Applied mixed models in medicine /

Applied mixed models in medicine /

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Bibliographic Details
Author / Creator:Brown, Helen.
Imprint:Chichester ; New York : J. Wiley, c1999.
Description:xx, 408 p. : ill. ; 24 cm.
Language:English
Series:Statistics in practice
Statistics in practice)
Subject:
Medicine -- Research -- Statistical methods.
Medicine -- Mathematical models.
Statistics.
Medicine.
Statistics -- methods.
Models, Statistical.
Medicine -- Mathematical models.
Medicine -- Research -- Statistical methods.
Statistics.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4217302
Hidden Bibliographic Details
Other authors / contributors:Prescott, Robin.
ISBN:0471965545 (alk. paper)
Notes:Includes bibliographical references (p. 387-390) and index.
Table of Contents:
  • Preface to Second Edition
  • Mixed Model Notations
  • 1. Introduction
  • 1.1. The Use of Mixed Models
  • 1.2. Introductory Example
  • 1.2.1. Simple model to assess the effects of treatment (Model A)
  • 1.2.2. A model taking patient effects into account (Model B)
  • 1.2.3. Random effects model (Model C)
  • 1.2.4. Estimation (or prediction) of random effects
  • 1.3. A Multi-Centre Hypertension Trial
  • 1.3.1. Modelling the data
  • 1.3.2. Including a baseline covariate (Model B)
  • 1.3.3. Modelling centre effects (Model C)
  • 1.3.4. Including centre-by-treatment interaction effects (Model D)
  • 1.3.5. Modelling centre and centre-treatment effects as random (Model E)
  • 1.4. Repeated Measures Data
  • 1.4.1. Covariance pattern models
  • 1.4.2. Random coefficients models
  • 1.5. More about Mixed Models
  • 1.5.1. What is a mixed model
  • 1.5.2. Why use mixed models
  • 1.5.3. Communicating results
  • 1.5.4. Mixed models in medicine
  • 1.5.5. Mixed models in perspective
  • 1.6. Some Useful Definitions
  • 1.6.1. Containment
  • 1.6.2. Balance
  • 1.6.3. Error strata
  • 2. Normal Mixed Models
  • 2.1. Model Definition
  • 2.1.1. The fixed effects model
  • 2.1.2. The mixed model
  • 2.1.3. The random effects model covariance structure
  • 2.1.4. The random coefficients model covariance structure
  • 2.1.5. The covariance pattern model covariance structure
  • 2.2. Model Fitting Methods
  • 2.2.1. The likelihood function and approaches to its maximisation
  • 2.2.2. Estimation of fixed effects
  • 2.2.3. Estimation (or prediction) of random effects and coefficients
  • 2.2.4. Estimation of variance parameters
  • 2.3. The Bayesian Approach
  • 2.3.1. Introduction
  • 2.3.2. Determining the posterior density
  • 2.3.3. Parameter estimation, probability intervals and p-values
  • 2.3.4. Specifying non-informative prior distributions
  • 2.3.5. Evaluating the posterior distribution
  • 2.4. Practical Application and Interpretation
  • 2.4.1. Negative variance components
  • 2.4.2. Accuracy of variance parameters
  • 2.4.3. Bias in fixed and random effects standard errors
  • 2.4.4. Significance testing
  • 2.4.5. Confidence intervals
  • 2.4.6. Model checking
  • 2.4.7. Missing data
  • 2.5. Example
  • 2.5.1. Analysis models
  • 2.5.2. Results
  • 2.5.3. Discussion of points from Section 2.4
  • 3. Generalised Linear Mixed Models
  • 3.1. Generalised Linear Models
  • 3.1.1. Introduction
  • 3.1.2. Distributions
  • 3.1.3. The general form for exponential distributions
  • 3.1.4. The GLM definition
