Generalized Linear and Nonlinear Models for Correlated Data

Edward F. Vonesh

Description

Edward Vonesh's Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS is devoted to the analysis of correlated response data using SAS, with special emphasis on applications that require the use of generalized linear models or generalized nonlinear models. Written in a clear, easy-to-understand manner, it provides applied statisticians with the necessary theory, tools, and understanding to conduct complex analyses of continuous and/or discrete correlated data in a longitudinal or clustered data setting. Using numerous and complex examples, the book emphasizes real-world applications where the underlying model requires a nonlinear rather than linear formulation and compares and contrasts the various estimation techniques for both marginal and mixed-effects models. The SAS procedures MIXED, GENMOD, GLIMMIX, and NLMIXED as well as user-specified macros will be used extensively in these applications. In addition, the book provides detailed software code with most examples so that readers can begin applying the various techniques immediately.

This book is part of the SAS Press program.

Sujets

• Longitudinal study
• Cluster analysis
• Statistical model

Informations

• Publié par: SAS Institute
• Date de parution: 07 juillet 2014
• Nombre de lectures: 3
• EAN13: 9781629592305
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Generalized Linear and Nonlinear Models for Correlated Data
Theory and Applications Using SAS
Edward F. Vonesh
The correct bibliographic citation for this manual is as follows: Vonesh, Edward F. 2012. Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS . Cary, NC: SAS Institute Inc.
Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS
Copyright 2012, SAS Institute Inc., Cary, NC, USA
ISBN 978-1-62959-230-5
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Contents
Preface
Acknowledgments
1 Introduction
1.1 Correlated response data
1.1.1 Repeated measurements
1.1.2 Clustered data
1.1.3 Spatially correlated data
1.1.4 Multivariate data
1.2 Explanatory variables
1.3 Types of models
1.3.1 Marginal versus mixed-effects models
1.3.2 Models in SAS
1.3.3 Alternative approaches
1.4 Some examples
1.5 Summary features
I Linear Models
2 Marginal Linear Models - Normal Theory
2.1 The marginal linear model (LM)
2.1.1 Estimation
2.1.2 Inference and test statistics
2.2 Examples
2.2.1 Dental growth data
2.2.2 Bone mineral density data
2.2.3 ADEMEX adequacy data
2.2.4 MCM2 biomarker data
2.3 Summary
3 Linear Mixed-Effects Models - Normal Theory
3.1 The linear mixed-effects (LME) model
3.1.1 Features of the LME model
3.1.2 Estimation
3.1.3 Inference and test statistics
3.2 Examples
3.2.1 Dental growth data - continued
3.2.2 Bone mineral density data - continued
3.2.3 Estrogen levels in healthy premenopausal women
3.3 Summary
II Nonlinear Models
4 Generalized Linear and Nonlinear Models
4.1 The generalized linear model (GLIM)
4.1.1 Estimation and inference in the univariate case
4.2 The GLIM for correlated response data
4.2.1 Estimation
4.2.2 Inference and test statistics
4.2.3 Model selection and diagnostics
4.3 Examples of GLIM s
4.3.1 ADEMEX peritonitis infection data
4.3.2 Respiratory disorder data
4.3.3 Epileptic seizure data
4.3.4 Schizophrenia data
4.4 The generalized nonlinear model (GNLM)
4.4.1 Normal-theory nonlinear model (NLM)
4.4.2 Estimation
4.4.3 Inference and test statistics
4.5 Examples of GNLM s
4.5.1 LDH enzyme leakage data
4.5.2 Orange tree data
4.5.3 Respiratory disorder data - continued
4.5.4 Epileptic seizure data - continued
4.6 Computational considerations
4.6.1 Model parameterization and scaling
4.6.2 Starting values
4.7 Summary
5 Generalized Linear and Nonlinear Mixed-Effects Models
5.1 The generalized linear mixed-effects (GLME) model
5.1.1 Estimation
5.1.2 Comparing different estimators
5.1.3 Inference and test statistics
5.1.4 Model selection, goodness-of-fit and diagnostics
