7.8.1. National Cooperative Gallstone Study
7.8.2. Reproductive Study
8. Missing Data Analysis
8.1. Introduction
8.2. Missing Data Mechanism
8.3. Missing Data Patterns
8.4. Missing Data Methodologies
8.4.1. Missing Data Methodologies: The Methods of Imputation
8.4.1.1. Last Value Carried Forward Imputation
8.4.1.2. Imputation by Related Observation
8.4.1.3. Imputation by Unconditional Mean
8.4.1.4. Imputation by Conditional Mean
8.4.1.5. Hot Deck Imputation
8.4.1.6. Cold Deck Imputation
8.4.1.7. Imputation by Substitution
8.4.1.8. Regression Imputation
8.4.2. Missing Data Methodologies: Likelihood Methods
8.5. Analysis of Zero-inflated Count Data With Missing Values
8.5.1. Estimation of the Parameters with No Missing Data
8.5.2. Estimation of the Parameters with Missing Responses
8.5.2.1. Estimation under MCAR
8.5.2.2. Estimation under MAR
8.5.2.3. Estimation under MNAR
8.6. Analysis of Longitudinal DataWith Missing Values
8.6.1. Normally Distributed Data
8.6.2. Complete-data Estimation via the EM
8.6.3. Estimation with Nonignorable Missing Response Data (MAR and MNAR)
8.6.4. Generalized Estimating Equations
8.6.4.1. Introduction
8.6.4.2. Weighted GEE for MAR Data
8.6.5. Some Applications of the Weighted GEE
8.6.5.1. Weighted GEE for Binary Data
8.6.5.2. Two Modifications
9. Random Effects and Transitional Models
9.1. A General Discussion
9.2. Random Intercept Models
9.3. Linear Mixed Effects models
9.4. Generalized Linear Mixed Effects Models
9.4.1. The Logistic Random Effects Models
9.4.2. The Binomial Random Effects Models
9.4.3. The Poisson Random Effects Models
9.4.4. Examples: Estimation for European Red Mites Data and the Ames Salmonella Assay Data
9.5. Transition Models
9.6. Fitting Transition Models
9.7. Transition Model for Categorical Data
9.8. Further reading
10. Handing High Dimensional Longitudinal Data
10.1. Introduction
10.2. Penalized Methods
10.2.1. Penalized GEE
10.2.2. Penalized Robust GEE-type Methods
10.3. Smooth-threshold Method
10.4. Yeast Data Study
10.5. Further Reading
Bibliography
Author Index
Subject Index