  • 3.1.5. Fitting the GLM
  • 3.1.6. Expressing individual distributions in the general exponential form
  • 3.1.7. Conditional logistic regression
  • 3.2. Generalised Linear Mixed Models
  • 3.2.1. The GLMM definition
  • 3.2.2. The likelihood and quasi-likelihood functions
  • 3.2.3. Fitting the GLMM
  • 3.3. Practical Application and Interpretation
  • 3.3.1. Specifying binary data
  • 3.3.2. Uniform effects categories
  • 3.3.3. Negative variance components
  • 3.3.4. Fixed and random effects estimates
  • 3.3.5. Accuracy of variance parameters and random effects shrinkage
  • 3.3.6. Bias in fixed and random effects standard errors
  • 3.3.7. The dispersion parameter
  • 3.3.8. Significance testing
  • 3.3.9. Confidence intervals
  • 3.3.10. Model checking
  • 3.4. Example
  • 3.4.1. Introduction and models fitted
  • 3.4.2. Results
  • 3.4.3. Discussion of points from Section 3.3
  • 4. Mixed Models for Categorical Data
  • 4.1. Ordinal Logistic Regression (Fixed Effects Model)
  • 4.2. Mixed Ordinal Logistic Regression
  • 4.2.1. Definition of the mixed ordinal logistic regression model
  • 4.2.2. Residual variance matrix
  • 4.2.3. Alternative specification for random effects models
  • 4.2.4. Likelihood and quasi-likelihood functions
  • 4.2.5. Model fitting methods
  • 4.3. Mixed Models for Unordered Categorical Data
  • 4.3.1. The G matrix
  • 4.3.2. The R matrix
  • 4.3.3. Fitting the model
  • 4.4. Practical Application and Interpretation
  • 4.4.1. Expressing fixed and random effects results
  • 4.4.2. The proportional odds assumption
  • 4.4.3. Number of covariance parameters
  • 4.4.4. Choosing a covariance pattern
  • 4.4.5. Interpreting covariance parameters
  • 4.4.6. Checking model assumptions
  • 4.4.7. The dispersion parameter
  • 4.4.8. Other points
  • 4.5. Example
  • 5. Multi-Centre Trials and Meta-Analyses
  • 5.1. Introduction to Multi-Centre Trials
  • 5.1.1. What is a multi-centre trial?
  • 5.1.2. Why use mixed models to analyse multi-centre data?
  • 5.2. The Implications of using Different Analysis Models
  • 5.2.1. Centre and centre-treatment effects fixed
  • 5.2.2. Centre effects fixed, centre-treatment effects omitted
  • 5.2.3. Centre and centre treatment effects random
  • 5.2.4. Centre effects random, centre-treatment effects omitted
  • 5.3. Example: A Multi-Centre Trial
  • 5.4. Practical Application and Interpretation
  • 5.4.1. Plausibility of a centre-treatment interaction
  • 5.4.2. Generalisation
  • 5.4.3. Number of centres
  • 5.4.4. Centre size
  • 5.4.5. Negative variance components
  • 5.4.6. Balance
  • 5.5. Sample Size Estimation
  • 5.5.1. Normal data
  • 5.5.2. Non-normal data
  • 5.6. Meta-Analysis
  • 5.7. Example: Meta-analysis
  • 5.7.1. Analyses
  • 5.7.2. Results
  • 5.7.3. Treatment estimates in individual trials
  • 6. Repeated Measures Data
  • 6.1. Introduction
  • 6.1.1. Reasons for repeated measurements
  • 6.1.2. Analysis objectives
  • 6.1.3. Fixed effects approaches
  • 6.1.4. Mixed models approaches
  • 6.2. Covariance Pattern Models
  • 6.2.1. Covariance patterns
  • 6.2.2. Choice of covariance pattern
  • 6.2.3. Choice of fixed effects
  • 6.2.4. General points
  • 6.3. Example: Covariance Pattern Models for Normal Data
  • 6.3.1. Analysis models
  • 6.3.2. Selection of covariance pattern
  • 6.3.3. Assessing fixed effects