5.2 Examples of GLME models
5.2.1 Respiratory disorder data - continued
5.2.2 Epileptic seizure data - continued
5.2.3 Schizophrenia data - continued
5.2.4 ADEMEX hospitalization data
5.3 The generalized nonlinear mixed-effects (GNLME) model
5.3.1 Fully parametric GNLME models
5.3.2 Normal-theory nonlinear mixed-effects (NLME) model
5.3.3 Overcoming modeling limitations in SAS
5.3.4 Estimation
5.3.5 Comparing different estimators
5.3.6 Computational issues - starting values
5.3.7 Inference and test statistics
5.4 Examples of GNLME models
5.4.1 Orange tree data - continued
5.4.2 Soybean growth data
5.4.3 High flux hemodialyzer data
5.4.4 Cefamandole pharmacokinetic data
5.4.5 Epileptic seizure data - continued
5.5 Summary
III Further Topics
6 Missing Data in Longitudinal Clinical Trials
6.1 Background
6.2 Missing data mechanisms
6.2.1 Missing Completely at Random (MCAR)
6.2.2 Missing at Random (MAR)
6.2.3 Missing Not at Random (MNAR)
6.3 Dropout mechanisms
6.3.1 Ignorable versus non-ignorable dropout
6.3.2 Practical issues with missing data and dropout
6.3.3 Developing an analysis plan for missing data
6.4 Methods of analysis under MAR
6.4.1 Likelihood-based methods
6.4.2 Imputation-based methods
6.4.3 Inverse probability of weighting (IPW)
6.4.4 Example: A repeated measures ANCOVA
6.5 Sensitivity analysis under MNAR
6.5.1 Selection models
6.5.2 Pattern mixture models
6.5.3 Shared parameter (SP) models
6.5.4 A repeated measures ANCOVA - continued
6.6 Missing data - case studies
6.6.1 Bone mineral density data - continued
6.6.2 MDRD study - GFR data
6.6.3 Schizophrenia data - continued
6.7 Summary
7 Additional Topics and Applications
7.1 Mixed models with non-Gaussian random effects
7.1.1 ADEMEX peritonitis and hospitalization data
7.2 Pharmacokinetic applications
7.2.1 Theophylline data
7.2.2 Phenobarbital data
7.3 Joint modeling of longitudinal data and survival data
7.3.1 ADEMEX study - GFR data and survival
IV Appendices
A Some useful matrix notation and results
A.1 Matrix notation and results
B Additional results on estimation
B.1 The different estimators for mixed-effects models
B.2 Comparing large sample properties of the different estimators
C Datasets
C.1 Dental growth data
C.2 Bone mineral density data
C.3 ADEMEX adequacy data
C.4 MCM2 biomarker data
C.5 Estrogen hormone data
C.6 ADEMEX peritonitis and hospitalization data
C.7 Respiratory disorder data
C.8 Epileptic seizure data
C.9 Schizophrenia data
C.10 LDH enzyme leakage data
C.11 Orange tree data
C.12 Soybean growth data
C.13 High flux hemodialyzer data
C.14 Cefamandole pharmacokinetic data
C.15 MDRD data
C.16 Theophylline data
C.17 Phenobarbital data
C.18 ADEMEX GFR and survival data
D Select SAS macros
D.1 The GOF Macro
D.2 The GLIMMIX_GOF Macro
D.3 The CCC Macro
D.4 The CONCORR Macro
D.5 The COVPARMS Macro
D.6 The VECH Macro
Preface
In the science that is statistics, correlation is a term used to describe the kind and degree of relationship that exists between two or more variables. As such, correlated data occurs at various levels. Correlation can occur whenever two or more dependent variables (also referred to as response variables or outcome variables) are measured on the same individual or experimental unit. Such correlation is often classified and studied under the heading of multivariate analysis. However, even when restricted to a single response variable, correlation can occur when repeated measurements of the response are taken over time on individuals (longitudinal data), or when observations from individuals are grouped into distinct homogeneous clusters (clustered data), or when the spatial location of individual observations is taken into account (spatially correlated data). Correlation can also occur between two or more independent variables (also referred to as explanatory variables, predictor variables or covariates) as well as between dependent and independent variables.
Correlation betwe