Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS

Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS

by Edward F. Vonesh
Released September 2012
Publisher(s): SAS Institute
ISBN: 9781599946474

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Book description

Edward F. 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.

Table of contents

  1. Preface
  2. Acknowledgments
    1. 1 Introduction
      1. 1.1 Correlated response data
        1. 1.1.1 Repeated measurements
        2. 1.1.2 Clustered data
        3. 1.1.3 Spatially correlated data
        4. 1.1.4 Multivariate data
      2. 1.2 Explanatory variables
      3. 1.3 Types of models
        1. 1.3.1 Marginal versus mixed-effects models
        2. 1.3.2 Models in SAS
        3. 1.3.3 Alternative approaches
      4. 1.4 Some examples
      5. 1.5 Summary features
  3. I Linear Models
    1. 2 Marginal Linear Models - Normal Theory
      1. 2.1 The marginal linear model (LM)
        1. 2.1.1 Estimation
        2. 2.1.2 Inference and test statistics
      2. 2.2 Examples
        1. 2.2.1 Dental growth data
        2. 2.2.2 Bone mineral density data
        3. 2.2.3 ADEMEX adequacy data
        4. 2.2.4 MCM2 biomarker data
      3. 2.3 Summary
    2. 3 Linear Mixed-Effects Models - Normal Theory
      1. 3.1 The linear mixed-effects (LME) model
        1. 3.1.1 Features of the LME model
        2. 3.1.2 Estimation
        3. 3.1.3 Inference and test statistics
      2. 3.2 Examples
        1. 3.2.1 Dental growth data - continued
        2. 3.2.2 Bone mineral density data - continued
        3. 3.2.3 Estrogen levels in healthy premenopausal women
      3. 3.3 Summary
  4. II Nonlinear Models
    1. 4 Generalized Linear and Nonlinear Models
      1. 4.1 The generalized linear model (GLIM)
        1. 4.1.1 Estimation and inference in the univariate case
      2. 4.2 The GLIM for correlated response data
        1. 4.2.1 Estimation
        2. 4.2.2 Inference and test statistics
        3. 4.2.3 Model selection and diagnostics
      3. 4.3 Examples of GLIM's
        1. 4.3.1 ADEMEX peritonitis infection data
        2. 4.3.2 Respiratory disorder data
        3. 4.3.3 Epileptic seizure data
        4. 4.3.4 Schizophrenia data
      4. 4.4 The generalized nonlinear model (GNLM)
        1. 4.4.1 Normal-theory nonlinear model (NLM)
        2. 4.4.2 Estimation
        3. 4.4.3 Inference and test statistics
      5. 4.5 Examples of GNLM's
        1. 4.5.1 LDH enzyme leakage data
        2. 4.5.2 Orange tree data
        3. 4.5.3 Respiratory disorder data - continued
        4. 4.5.4 Epileptic seizure data - continued
      6. 4.6 Computational considerations
        1. 4.6.1 Model parameterization and scaling
        2. 4.6.2 Starting values
      7. 4.7 Summary
    2. 5 Generalized Linear and Nonlinear Mixed-Effects Models
      1. 5.1 The generalized linear mixed-effects (GLME) model
        1. 5.1.1 Estimation
        2. 5.1.2 Comparing different estimators
        3. 5.1.3 Inference and test statistics
        4. 5.1.4 Model selection, goodness-of-fit and diagnostics
      2. 5.2 Examples of GLME models
        1. 5.2.1 Respiratory disorder data - continued
        2. 5.2.2 Epileptic seizure data - continued
        3. 5.2.3 Schizophrenia data - continued
        4. 5.2.4 ADEMEX hospitalization data
      3. 5.3 The generalized nonlinear mixed-effects (GNLME) model
        1. 5.3.1 Fully parametric GNLME models
        2. 5.3.2 Normal-theory nonlinear mixed-effects (NLME) model