  • 6.3.4. Model checking
  • 6.4. Example: Covariance Pattern Models for Count Data
  • 6.4.1. Analysis models
  • 6.4.2. Analysis using a categorical mixed model
  • 6.5. Random Coefficients Models
  • 6.5.1. Introduction
  • 6.5.2. General points
  • 6.5.3. Comparisons with fixed effects approaches
  • 6.6. Examples of Random Coefficients Models
  • 6.6.1. A linear random coefficients model
  • 6.6.2. A polynomial random coefficients model
  • 6.7. Sample Size Estimation
  • 6.7.1. Normal data
  • 6.7.2. Non-normal data
  • 6.7.3. Categorical data
  • 7. Cross-Over Trials
  • 7.1. Introduction
  • 7.2. Advantages of Mixed Models in Cross-Over Trials
  • 7.3. The AB/BA Cross-Over Trial
  • 7.3.1. Example: AB/BA cross-over design
  • 7.4. Higher Order Complete Block Designs
  • 7.4.1. Inclusion of carry-over effects
  • 7.4.2. Example: four-period, four-treatment cross-over trial
  • 7.5. Incomplete Block Designs
  • 7.5.1. The three-treatment, two-period design (Koch's design)
  • 7.5.2. Example: two-period cross-over trial
  • 7.6. Optimal Designs
  • 7.6.1. Example: Balaam's design
  • 7.7. Covariance Pattern Models
  • 7.7.1. Structured by period
  • 7.7.2. Structured by treatment
  • 7.7.3. Example: four-way cross-over trial
  • 7.8. Analysis of Binary Data
  • 7.9. Analysis of Categorical Data
  • 7.10. Use of Results from Random Effects Models in Trial Design
  • 7.10.1. Example
  • 7.11. General Points
  • 8. Other Applications of Mixed Models
  • 8.1. Trials with Repeated Measurements within Visits
  • 8.1.1. Covariance pattern models
  • 8.1.2. Example
  • 8.1.3. Random coefficients models
  • 8.1.4. Example: random coefficients models
  • 8.2. Multi-Centre Trials with Repeated Measurements
  • 8.2.1. Example: multi-centre hypertension trial
  • 8.2.2. Covariance pattern models
  • 8.3. Multi-Centre Cross-Over Trials
  • 8.4. Hierarchical Multi-Centre Trials and Meta-Analysis
  • 8.5. Matched Case-Control Studies
  • 8.5.1. Example
  • 8.5.2. Analysis of a quantitative variable
  • 8.5.3. Check of model assumptions
  • 8.5.4. Analysis of binary variables
  • 8.6. Different Variances for Treatment Groups in a Simple Between-Patient Trial
  • 8.6.1. Example
  • 8.7. Estimating Variance Components in an Animal Physiology Trial
  • 8.7.1. Sample size estimation for a future experiment
  • 8.8. Inter- and Intra-Observer Variation in Foetal Scan Measurements
  • 8.9. Components of Variation and Mean Estimates in a Cardiology Experiment
  • 8.10. Cluster Sample Surveys
  • 8.10.1. Example: cluster sample survey
  • 8.11. Small Area Mortality Estimates
  • 8.12. Estimating Surgeon Performance
  • 8.13. Event History Analysis
  • 8.13.1. Example
  • 8.14. A Laboratory Study Using a Within-Subject 4 x 4 Factorial Design
  • 8.15. Bioequivalence Studies with Replicate Cross-Over Designs
  • 8.15.1. Example
  • 8.16. Cluster Randomised Trials
  • 8.16.1. Example: a trial to evaluate integrated care pathways for treatment of children with asthma in hospital
  • 8.16.2. Example: Edinburgh randomised trial of breast screening
  • 9. Software for Fitting Mixed Models
  • 9.1. Packages for Fitting Mixed Models
  • 9.2. Basic use of PROC Mixed
  • 9.3. Using SAS to Fit Mixed Models to Non-Normal Data
  • 9.3.1. PROC GLIMMIX
  • 9.3.2. PROC GENMOD
  • Glossary
  • References
  • Index
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