        3. 5.3.3 Overcoming modeling limitations in SAS
        4. 5.3.4 Estimation
        5. 5.3.5 Comparing different estimators
        6. 5.3.6 Computational issues - starting values
        7. 5.3.7 Inference and test statistics
      4. 5.4 Examples of GNLME models
        1. 5.4.1 Orange tree data - continued
        2. 5.4.2 Soybean growth data
        3. 5.4.3 High flux hemodialyzer data
        4. 5.4.4 Cefamandole pharmacokinetic data
        5. 5.4.5 Epileptic seizure data - continued
      5. 5.5 Summary
  5. III Further Topics
    1. 6 Missing Data in Longitudinal Clinical Trials
      1. 6.1 Background
      2. 6.2 Missing data mechanisms
        1. 6.2.1 Missing Completely at Random (MCAR)
        2. 6.2.2 Missing at Random (MAR)
        3. 6.2.3 Missing Not at Random (MNAR)
      3. 6.3 Dropout mechanisms
        1. 6.3.1 Ignorable versus non-ignorable dropout
        2. 6.3.2 Practical issues with missing data and dropout
        3. 6.3.3 Developing an analysis plan for missing data
      4. 6.4 Methods of analysis under MAR
        1. 6.4.1 Likelihood-based methods
        2. 6.4.2 Imputation-based methods
        3. 6.4.3 Inverse probability of weighting (IPW)
        4. 6.4.4 Example: A repeated measures ANCOVA
      5. 6.5 Sensitivity analysis under MNAR
        1. 6.5.1 Selection models
        2. 6.5.2 Pattern mixture models
        3. 6.5.3 Shared parameter (SP) models
        4. 6.5.4 A repeated measures ANCOVA - continued
      6. 6.6 Missing data - case studies
        1. 6.6.1 Bone mineral density data - continued
        2. 6.6.2 MDRD study - GFR data
        3. 6.6.3 Schizophrenia data - continued
      7. 6.7 Summary
    2. 7 Additional Topics and Applications
      1. 7.1 Mixed models with non-Gaussian random effects
        1. 7.1.1 ADEMEX peritonitis and hospitalization data
      2. 7.2 Pharmacokinetic applications
        1. 7.2.1 Theophylline data
        2. 7.2.2 Phenobarbital data
      3. 7.3 Joint modeling of longitudinal data and survival data
        1. 7.3.1 ADEMEX study - GFR data and survival
  6. IV Appendices
    1. A Some useful matrix notation and results
      1. A.1 Matrix notation and results
    2. B Additional results on estimation
      1. B.1 The different estimators for mixed-effects models
      2. B.2 Comparing large sample properties of the different estimators
    3. C Datasets
      1. C.1 Dental growth data
      2. C.2 Bone mineral density data
      3. C.3 ADEMEX adequacy data
      4. C.4 MCM2 biomarker data
      5. C.5 Estrogen hormone data
      6. C.6 ADEMEX peritonitis and hospitalization data
      7. C.7 Respiratory disorder data
      8. C.8 Epileptic seizure data
      9. C.9 Schizophrenia data
      10. C.10 LDH enzyme leakage data
      11. C.11 Orange tree data
      12. C.12 Soybean growth data
      13. C.13 High flux hemodialyzer data
      14. C.14 Cefamandole pharmacokinetic data
      15. C.15 MDRD data
      16. C.16 Theophylline data
      17. C.17 Phenobarbital data
      18. C.18 ADEMEX GFR and survival data
    4. D Select SAS macros
      1. D.1 The GOF Macro
      2. D.2 The GLIMMIX_GOF Macro
      3. D.3 The CCC Macro
      4. D.4 The CONCORR Macro
      5. D.5 The COVPARMS Macro
      6. D.6 The VECH Macro

Product information

  • Title: Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS
  • Author(s): Edward F. Vonesh
  • Release date: September 2012
  • Publisher(s): SAS Institute
  • ISBN: 9781599946474